@preamble{"\providecommand{\noopsort}[1]{}"}

@article{BekkerZarhin,
  author  = {Bekker, Boris M. and Zarhin, Yuri G.},
  title   = {Division by 2 of rational points on elliptic curves},
  journal = {St. Petersburg Math. J.},
  volume  = {29},
  number  = {4},
  year    = {2018},
  pages   = {683--713},
  note    = {\DOI{10.1090/spmj/1512}; \arXiv{1702.02255v2}}
}

@article{CFS,
  author  = {Cremona, John E. and Fisher, Tom A. and Stoll, Michael},
  title   = {Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves},
  journal = {Algebra Number Theory},
  volume  = {4},
  number  = {6},
  year    = {2010},
  pages   = {763--820},
  note    = {\DOI{10.2140/ant.2010.4.763}; \arXiv{0908.1741v1}}
}

@book{CremonaBook,
  author    = {Cremona, John E.},
  title     = {{A}lgorithms for {M}odular {E}lliptic {C}urves},
  edition   = {Second},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {1997}
}

@article{Cremona,
  author  = {Cremona, John E.},
  title   = {Classical invariants and 2-descent on elliptic curves},
  journal = {J. Symbolic Comput.},
  volume  = {31},
  number  = {1--2},
  year    = {2001},
  pages   = {71--87},
  note    = {\DOI{10.1006/jsco.1998.1004}}
}

@article{Duj07,
  author  = {Dujella, Andrej},
  title   = {On {M}ordell--{W}eil groups of elliptic curves induced by {D}iophantine triples},
  journal = {Glas. Mat. Ser. III},
  volume  = {42},
  number  = {1},
  year    = {2007},
  pages   = {3--18},
  note    = {\DOI{10.3336/gm.42.1.01}; \arXiv{0705.1875v1}}
}

@article{Duj23,
  author  = {Dujella, Andrej},
  title   = {High-rank elliptic curves with given torsion group and some applications},
  journal = {Banach Center Publ.},
  volume  = {126},
  year    = {2023},
  pages   = {9--26},
  note    = {\DOI{10.4064/bc126-1}}
}

@misc{DujTors,
  author = {Dujella, Andrej},
  title  = {High rank elliptic curves with prescribed torsion},
  note   = {\url{https://web.math.pmf.unizg.hr/~duje/tors/tors.html} (accessed October 15, 2026)}
}

@misc{DujGeneric,
  author = {Dujella, Andrej},
  title  = {Infinite families of elliptic curves with high rank and prescribed torsion},
  note   = {\url{https://web.math.pmf.unizg.hr/~duje/tors/generic.html} (accessed October 15, 2026)}
}

@misc{DujZ2Z4,
  author = {Dujella, Andrej},
  title  = {Torsion group {$\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/4\mathbb{Z}$}, rank $=9$},
  note   = {\url{https://web.math.pmf.unizg.hr/~duje/tors/z2z4.html} (accessed October 15, 2026)}
}

@misc{Dopen,
  author = {Dujella, Andrej},
  title  = {Open problems on {D}iophantine {$m$}-tuples and elliptic curves},
  note   = {\url{https://web.math.pmf.unizg.hr/~duje/pdf/open2.pdf}, version of October 15, 2026}
}

@article{DKP21,
  author  = {Dujella, Andrej and Kazalicki, Matija and Peral, Juan Carlos},
  title   = {Elliptic curves with torsion groups {$\mathbb{Z}/8\mathbb{Z}$} and {$\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z}$}},
  journal = {Rev. R. Acad. Cienc. Exactas F\'{\i}s. Nat. Ser. A Mat. RACSAM},
  volume  = {115},
  number  = {4},
  year    = {2021},
  pages   = {Paper No. 169},
  note    = {\DOI{10.1007/s13398-021-01112-5}; \arXiv{2105.06215v2}}
}

@article{DP14,
  author  = {Dujella, Andrej and Peral, Juan Carlos},
  title   = {High-rank elliptic curves with torsion {$\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/4\mathbb{Z}$} induced by {D}iophantine triples},
  journal = {LMS J. Comput. Math.},
  volume  = {17},
  number  = {1},
  year    = {2014},
  pages   = {282--288},
  note    = {\DOI{10.1112/S1461157014000023}}
}

@incollection{DP15,
  author    = {Dujella, Andrej and Peral, Juan Carlos},
  title     = {Elliptic curves with torsion group {$\mathbb{Z}/8\mathbb{Z}$} or {$\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z}$}},
  booktitle = {Trends in Number Theory},
  series    = {Contemp. Math.},
  volume    = {649},
  publisher = {Amer. Math. Soc.},
  address   = {Providence, RI},
  year      = {2015},
  note      = {pp.~47--62, \DOI{10.1090/conm/649/13019}; \arXiv{1306.0027v1}, where \S\S 5.4 and 6.6 are \S\S 4.4 and 5.5}
}

@article{DP19,
  author  = {Dujella, Andrej and Peral, Juan Carlos},
  title   = {Elliptic curves induced by {D}iophantine triples},
  journal = {Rev. R. Acad. Cienc. Exactas F\'{\i}s. Nat. Ser. A Mat. RACSAM},
  volume  = {113},
  number  = {2},
  year    = {2019},
  pages   = {791--806},
  note    = {\DOI{10.1007/s13398-018-0513-0}; \arXiv{1712.02082v2}}
}

@article{DP21,
  author  = {Dujella, Andrej and Peral, Juan Carlos},
  title   = {Construction of high rank elliptic curves},
  journal = {J. Geom. Anal.},
  volume  = {31},
  number  = {7},
  year    = {2021},
  pages   = {6698--6724},
  note    = {\DOI{10.1007/s12220-020-00373-7}}
}

@article{DP24,
  author  = {Dujella, Andrej and Peral, Juan Carlos},
  title   = {An elliptic curve over {$\mathbb{Q}(u)$} with torsion {$\mathbb{Z}/4\mathbb{Z}$} and rank 6},
  journal = {Rad Hrvat. Akad. Znan. Umjet. Mat. Znan.},
  volume  = {28},
  year    = {2024},
  pages   = {185--192},
  note    = {\DOI{10.21857/y54jof4o2m}; \arXiv{2207.08206v2}}
}

@misc{Elkies07,
  author = {Elkies, Noam D.},
  title  = {Three lectures on elliptic surfaces and curves of high rank},
  year   = {2007},
  note   = {Preprint, \arXiv{0709.2908v1}}
}

@misc{Elkies26,
  author = {Elkies, Noam D.},
  title  = {An elliptic {K3} surface {$X/\mathbb{Q}(t)$} with {M}ordell--{W}eil rank 17, {I}: {F}ormulas for {$X$} and base changes of rank 18 and 19},
  year   = {2026},
  note   = {Preprint, \arXiv{2608.25406v1}}
}

@article{Faltings,
  author  = {Faltings, Gerd},
  title   = {{E}ndlichkeitss{\"a}tze f{\"u}r abelsche {V}ariet{\"a}ten {\"u}ber {Z}ahlk{\"o}rpern},
  journal = {Invent. Math.},
  volume  = {73},
  number  = {3},
  year    = {1983},
  pages   = {349--366},
  note    = {\DOI{10.1007/BF01388432}}
}

@misc{FLINT,
  author = {{\noopsort{FLINT}The FLINT team}},
  title  = {{FLINT}: {F}ast {L}ibrary for {N}umber {T}heory},
  year   = {2025},
  note   = {\url{https://flintlib.org}, version 3.3.1, with the Python interface python-flint 0.8.0}
}

@article{GusicTadic,
  author  = {Gusi{\'c}, Ivica and Tadi{\'c}, Petra},
  title   = {Injectivity of the specialization homomorphism of elliptic curves},
  journal = {J. Number Theory},
  volume  = {148},
  year    = {2015},
  pages   = {137--152},
  note    = {\DOI{10.1016/j.jnt.2014.09.023}; \arXiv{1409.7189v2}}
}

@article{HarronSnowden,
  author  = {Harron, Robert and Snowden, Andrew},
  title   = {Counting elliptic curves with prescribed torsion},
  journal = {J. Reine Angew. Math.},
  volume  = {729},
  year    = {2017},
  pages   = {151--170},
  note    = {\DOI{10.1515/crelle-2014-0107}; \arXiv{1311.4920v1}}
}

@misc{Jaswal,
  author = {Jaswal, Manvir},
  title  = {Infinitely many elliptic curves with torsion {$\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z}$} and rank at least four},
  year   = {2026},
  note   = {Zenodo, \DOI{10.5281/zenodo.23364157}}
}

@misc{Record,
  author = {Jaswal, Manvir},
  title  = {Programs and data for ``{I}nfinitely many elliptic curves with torsion {$\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/4\mathbb{Z}$} and rank at least six''},
  year   = {2026},
  note   = {Zenodo, \DOI{10.5281/zenodo.23437115}}
}

@misc{Lean,
  author = {Jaswal, Manvir},
  title  = {Lean formalization: ``{I}nfinitely many elliptic curves with torsion {$\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/4\mathbb{Z}$} and rank at least six''},
  year   = {2026},
  note   = {Zenodo, \DOI{10.5281/zenodo.23682552}}
}

@article{LangNeron,
  author  = {Lang, Serge and N{\'e}ron, Andr{\'e}},
  title   = {Rational points of abelian varieties over function fields},
  journal = {Amer. J. Math.},
  volume  = {81},
  number  = {1},
  year    = {1959},
  pages   = {95--118},
  note    = {\DOI{10.2307/2372851}}
}

@article{Lecacheux,
  author  = {Lecacheux, Odile},
  title   = {Rang de courbes elliptiques avec groupe de torsion non trivial},
  journal = {J. Th\'{e}or. Nombres Bordeaux},
  volume  = {15},
  number  = {1},
  year    = {2003},
  pages   = {231--247},
  note    = {\DOI{10.5802/jtnb.400}}
}

@misc{LMFDB,
  author = {{\noopsort{LMFDB}The LMFDB Collaboration}},
  title  = {The {$L$}-functions and modular forms database},
  note   = {\url{https://www.lmfdb.org}, elliptic curve 9240.bf4 (accessed October 16, 2026)}
}

@article{Mazur,
  author  = {Mazur, Barry},
  title   = {Modular curves and the {E}isenstein ideal},
  journal = {Inst. Hautes \'{E}tudes Sci. Publ. Math.},
  volume  = {47},
  year    = {1977},
  pages   = {33--186},
  note    = {\DOI{10.1007/BF02684339}}
}

@book{Miranda,
  author    = {Miranda, Rick},
  title     = {{T}he {B}asic {T}heory of {E}lliptic {S}urfaces},
  series    = {Dottorato di Ricerca in Matematica},
  publisher = {ETS Editrice},
  address   = {Pisa},
  year      = {1989}
}

@article{Nagao,
  author  = {Nagao, Koh-ichi},
  title   = {{$\mathbb{Q}(T)$}-rank of elliptic curves and certain limit coming from the local points},
  journal = {Manuscripta Math.},
  volume  = {92},
  number  = {1},
  year    = {1997},
  pages   = {13--32},
  note    = {\DOI{10.1007/BF02678178}}
}

@article{Neron52,
  author  = {N{\'e}ron, Andr{\'e}},
  title   = {Probl{\`e}mes arithm{\'e}tiques et g{\'e}om{\'e}triques rattach{\'e}s {\`a} la notion de rang d'une courbe alg{\'e}brique dans un corps},
  journal = {Bull. Soc. Math. France},
  volume  = {80},
  year    = {1952},
  pages   = {101--166},
  note    = {\DOI{10.24033/bsmf.1427}}
}

@article{Ono,
  author  = {Ono, Ken},
  title   = {{E}uler's concordant forms},
  journal = {Acta Arith.},
  volume  = {78},
  number  = {2},
  year    = {1996},
  pages   = {101--123},
  note    = {\DOI{10.4064/aa-78-2-101-123}}
}

@misc{PARI,
  author = {{\noopsort{PARI}The PARI~Group}},
  title  = {{PARI/GP} version 2.17.3},
  year   = {2025},
  note   = {Univ. Bordeaux, \url{https://pari.math.u-bordeaux.fr/}}
}

@article{PPVW,
  author  = {Park, Jennifer and Poonen, Bjorn and Voight, John and Wood, Melanie Matchett},
  title   = {A heuristic for boundedness of ranks of elliptic curves},
  journal = {J. Eur. Math. Soc. (JEMS)},
  volume  = {21},
  number  = {9},
  year    = {2019},
  pages   = {2859--2903},
  note    = {\DOI{10.4171/JEMS/893}; \arXiv{1602.01431v3}}
}

@article{RosenSilverman,
  author  = {Rosen, Michael and Silverman, Joseph H.},
  title   = {On the rank of an elliptic surface},
  journal = {Invent. Math.},
  volume  = {133},
  number  = {1},
  year    = {1998},
  pages   = {43--67},
  note    = {\DOI{10.1007/s002220050238}}
}

@misc{Sage,
  author = {{\noopsort{Sage}The Sage Developers}},
  title  = {{SageMath}, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion 10.9)},
  year   = {2026},
  note   = {\url{https://www.sagemath.org}}
}

@article{Silverman83,
  author  = {Silverman, Joseph H.},
  title   = {Heights and the specialization map for families of abelian varieties},
  journal = {J. Reine Angew. Math.},
  volume  = {342},
  year    = {1983},
  pages   = {197--211},
  note    = {\DOI{10.1515/crll.1983.342.197}}
}

@book{SilvermanAEC,
  author    = {Silverman, Joseph H.},
  title     = {{T}he {A}rithmetic of {E}lliptic {C}urves},
  edition   = {Second},
  series    = {Grad. Texts in Math.},
  volume    = {106},
  publisher = {Springer},
  address   = {New York},
  year      = {2009},
  note      = {\DOI{10.1007/978-0-387-09494-6}}
}