Genus 2 curves in isogeny class 295.a of discriminant 295

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
295.a.295.1	295.a	\( 5 \cdot 59 \)	\( - 5 \cdot 59 \)	$0$	$1$	$\Z/14\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.60.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(29.256600\)	\(0.149268\)	$[108,-39,20835,37760]$	$[27,32,-256,-1984,295]$	$[14348907/295,629856/295,-186624/295]$	$y^2 + (x^3 + 1)y = -x^2$
295.a.295.2	295.a	\( 5 \cdot 59 \)	\( - 5 \cdot 59 \)	$0$	$1$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.60.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(0.597073\)	\(0.149268\)	$[198804,305807001,18482629056189,-37760]$	$[49701,90182600,203402032096,494095763610824,-295]$	$[-303267334973269931148501/295,-2214359494206283568520/59,-502441543825401014496/295]$	$y^2 + (x^2 + x + 1)y = x^5 - 40x^3 + 22x^2 + 389x - 608$