Genus 2 curves of conductor 1312

Results (4 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
1312.a.2624.1	1312.a	\( 2^{5} \cdot 41 \)	\( - 2^{6} \cdot 41 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$6$	$0$	2.90.1	✓	✓	$1$	\( 2 \)	\(0.028941\)	\(16.518821\)	\(0.239039\)	$[112,91,1912,328]$	$[112,462,3440,42959,2624]$	$[275365888/41,10141824/41,674240/41]$	$y^2 + (x + 1)y = x^6 + 2x^5 + 3x^4 + 2x^3 + x^2$
1312.b.10496.1	1312.b	\( 2^{5} \cdot 41 \)	\( - 2^{8} \cdot 41 \)	$0$	$1$	$\Z/12\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$4$	$0$	2.90.1, 3.80.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(14.584701\)	\(0.405131\)	$[148,373,15335,1312]$	$[148,664,4096,41328,10496]$	$[277375828/41,8408398/41,350464/41]$	$y^2 + (x + 1)y = x^6 + x^4 + x^3 + x^2$
1312.b.83968.1	1312.b	\( 2^{5} \cdot 41 \)	\( 2^{11} \cdot 41 \)	$0$	$2$	$\Z/2\Z\oplus\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.180.3, 3.80.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(14.584701\)	\(0.405131\)	$[1556,36553,20209667,10496]$	$[1556,76512,1289104,-962060080,83968]$	$[8907339520949/82,140743510779/41,12191781649/328]$	$y^2 + xy = 8x^5 - 21x^4 + 15x^3 - x^2 - x$
1312.c.671744.1	1312.c	\( 2^{5} \cdot 41 \)	\( - 2^{14} \cdot 41 \)	$0$	$1$	$\Z/22\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,11$	✓	✓	$C_2$	$C_2$	$6$	$0$	2.90.1	✓	✓	$1$	\( 2 \cdot 11 \)	\(1.000000\)	\(11.857814\)	\(0.538992\)	$[164,1441,58489,83968]$	$[164,160,1984,74944,671744]$	$[2825761/16,8405/8,1271/16]$	$y^2 + (x + 1)y = x^6 + 4x^5 + 7x^4 + 5x^3 + 2x^2$