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
7225.a.36125.1	7225.a	\( 5^{2} \cdot 17^{2} \)	\( - 5^{3} \cdot 17^{2} \)	$2$	$3$	$\Z/2\Z$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$12$	$0$	2.45.1, 3.72.2	✓	✓	$1$	\( 2 \)	\(0.037430\)	\(18.345600\)	\(0.343342\)	$[980,-2039,-2619067,-4624000]$	$[245,2586,64636,2287106,-36125]$	$[-7061881225/289,-304240314/289,-155191036/1445]$	$y^2 + (x^3 + 1)y = -x^5 + 2x^4 - 3x^2 - x$