Genus 2 curves in isogeny class 8281.b of discriminant 405769

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
8281.b.405769.1	8281.b	\( 7^{2} \cdot 13^{2} \)	\( 7^{4} \cdot 13^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_6$		✓		$C_6$	$D_6$	$12$	$0$	2.80.1, 3.480.12	✓	✓	$1$	\( 3 \)	\(0.005669\)	\(19.785401\)	\(0.336475\)	$[2596,375193,248614093,51938432]$	$[649,1917,-1907,-1228133,405769]$	$[115139273278249/405769,524030063733/405769,-803230307/405769]$	$y^2 + (x^3 + x + 1)y = -3x^5 + 9x^4 - 7x^3 - 2x^2 + x$