Genus 2 curves in isogeny class 10115.a of discriminant 10115

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
10115.a.10115.1	10115.a	\( 5 \cdot 7 \cdot 17^{2} \)	\( 5 \cdot 7 \cdot 17^{2} \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$0$	2.15.1	✓	✓	$1$	\( 1 \)	\(0.269552\)	\(11.751001\)	\(0.791876\)	$[1236,3825,1561977,1294720]$	$[309,3819,60281,1010517,10115]$	$[2817036000549/10115,112674359151/10115,5755690161/10115]$	$y^2 + (x^3 + x^2 + x)y = -x^4 + 3x^2 + x - 2$