Genus 2 curves of conductor 1416

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
1416.a.8496.1	1416.a	\( 2^{3} \cdot 3 \cdot 59 \)	\( - 2^{4} \cdot 3^{2} \cdot 59 \)	$0$	$2$	$\Z/2\Z\oplus\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3, 3.80.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(14.958620\)	\(0.415517\)	$[256,-2144,-178692,-33984]$	$[128,1040,12004,113728,-8496]$	$[-2147483648/531,-136314880/531,-12292096/531]$	$y^2 + (x^3 + x)y = x^5 - x^3 - 1$
1416.b.135936.1	1416.b	\( 2^{3} \cdot 3 \cdot 59 \)	\( - 2^{8} \cdot 3^{2} \cdot 59 \)	$0$	$2$	$\Z/2\Z\oplus\Z/14\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$7$	$3$	2.120.3	✓	✓	$1$	\( 2^{2} \cdot 7 \)	\(1.000000\)	\(15.707538\)	\(0.560984\)	$[192,-96,90660,543744]$	$[96,400,-8452,-242848,135936]$	$[3538944/59,153600/59,-33808/59]$	$y^2 + (x^3 + x)y = -2x^4 - x^3 + x + 1$