Genus 2 curves in isogeny class 35131.a of discriminant 35131

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
35131.a.35131.1	35131.a	\( 19 \cdot 43^{2} \)	\( - 19 \cdot 43^{2} \)	$3$	$3$	$\mathsf{trivial}$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$14$	$0$	2.15.2, 3.90.1	✓	✓	$1$	\( 1 \)	\(0.032194\)	\(16.714784\)	\(0.538120\)	$[280,2452,209776,140524]$	$[140,408,-1064,-78856,35131]$	$[53782400000/35131,1119552000/35131,-1097600/1849]$	$y^2 + x^3y = x^4 - 3x^3 + 4x^2 - 3x + 1$