Genus 2 curves in isogeny class 1137.a of discriminant 1137

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
1137.a.1137.1	1137.a	\( 3 \cdot 379 \)	\( 3 \cdot 379 \)	$0$	$1$	$\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1, 3.80.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(15.522353\)	\(0.431176\)	$[148,-191,28401,145536]$	$[37,65,-359,-4377,1137]$	$[69343957/1137,3292445/1137,-491471/1137]$	$y^2 + (x^2 + x + 1)y = x^5 + x^4 + x^3$