Genus 2 curves in isogeny class 40000.e 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
40000.e.200000.1	40000.e	\( 2^{6} \cdot 5^{4} \)	\( - 2^{6} \cdot 5^{5} \)	$2$	$3$	$\Z/2\Z$	\(\mathrm{M}_2(\mathsf{CM})\)	\(\mathsf{CM}\)	✓	$J(C_4)$		✓		$C_4$	$GL(2,3)$	$8$	$0$	2.90.7, 3.3240.15	✓	✓	$1$	\( 2 \)	\(0.126734\)	\(11.350269\)	\(0.719235\)	$[20,-20,-40,8]$	$[100,750,-2500,-203125,200000]$	$[50000,3750,-125]$	$y^2 + x^3y = x^5 - 5x^3 - 10x^2 - 8x - 2$