Genus 2 curves in isogeny class 597.a of discriminant 597

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
597.a.597.1	597.a	\( 3 \cdot 199 \)	\( 3 \cdot 199 \)	$0$	$0$	$\Z/7\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(14.411617\)	\(0.294115\)	$[120,192,9912,2388]$	$[60,118,-68,-4501,597]$	$[259200000/199,8496000/199,-81600/199]$	$y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x$