Genus 2 curve search results

Results (displaying both matches)

 

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
563011.a.563011.1	563011.a	\( 563011 \)	\( -563011 \)	$4$	$4$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$26$	$0$		✓	✓	$1$	\( 1 \)	\(0.073355\)	\(16.330521\)	\(1.197933\)	$[1380,47193,18229677,-72065408]$	$[345,2993,30309,374639,-563011]$	$[-4887597965625/563011,-122903429625/563011,-3607528725/563011]$	$y^2 + (x^3 + x + 1)y = -2x^4 + x^3 + 7x^2 + 4x$
792079.a.792079.1	792079.a	\( 41 \cdot 19319 \)	\( - 41 \cdot 19319 \)	$4$	$4$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$26$	$0$		✓	✓	$1$	\( 1 \)	\(0.084450\)	\(18.004162\)	\(1.520457\)	$[3012,432585,340579413,-101386112]$	$[753,5601,28157,-2542245,-792079]$	$[-242088902178993/792079,-2391390508977/792079,-15965272413/792079]$	$y^2 + (x^3 + x + 1)y = -3x^5 + 7x^4 - 4x^2$