Genus 2 curves in isogeny class 4312.a of discriminant 189728

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
4312.a.189728.1	4312.a	\( 2^{3} \cdot 7^{2} \cdot 11 \)	\( 2^{5} \cdot 7^{2} \cdot 11^{2} \)	$0$	$1$	$\Z/10\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.90.3	✓	✓	$1$	\( 2 \cdot 5 \)	\(1.000000\)	\(10.282597\)	\(1.028260\)	$[384,-6912,-404100,758912]$	$[192,2688,-156,-1813824,189728]$	$[8153726976/5929,84934656/847,-179712/5929]$	$y^2 + (x + 1)y = -2x^5 + 4x^4 - 2x^3 - 2x^2$