Genus 2 curves in isogeny class 10017.a of discriminant 10017

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
10017.a.10017.1	10017.a	\( 3^{3} \cdot 7 \cdot 53 \)	\( 3^{3} \cdot 7 \cdot 53 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$4$	$0$		✓	✓	$1$	\( 1 \)	\(0.093885\)	\(7.225875\)	\(0.678402\)	$[996,3825,1057257,1282176]$	$[249,2424,32076,527787,10017]$	$[35451365787/371,1386011688/371,73657188/371]$	$y^2 + (x^3 + x^2 + 1)y = -x^4 - 2x^3 - 2$