Genus 2 curves in isogeny class 1225.a of discriminant 6125

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
1225.a.6125.1	1225.a	\( 5^{2} \cdot 7^{2} \)	\( 5^{3} \cdot 7^{2} \)	$0$	$1$	$\Z/8\Z$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1, 3.72.2	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(11.927897\)	\(0.372747\)	$[320,14344,962481,-24500]$	$[160,-1324,8791,-86604,-6125]$	$[-838860800/49,43384832/49,-9001984/245]$	$y^2 + (x^3 + x^2)y = 2x^3 + x^2 + x + 2$