Genus 2 curves in isogeny class 4428.a of discriminant 239112

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
4428.a.239112.1	4428.a	\( 2^{2} \cdot 3^{3} \cdot 41 \)	\( 2^{3} \cdot 3^{6} \cdot 41 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$10$	$0$	2.10.1, 3.80.2	✓	✓	$1$	\( 2^{2} \cdot 3 \)	\(0.003691\)	\(11.609152\)	\(0.514253\)	$[76,-311,-17605,125952]$	$[57,252,5184,57996,239112]$	$[2476099/984,48013/246,2888/41]$	$y^2 + (x^3 + x + 1)y = -2x^5 - x^4 - x$