\usepackage[T1]{fontenc}
\usepackage[letterpaper,margin=1.25in]{geometry}
\usepackage{verbatim}
\usepackage{amssymb,amsmath,amsthm}
\usepackage{booktabs}
\usepackage{longtable}
\usepackage{float}
\usepackage{aliascnt}
\usepackage[colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue]{hyperref}
\usepackage{cleveref}
\DeclareMathOperator{\rk}{rk}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\Gal}{Gal}
\DeclareMathOperator{\Cl}{Cl}
\DeclareMathOperator{\gon}{gon}
\DeclareMathOperator{\ddiv}{div}
\DeclareMathOperator{\Div}{Div}
\DeclareMathOperator{\Jac}{Jac}
\DeclareMathOperator{\PSL}{PSL}
\DeclareMathOperator{\SL}{SL}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\ord}{ord}
\DeclareMathOperator{\Frob}{Frob}
\DeclareMathOperator{\Ver}{Ver}
\DeclareMathOperator{\red}{red}
\DeclareMathOperator{\disc}{disc}
\DeclareMathOperator{\Supp}{Supp}
\DeclareMathOperator{\Norm}{N}
\DeclareMathOperator{\Pic}{Pic}
\DeclareMathOperator{\Res}{Res}
\DeclareMathOperator{\Tr}{Tr}

\newcommand{\Q}{\mathbb{Q}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\PP}{\mathbb{P}}
\newcommand{\Qbar}{\overline{\Q}}
\newcommand{\tors}{\mathrm{tors}}
\newcommand{\torz}[1]{\Z/#1\Z}
\newcommand{\tg}[2]{\Z/#1\Z\times\Z/#2\Z}
\newcommand{\dm}[1]{\langle #1\rangle}
\newcommand{\ClCusp}{\Cl^{c}}
\newcommand{\Cart}{\mathcal{C}}

% Each environment has its own counter, an alias of the theorem counter, so that cleveref names the
% references correctly also with recent LaTeX kernels (otherwise they all print as "Theorem").
\newtheorem{theorem}{Theorem}[section]
\newcommand{\sharedtheorem}[2]{\newaliascnt{#1}{theorem}\newtheorem{#1}[#1]{#2}\aliascntresetthe{#1}}
\sharedtheorem{lemma}{Lemma}
\sharedtheorem{proposition}{Proposition}
\sharedtheorem{corollary}{Corollary}
\theoremstyle{definition}
\sharedtheorem{remark}{Remark}
\sharedtheorem{example}{Example}
\numberwithin{equation}{section}
\crefname{theorem}{Theorem}{Theorems}
\crefname{lemma}{Lemma}{Lemmas}
\crefname{proposition}{Proposition}{Propositions}
\crefname{corollary}{Corollary}{Corollaries}
\crefname{remark}{Remark}{Remarks}
\crefname{example}{Example}{Examples}

\newcommand{\lmfdbec}[3]{\href{https://www.lmfdb.org/EllipticCurve/Q/#1/#2/#3}{#1.#2#3}}
\newcommand{\lmfdcharorbit}[2]{\href{https://www.lmfdb.org/Character/Dirichlet/#1/#2}{#1.#2}}
\newcommand{\lmfdbnewform}[4]{\href{https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/#1/#2/#3/#4}{#1.#2.#3.#4}}
\newcommand{\lmfdbnf}[1]{\href{https://www.lmfdb.org/NumberField/#1}{#1}}
\newcommand{\xpoint}[1]{\href{https://x1mn-sporadic.github.io/point.html?id=#1}{#1}}

% Links to the code repository, pinned to one revision.
\newcommand{\gitrev}{0903ee635a39de6a5bed70de650515f02ad73cde}
\newcommand{\gitrevshort}{0903ee6}
\newcommand{\gitlink}[2]{\href{https://github.com/F-Najman/deg10_torsion/blob/\gitrev/#1}{#2}}
\newcommand{\githubbare}[1]{\href{https://github.com/F-Najman/deg10_torsion/blob/\gitrev/#1}{\path{#1}}}
\newcommand{\githubdir}[1]{\href{https://github.com/F-Najman/deg10_torsion/tree/\gitrev/#1}{\path{#1}}}