Genus 2 curves in isogeny class 4624.d of discriminant 295936

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
4624.d.295936.1	4624.d	\( 2^{4} \cdot 17^{2} \)	\( 2^{10} \cdot 17^{2} \)	$0$	$0$	$\Z/13\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,13$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.12.1	✓	✓	$1$	\( 13 \)	\(1.000000\)	\(12.766189\)	\(0.982015\)	$[88,-1292,-144636,1183744]$	$[44,296,13636,128092,295936]$	$[161051/289,49247/578,412489/4624]$	$y^2 + (x^3 + x^2)y = x^3 + x^2 - 2x - 1$