Genus 2 curves in isogeny class 925.a of discriminant 23125

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
925.a.23125.1	925.a	\( 5^{2} \cdot 37 \)	\( 5^{4} \cdot 37 \)	$0$	$2$	$\Z/2\Z\oplus\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(20.878934\)	\(0.326233\)	$[3496,50536,55764955,92500]$	$[1748,118890,10257041,948618892,23125]$	$[16319511005139968/23125,126998797147776/4625,31340429803664/23125]$	$y^2 + xy = 5x^5 + x^4 - 19x^3 + 18x^2 - 5x$