Genus 2 curves of conductor 3721

Results (unique match)

 

Label	Class	Conductor	Discriminant	Rank*	2-Selmer rank	Torsion	$\textrm{End}^0(J_{\overline\Q})$	$\textrm{End}^0(J)$	$\GL_2\textsf{-type}$	Sato-Tate	Nonmaximal primes	$\Q$-simple	\(\overline{\Q}\)-simple	\(\Aut(X)\)	\(\Aut(X_{\overline{\Q}})\)	$\Q$-points	$\Q$-Weierstrass points	mod-$\ell$ images	Locally solvable	Square Ш*	Analytic Ш*	Tamagawa	Regulator	Real period	Leading coefficient	Igusa-Clebsch invariants	Igusa invariants	G2-invariants	Equation
3721.a.3721.1	3721.a	\( 61^{2} \)	\( - 61^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_6$		✓		$C_6$	$D_6$	$12$	$0$	2.40.3, 3.480.12	✓	✓	$1$	\( 1 \)	\(0.007315\)	\(28.081352\)	\(0.205420\)	$[196,6649,304573,-476288]$	$[49,-177,-187,-10123,-3721]$	$[-282475249/3721,20823873/3721,448987/3721]$	$y^2 + (x^3 + x + 1)y = -x^4 + x^3 + 3x^2 + x$