Genus 2 curves in isogeny class 100035.a of discriminant 300105

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
100035.a.300105.1	100035.a	\( 3^{4} \cdot 5 \cdot 13 \cdot 19 \)	\( 3^{5} \cdot 5 \cdot 13 \cdot 19 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$0$	2.20.2	✓	✓	$1$	\( 2 \)	\(0.057803\)	\(13.602351\)	\(1.572500\)	$[340,4585,433269,-158080]$	$[255,990,-2304,-391905,-300105]$	$[-887410625/247,-13510750/247,369920/741]$	$y^2 + (x^3 + x + 1)y = -x^4 + x^3 - x^2 - 2x + 2$