Genus 2 curves in isogeny class 1216.a of discriminant 19456

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
1216.a.19456.1	1216.a	\( 2^{6} \cdot 19 \)	\( - 2^{10} \cdot 19 \)	$0$	$1$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.60.1, 3.80.2	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(1.625809\)	\(0.406452\)	$[3996,347595,394636194,-2432]$	$[3996,433604,54136720,7079476076,-19456]$	$[-995009990004999/19,-108076122094599/76,-3376781293545/76]$	$y^2 + x^2y = 4x^5 + 3x^4 - 11x^3 - 6x^2 + 6x - 1$