Genus 2 curves in isogeny class 7643.a of discriminant 7643

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
7643.a.7643.1	7643.a	\( 7643 \)	\( -7643 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$10$	$0$		✓	✓	$1$	\( 1 \)	\(0.015846\)	\(23.292205\)	\(0.369100\)	$[44,6601,93275,978304]$	$[11,-270,-452,-19468,7643]$	$[161051/7643,-359370/7643,-54692/7643]$	$y^2 + (x^3 + 1)y = x^5 + x^4 + 2x^2 + x$