% Bibliography. Entries marked "note = {[verify]}" have not yet been checked against the published
% version (journal, volume, pages); every entry must be checked before submission.

@article{Abramovich1996,
  author  = {Abramovich, Dan},
  title   = {A linear lower bound on the gonality of modular curves},
  journal = {Internat. Math. Res. Notices},
  year    = {1996},
  number  = {20},
  pages   = {1005--1011}}

@article{Bars1999,
  author  = {Bars, Francesc},
  title   = {Bielliptic modular curves},
  journal = {J. Number Theory},
  volume  = {76},
  year    = {1999},
  pages   = {154--165}}

@article{Magma,
  author  = {Bosma, Wieb and Cannon, John and Playoust, Catherine},
  title   = {The {M}agma algebra system. {I}. {T}he user language},
  journal = {J. Symbolic Comput.},
  volume  = {24},
  year    = {1997},
  pages   = {235--265}}

@article{Dalal2023,
  author  = {Dalal, Tarun},
  title   = {Intermediate modular curves with infinitely many cubic points over {$\mathbb Q$}},
  journal = {Int. J. Number Theory},
  volume  = {20},
  number  = {3},
  year    = {2024},
  pages   = {701--713}}

@article{DebarreFahlaoui1993,
  author  = {Debarre, Olivier and Fahlaoui, Rachid},
  title   = {Abelian varieties in {$W^r_d(C)$} and points of bounded degree on algebraic curves},
  journal = {Compositio Math.},
  volume  = {88},
  year    = {1993},
  pages   = {235--249}}

@article{DHJO,
  author  = {Derickx, Maarten and Hwang, Wontae and Jeon, Daeyeol and Orli{\'c}, Petar},
  title   = {Modular curves {$X_0(N)$} of density degree 5},
  journal = {Math. Comp.},
  year    = {2026},
  note    = {published electronically 27 July 2026, doi:10.1090/mcom/4221, arXiv:2503.08975}}

@article{DerickxNajman,
  author  = {Derickx, Maarten and Najman, Filip},
  title   = {Hyperelliptic and trigonal modular curves in characteristic $p$},
  journal = {Q. J. Math.},
  volume  = {76},
  number  = {1},
  year    = {2025},
  pages   = {1--18}}

@article{DerickxOrlicX0,
  author  = {Derickx, Maarten and Orli{\'c}, Petar},
  title   = {Modular curves {$X_0(N)$} with infinitely many quartic points},
  journal = {Res. Number Theory},
  volume  = {10},
  number  = {2},
  year    = {2024},
  pages   = {Paper No. 42}}

@article{DerickxOrlic2026,
  author  = {Derickx, Maarten and Orli{\'c}, Petar},
  title   = {Intermediate modular curves with infinitely many quartic points},
  journal = {Int. J. Number Theory},
  volume  = {22},
  number  = {5},
  year    = {2026},
  pages   = {1053--1074}}

@article{DerickxSutherland2017,
  author  = {Derickx, Maarten and Sutherland, Andrew V.},
  title   = {Torsion subgroups of elliptic curves over quintic and sextic number fields},
  journal = {Proc. Amer. Math. Soc.},
  volume  = {145},
  number  = {10},
  year    = {2017},
  pages   = {4233--4245}}

@misc{DerickxTerao,
  author  = {Derickx, Maarten and Terao, Kenji},
  title   = {Computing class groups and gonalities of algebraic curves over finite fields},
  year    = {2026},
  note    = {arXiv:2602.17417; software CurveArith, \url{https://github.com/nt-lib/CurveArith}}}

@article{DerickxVanHoeij2014,
  author  = {Derickx, Maarten and van Hoeij, Mark},
  title   = {Gonality of the modular curve {$X_1(N)$}},
  journal = {J. Algebra},
  volume  = {417},
  year    = {2014},
  pages   = {52--71}}

@misc{MDSage,
  author  = {Derickx, Maarten},
  title   = {{MD Sage}: a {S}age{M}ath package for modular curves},
  howpublished = {\url{https://github.com/koffie/mdsage}},
  note    = {commit 6022429}}

@article{Faltings1991,
  author  = {Faltings, Gerd},
  title   = {Diophantine approximation on abelian varieties},
  journal = {Ann. of Math. (2)},
  volume  = {133},
  year    = {1991},
  pages   = {549--576}}

@article{Frey1994,
  author  = {Frey, Gerhard},
  title   = {Curves with infinitely many points of fixed degree},
  journal = {Israel J. Math.},
  volume  = {85},
  year    = {1994},
  pages   = {79--83}}

@article{HarrisSilverman1991,
  author  = {Harris, Joe and Silverman, Joseph H.},
  title   = {Bielliptic curves and symmetric products},
  journal = {Proc. Amer. Math. Soc.},
  volume  = {112},
  year    = {1991},
  pages   = {347--356}}

@article{HwangJeon2024,
  author  = {Hwang, Wontae and Jeon, Daeyeol},
  title   = {Modular curves with infinitely many quartic points},
  journal = {Math. Comp.},
  volume  = {93},
  year    = {2024},
  pages   = {383--395}}

@article{IshiiMomose1991,
  author  = {Ishii, Noburo and Momose, Fumiyuki},
  title   = {Hyperelliptic modular curves},
  journal = {Tsukuba J. Math.},
  volume  = {15},
  number  = {2},
  year    = {1991},
  pages   = {413--423}}

@article{Jeon2021,
  author  = {Jeon, Daeyeol},
  title   = {Modular curves with infinitely many cubic points},
  journal = {J. Number Theory},
  volume  = {219},
  year    = {2021},
  pages   = {344--355}}

@article{JeonKim2007,
  author  = {Jeon, Daeyeol and Kim, Chang Heon},
  title   = {On the arithmetic of certain modular curves},
  journal = {Acta Arith.},
  volume  = {130},
  year    = {2007},
  pages   = {181--193}}

@article{JeonKimSchweizer2020,
  author  = {Jeon, Daeyeol and Kim, Chang Heon and Schweizer, Andreas},
  title   = {Bielliptic intermediate modular curves},
  journal = {J. Pure Appl. Algebra},
  volume  = {224},
  number  = {1},
  year    = {2020},
  pages   = {272--299}}

@article{KadetsVogt2025,
  author  = {Kadets, Borys and Vogt, Isabel},
  title   = {Subspace configurations and low degree points on curves},
  journal = {Adv. Math.},
  volume  = {460},
  year    = {2025},
  pages   = {Paper No. 110021}}

@article{Kato2004,
  author  = {Kato, Kazuya},
  title   = {{$p$}-adic {H}odge theory and values of zeta functions of modular forms},
  journal = {Ast{\'e}risque},
  volume  = {295},
  year    = {2004},
  pages   = {117--290}}

@article{KimSarnak2003,
  author  = {Kim, Henry H.},
  title   = {Functoriality for the exterior square of {${\rm GL}_4$} and the symmetric fourth of {${\rm GL}_2$}},
  journal = {J. Amer. Math. Soc.},
  volume  = {16},
  year    = {2003},
  pages   = {139--183},
  note    = {With Appendix 1 by D.~Ramakrishnan and Appendix 2 by H.~Kim and P.~Sarnak}}

@article{KolyvaginLogachev1989,
  author  = {Kolyvagin, V. A. and Logach{\"e}v, D. Yu.},
  title   = {Finiteness of the {S}hafarevich--{T}ate group and the group of rational points for some modular abelian varieties},
  journal = {Leningrad Math. J.},
  volume  = {1},
  year    = {1990},
  pages   = {1229--1253}}

@misc{LMFDB,
  author  = {{The LMFDB Collaboration}},
  title   = {The {L}-functions and modular forms database},
  howpublished = {\url{https://www.lmfdb.org}},
  year    = {2026}}

@article{NajmanOrlic2024,
  author  = {Najman, Filip and Orli{\'c}, Petar},
  title   = {Gonality of the modular curve {$X_0(N)$}},
  journal = {Math. Comp.},
  volume  = {93},
  year    = {2024},
  pages   = {863--886}}

@misc{NajmanVarivoda,
  author  = {Najman, Filip and Varivoda, Marin},
  title   = {Torsion groups of elliptic curves that appear infinitely often over septic, octic and nonic fields},
  year    = {2026},
  note    = {arXiv:2602.03513v4}}

@article{Poonen2007,
  author  = {Poonen, Bjorn},
  title   = {Gonality of modular curves in characteristic {$p$}},
  journal = {Math. Res. Lett.},
  volume  = {14},
  year    = {2007},
  pages   = {691--701}}

@article{Ogg1974,
  author  = {Ogg, Andrew P.},
  title   = {Hyperelliptic modular curves},
  journal = {Bull. Soc. Math. France},
  volume  = {102},
  year    = {1974},
  pages   = {449--462}}

@article{Orlic2025,
  author  = {Orli{\'c}, Petar},
  title   = {Tetragonal intermediate modular curves},
  journal = {Acta Arith.},
  volume  = {220},
  year    = {2025},
  pages   = {263--288}}

@article{RSZB2022,
  author  = {Rouse, Jeremy and Sutherland, Andrew V. and Zureick-Brown, David},
  title   = {{$\ell$}-adic images of {G}alois for elliptic curves over {$\mathbb Q$}},
  journal = {Forum Math. Sigma},
  volume  = {10},
  year    = {2022},
  pages   = {e62},
  note    = {With an appendix by John Voight}}

@book{Stichtenoth2009,
  author    = {Stichtenoth, Henning},
  title     = {Algebraic function fields and codes},
  edition   = {Second},
  series    = {Graduate Texts in Mathematics},
  volume    = {254},
  publisher = {Springer-Verlag, Berlin},
  year      = {2009}}

@misc{SutherlandX1,
  author  = {Sutherland, Andrew V.},
  title   = {Optimized equations for {$X_1(N)$}},
  howpublished = {\url{https://math.mit.edu/~drew/X1_optcurves.html}},
  note    = {models of Sutherland and van Hoeij}}

@misc{ZywinaModular,
  author  = {Zywina, David},
  title   = {Modular: a {M}agma package for modular forms and modular curves},
  howpublished = {\url{https://github.com/davidzywina/Modular}},
  note    = {commit ce31d78}}

@article{Zograf1984,
  author  = {Zograf, P. G.},
  title   = {Small eigenvalues of automorphic {L}aplacians in spaces of cusp forms},
  journal = {Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)},
  volume  = {134},
  year    = {1984},
  pages   = {157--168}}

@book{Hartshorne1977,
  author    = {Hartshorne, Robin},
  title     = {Algebraic geometry},
  series    = {Graduate Texts in Mathematics},
  volume    = {52},
  publisher = {Springer-Verlag, New York-Heidelberg},
  year      = {1977}}

@incollection{DeligneRapoport1973,
  author    = {Deligne, P. and Rapoport, M.},
  title     = {Les sch{\'e}mas de modules de courbes elliptiques},
  booktitle = {Modular functions of one variable, {II}},
  series    = {Lecture Notes in Math.},
  volume    = {349},
  publisher = {Springer, Berlin},
  year      = {1973},
  pages     = {143--316}}

@book{Liu2002,
  author    = {Liu, Qing},
  title     = {Algebraic geometry and arithmetic curves},
  series    = {Oxford Graduate Texts in Mathematics},
  volume    = {6},
  publisher = {Oxford University Press, Oxford},
  year      = {2002}}

@article{CES2003,
  author  = {Conrad, Brian and Edixhoven, Bas and Stein, William},
  title   = {{$J_1(p)$} has connected fibers},
  journal = {Doc. Math.},
  volume  = {8},
  year    = {2003},
  pages   = {331--408}}

@article{DEH2021,
  author  = {Derickx, Maarten and Etropolski, Anastassia and van Hoeij, Mark and Morrow, Jackson S. and Zureick-Brown, David},
  title   = {Sporadic cubic torsion},
  journal = {Algebra Number Theory},
  volume  = {15},
  number  = {7},
  year    = {2021},
  pages   = {1837--1864}}

@article{Drinfeld1973,
  author  = {Drinfeld, V. G.},
  title   = {Two theorems on modular curves},
  journal = {Funkcional. Anal. i Prilo\v{z}en.},
  volume  = {7},
  year    = {1973},
  number  = {2},
  pages   = {83--84}}

@article{Manin1972,
  author  = {Manin, Ju. I.},
  title   = {Parabolic points and zeta functions of modular curves},
  journal = {Izv. Akad. Nauk SSSR Ser. Mat.},
  volume  = {36},
  year    = {1972},
  pages   = {19--66}}

@article{Katz1981,
  author  = {Katz, Nicholas M.},
  title   = {Galois properties of torsion points on abelian varieties},
  journal = {Invent. Math.},
  volume  = {62},
  year    = {1981},
  pages   = {481--502}}

@misc{vanHoeij2012,
  author  = {van Hoeij, Mark},
  title   = {Low degree places on the modular curve {$X_1(N)$}},
  year    = {2012},
  note    = {arXiv:1202.4355; the places are in the data files on the author's web page}}

@book{ACGH1985,
  author    = {Arbarello, E. and Cornalba, M. and Griffiths, P. A. and Harris, J.},
  title     = {Geometry of algebraic curves. {V}ol. {I}},
  series    = {Grundlehren der mathematischen Wissenschaften},
  volume    = {267},
  publisher = {Springer-Verlag, New York},
  year      = {1985}}

@article{Sutherland2012,
  author  = {Sutherland, Andrew V.},
  title   = {Constructing elliptic curves over finite fields with prescribed torsion},
  journal = {Math. Comp.},
  volume  = {81},
  number  = {278},
  year    = {2012},
  pages   = {1131--1147}}