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
10075.c.654875.1	10075.c	\( 5^{2} \cdot 13 \cdot 31 \)	\( - 5^{3} \cdot 13^{2} \cdot 31 \)	$0$	$4$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$3$	2.120.3	✓	✓	$4$	\( 2^{2} \)	\(1.000000\)	\(1.535742\)	\(1.535742\)	$[144016,182644,6685568599,-2619500]$	$[72008,216017562,864154072025,3890604831488089,-654875]$	$[-1935992825145263554592768/654875,-80655002008707170079744/654875,-179230810806977336384/26195]$	$y^2 + xy = 5x^5 + 41x^4 + 88x^3 + 16x^2 + x$