Genus 2 curves in isogeny class 7627.a of discriminant 7627

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
7627.a.7627.1	7627.a	\( 29 \cdot 263 \)	\( 29 \cdot 263 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$11$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(0.016411\)	\(22.363297\)	\(0.366999\)	$[340,2329,42109,976256]$	$[85,204,3128,56066,7627]$	$[4437053125/7627,125281500/7627,22599800/7627]$	$y^2 + (x^2 + x + 1)y = x^5 - x^4 - 2x^3$