Genus 2 curves in isogeny class 50000.a of discriminant 200000

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
50000.a.200000.1	50000.a	\( 2^{4} \cdot 5^{5} \)	\( 2^{6} \cdot 5^{5} \)	$1$	$1$	$\Z/5\Z$	\(\mathsf{CM}\)	\(\Q\)		$F_{ac}$		✓	✓	$C_2$	$C_{10}$	$5$	$1$	2.36.1, 3.1296.1	✓	✓	$1$	\( 5 \)	\(0.821052\)	\(11.847756\)	\(1.945524\)	$[0,0,0,8]$	$[0,0,0,0,200000]$	$[0,0,0]$	$y^2 + y = 2x^5$