Genus 2 curves in isogeny class 256.a of discriminant 512

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
256.a.512.1	256.a	\( 2^{8} \)	\( - 2^{9} \)	$0$	$2$	$\Z/2\Z\oplus\Z/10\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_4$		✓		$C_4$	$D_4$	$6$	$2$	2.180.3, 3.540.6	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(26.841829\)	\(0.134209\)	$[26,-2,40,2]$	$[52,118,-36,-3949,512]$	$[742586,129623/4,-1521/8]$	$y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$