Genus 2 curves of conductor 11751

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
11751.a.11751.1	11751.a	\( 3 \cdot 3917 \)	\( - 3 \cdot 3917 \)	$1$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$0$	$0$				$2$	\( 1 \)	\(0.091291\)	\(6.834898\)	\(1.247931\)	$[6460,32161,66651951,1504128]$	$[1615,107336,9426092,925530421,11751]$	$[10986582805759375/11751,452129648339000/11751,24585368806700/11751]$	$y^2 + (x^3 + x + 1)y = -x^6 + x^5 - 5x^4 + 3x^3 - 7x^2 + 2x - 3$
11751.b.105759.1	11751.b	\( 3 \cdot 3917 \)	\( - 3^{3} \cdot 3917 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$14$	$0$		✓	✓	$1$	\( 3 \)	\(0.006222\)	\(20.723528\)	\(0.386795\)	$[516,41385,4850661,-13537152]$	$[129,-1031,-611,-285445,-105759]$	$[-1323075987/3917,81971717/3917,1129739/11751]$	$y^2 + (x^3 + x + 1)y = -2x^4 + 3x^2 - x$