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
762.a.82296.1	762.a	\( 2 \cdot 3 \cdot 127 \)	\( 2^{3} \cdot 3^{4} \cdot 127 \)	$0$	$2$	$\Z/2\Z\oplus\Z/12\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3, 3.80.1	✓	✓	$1$	\( 2^{2} \cdot 3 \)	\(1.000000\)	\(16.733449\)	\(0.348614\)	$[12004,205249,810020577,10533888]$	$[3001,366698,58441312,10228738527,82296]$	$[243405270090015001/82296,4955375073324349/41148,65790314289164/10287]$	$y^2 + (x^2 + x)y = x^5 - 8x^4 + 14x^3 + 2x^2 - x$