Genus 2 curves in isogeny class 1047.a of discriminant 3141

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
1047.a.3141.1	1047.a	\( 3 \cdot 349 \)	\( 3^{2} \cdot 349 \)	$0$	$1$	$\Z/10\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(17.821680\)	\(0.356434\)	$[8,604,1017,-12564]$	$[4,-100,-1,-2501,-3141]$	$[-1024/3141,6400/3141,16/3141]$	$y^2 + (x^3 + x)y = x$