Genus 2 curves of conductor 10114

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
10114.a.262964.1	10114.a	\( 2 \cdot 13 \cdot 389 \)	\( 2^{2} \cdot 13^{2} \cdot 389 \)	$0$	$1$	$\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$2$	$2$	2.30.3, 3.80.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(14.310026\)	\(1.590003\)	$[1256,3016,-13131397,1051856]$	$[628,15930,2120049,269406468,262964]$	$[24419582094592/65741,986358327840/65741,209028351204/65741]$	$y^2 + (x^2 + 1)y = 2x^5 - 4x^4 - 2x^3 + 3x^2 + x + 1$