Genus 2 curves in isogeny class 708.a of discriminant 181248

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
708.a.181248.1	708.a	\( 2^{2} \cdot 3 \cdot 59 \)	\( - 2^{10} \cdot 3 \cdot 59 \)	$0$	$3$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$0$	$0$	2.15.1	✓	✓	$4$	\( 1 \)	\(1.000000\)	\(0.325344\)	\(0.325344\)	$[234100,3468879025,202585466081177,-23199744]$	$[58525,-1820975,60952909,62829762150,-181248]$	$[-686605237334059580078125/181248,365029741228054296875/181248,-208774418179643125/181248]$	$y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36$