Genus 2 curves in isogeny class 39497.a of discriminant 39497

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
39497.a.39497.1	39497.a	\( 127 \cdot 311 \)	\( 127 \cdot 311 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$14$	$0$		✓	✓	$1$	\( 1 \)	\(0.039402\)	\(14.578300\)	\(0.574414\)	$[120,1140,26304,-157988]$	$[60,-40,744,10760,-39497]$	$[-777600000/39497,8640000/39497,-2678400/39497]$	$y^2 + y = x^6 - x^5 + x^4 - x^3 + x^2 - x$