Genus 2 curves in isogeny class 6718.a of discriminant 13436

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
6718.a.13436.1	6718.a	\( 2 \cdot 3359 \)	\( - 2^{2} \cdot 3359 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$12$	$0$		✓	✓	$1$	\( 2 \)	\(0.008000\)	\(21.445453\)	\(0.343120\)	$[620,9913,2068403,1719808]$	$[155,588,-2324,-176491,13436]$	$[89466096875/13436,547409625/3359,-13958525/3359]$	$y^2 + (x^2 + x + 1)y = x^6 + x^5 - x^2 - x$