Genus 2 curves of conductor 1612

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
1612.a.3224.1	1612.a	\( 2^{2} \cdot 13 \cdot 31 \)	\( 2^{3} \cdot 13 \cdot 31 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$8$	$0$		✓	✓	$1$	\( 3 \)	\(0.004500\)	\(20.032411\)	\(0.270409\)	$[156,609,32271,-412672]$	$[39,38,-36,-712,-3224]$	$[-6940323/248,-86697/124,1053/62]$	$y^2 + (x^3 + x + 1)y = x^3 + 2x^2 + x$