Genus 2 curves in isogeny class 461.a of discriminant 461

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
461.a.461.1	461.a	\( 461 \)	\( 461 \)	$0$	$0$	$\Z/7\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(12.048435\)	\(0.245886\)	$[1176,144,66456,1844]$	$[588,14382,467132,16957923,461]$	$[70288881159168/461,2923824242304/461,161508086208/461]$	$y^2 + x^3y = x^5 - 3x^3 + 3x - 2$
461.a.461.2	461.a	\( 461 \)	\( 461 \)	$0$	$0$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(0.245886\)	\(0.245886\)	$[80664,166117104,3752725952952,1844]$	$[40332,40091742,45075737276,52661714805267,461]$	$[106720731303787612818432/461,2630293443843585469056/461,73323359651716069824/461]$	$y^2 + y = x^5 - x^4 - 39x^3 + 10x^2 + 272x - 306$