Genus 2 curves of conductor 826

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
826.a.11564.1	826.a	\( 2 \cdot 7 \cdot 59 \)	\( - 2^{2} \cdot 7^{2} \cdot 59 \)	$0$	$2$	$\Z/2\Z\oplus\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3, 3.80.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(13.174483\)	\(0.365958\)	$[92,-554591,-3126961,1480192]$	$[23,23130,-104176,-134348237,11564]$	$[6436343/11564,140711355/5782,-13777276/2891]$	$y^2 + (x^2 + x)y = x^5 + x^4 + 3x^3 - 4x^2 - 4x + 3$