Genus 2 curves in isogeny class 15625.a of discriminant 15625

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
15625.a.15625.1	15625.a	\( 5^{6} \)	\( 5^{6} \)	$2$	$2$	$\mathsf{trivial}$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$6$	$0$	2.12.2, 3.2592.2	✓	✓	$1$	\( 1 \)	\(0.048361\)	\(13.026212\)	\(0.629964\)	$[20,25,1565,640]$	$[25,0,-2500,-15625,15625]$	$[625,0,-100]$	$y^2 + (x^3 + x + 1)y = 2x^5 + 2x^4 + 2x^3 + x^2$