Genus 2 curves in isogeny class 11529.a of discriminant 726327

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
11529.a.726327.1	11529.a	\( 3^{3} \cdot 7 \cdot 61 \)	\( 3^{5} \cdot 7^{2} \cdot 61 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$14$	$0$		✓	✓	$1$	\( 2 \cdot 3 \)	\(0.003877\)	\(17.730933\)	\(0.412497\)	$[1572,162441,61761429,92969856]$	$[393,-333,21589,2093397,726327]$	$[38579489651/2989,-83179367/2989,370488829/80703]$	$y^2 + (x^3 + x + 1)y = -3x^4 + 5x^2$