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
10040.a.20080.1	10040.a	\( 2^{3} \cdot 5 \cdot 251 \)	\( - 2^{4} \cdot 5 \cdot 251 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 2 \)	\(0.079534\)	\(19.409052\)	\(0.771844\)	$[272,-620,-181772,-80320]$	$[136,874,22116,560975,-20080]$	$[-2907867136/1255,-137406784/1255,-25566096/1255]$	$y^2 + (x + 1)y = 2x^5 - x^4 - 2x^3$