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
5008.a.641024.1	5008.a	\( 2^{4} \cdot 313 \)	\( 2^{11} \cdot 313 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$10$	$0$	2.10.1	✓	✓	$1$	\( 17 \)	\(0.002839\)	\(14.512519\)	\(0.700367\)	$[12,1005,-33069,80128]$	$[12,-664,31632,-15328,641024]$	$[243/626,-2241/1252,17793/2504]$	$y^2 + (x^3 + x)y = x^5 - x^4 - 2x^3 + x + 1$