Genus 2 curves in isogeny class 114240.d of discriminant 114240

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
114240.d.114240.1	114240.d	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \)	$0$	$6$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.180.7, 3.90.1	✓	✓	$256$	\( 1 \)	\(1.000000\)	\(0.165182\)	\(2.642912\)	$[1256652,52204481283,17891676439496172,14280]$	$[1256652,30995939524,838652756430720,23286599174677950716,114240]$	$[16322019979578992366124730896/595,320367650677941067851565476/595,11592952003636922822112]$	$y^2 + (x^2 + 1)y = 51x^6 - 315x^4 + 103x^2 - 9$