Genus 2 curves of conductor 49507

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
49507.a.49507.1	49507.a	\( 31 \cdot 1597 \)	\( - 31 \cdot 1597 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$18$	$0$		✓	✓	$1$	\( 1 \)	\(0.040745\)	\(15.858977\)	\(0.646167\)	$[300,8889,544659,6336896]$	$[75,-136,1128,16526,49507]$	$[2373046875/49507,-57375000/49507,6345000/49507]$	$y^2 + (x^3 + 1)y = 2x^4 + 3x^3 + 3x^2 + x$