Genus 2 curves in isogeny class 1312.c of discriminant 671744

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
1312.c.671744.1	1312.c	\( 2^{5} \cdot 41 \)	\( - 2^{14} \cdot 41 \)	$0$	$1$	$\Z/22\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,11$	✓	✓	$C_2$	$C_2$	$6$	$0$	2.90.1	✓	✓	$1$	\( 2 \cdot 11 \)	\(1.000000\)	\(11.857814\)	\(0.538992\)	$[164,1441,58489,83968]$	$[164,160,1984,74944,671744]$	$[2825761/16,8405/8,1271/16]$	$y^2 + (x + 1)y = x^6 + 4x^5 + 7x^4 + 5x^3 + 2x^2$