Genus 2 curves in isogeny class 531122.a of discriminant 531122

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
531122.a.531122.1	531122.a	\( 2 \cdot 265561 \)	\( 2 \cdot 265561 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$2$	$0$		✓	✓	$1$	\( 1 \)	\(0.342238\)	\(13.843144\)	\(4.737644\)	$[556,35089,5741335,-67983616]$	$[139,-657,-17073,-701199,-531122]$	$[-51888844699/531122,1764451683/531122,329867433/531122]$	$y^2 + (x^3 + x^2 + x)y = -x^4 + 2x^2 + 2x + 2$