Genus 2 curves in isogeny class 1083.b of discriminant 87723

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
1083.b.87723.1	1083.b	\( 3 \cdot 19^{2} \)	\( - 3^{5} \cdot 19^{2} \)	$0$	$1$	$\Z/15\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.15.2, 3.720.4			$2$	\( 5 \)	\(1.000000\)	\(5.981341\)	\(0.265837\)	$[5464,8692,15768656,350892]$	$[2732,309544,46549080,7838649656,87723]$	$[152196082896530432/87723,6311963449851392/87723,1429770125440/361]$	$y^2 + y = -x^6 - 3x^5 - 8x^4 - 11x^3 - 14x^2 - 9x - 6$