Genus 2 curve search results

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
784.b.25088.1	784.b	\( 2^{4} \cdot 7^{2} \)	\( - 2^{9} \cdot 7^{2} \)	$0$	$2$	$\Z/2\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2$	$C_2$	$0$	$0$	2.45.1, 3.720.5			$2$	\( 1 \)	\(1.000000\)	\(0.626117\)	\(0.313058\)	$[2740,15382525,36170522453,3136]$	$[2740,-9942200,-24298750736,-41356479464160,25088]$	$[301635777856250/49,-399451653071875/49,-712598832131225/98]$	$y^2 + (x^2 + 1)y = -x^6 - 3x^5 + 7x^4 + 2x^3 - 49x^2 + 41x - 9$