Genus 2 curves in isogeny class 5464.a of discriminant 349696

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
5464.a.349696.1	5464.a	\( 2^{3} \cdot 683 \)	\( - 2^{9} \cdot 683 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$10$	$0$		✓	✓	$1$	\( 17 \)	\(0.002969\)	\(14.473471\)	\(0.730561\)	$[72,4092,31572,1398784]$	$[36,-628,3420,-67816,349696]$	$[118098/683,-114453/1366,69255/5464]$	$y^2 + (x + 1)y = x^6 + 2x^5 + x^4 - x^3$