Genus 2 curves in isogeny class 63506.a of discriminant 127012

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
63506.a.127012.1	63506.a	\( 2 \cdot 113 \cdot 281 \)	\( - 2^{2} \cdot 113 \cdot 281 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$18$	$0$	2.10.1	✓	✓	$1$	\( 2 \)	\(0.018715\)	\(19.161053\)	\(0.717203\)	$[180,29049,814221,-16257536]$	$[45,-1126,4032,-271609,-127012]$	$[-184528125/127012,51303375/63506,-2041200/31753]$	$y^2 + (x^3 + 1)y = 2x^3 + 2x^2 - x$