Genus 2 curve search results

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
10075.a.10075.1	10075.a	\( 5^{2} \cdot 13 \cdot 31 \)	\( - 5^{2} \cdot 13 \cdot 31 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 1 \)	\(0.182151\)	\(18.074402\)	\(0.823066\)	$[224,304,41431,-40300]$	$[112,472,225,-49396,-10075]$	$[-17623416832/10075,-663126016/10075,-112896/403]$	$y^2 + xy = x^5 - 4x^3 - 4x^2 - x$