Genus 2 curves in isogeny class 50625.a of discriminant 253125

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
50625.a.253125.1	50625.a	\( 3^{4} \cdot 5^{4} \)	\( 3^{4} \cdot 5^{5} \)	$1$	$1$	$\mathsf{trivial}$	\(\mathsf{CM}\)	\(\Q\)		$F_{ac}$		✓	✓	$C_2$	$C_{10}$	$3$	$1$	2.36.1, 3.6480.5	✓	✓	$1$	\( 2 \)	\(0.189560\)	\(5.175122\)	\(1.961993\)	$[0,0,0,324]$	$[0,0,0,0,253125]$	$[0,0,0]$	$y^2 + y = x^5 - 1$