Genus 2 curves in isogeny class 2336.a of discriminant 37376

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
2336.a.37376.1	2336.a	\( 2^{5} \cdot 73 \)	\( 2^{9} \cdot 73 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$10$	$0$	2.10.1	✓	✓	$1$	\( 2^{3} \)	\(0.002262\)	\(21.598867\)	\(0.390768\)	$[84,825,13389,4672]$	$[84,-256,2304,32000,37376]$	$[8168202/73,-296352/73,31752/73]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^4 - 3x^3 + x$