Genus 2 curves of conductor 676

Results (3 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
676.a.5408.1	676.a	\( 2^{2} \cdot 13^{2} \)	\( - 2^{5} \cdot 13^{2} \)	$0$	$0$	$\Z/21\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$6$	$0$	2.60.2, 3.2160.21	✓	✓	$1$	\( 7 \)	\(1.000000\)	\(20.169780\)	\(0.320155\)	$[204,3273,161211,692224]$	$[51,-28,0,-196,5408]$	$[345025251/5408,-928557/1352,0]$	$y^2 + (x^3 + x^2 + x)y = x^3 + 3x^2 + 3x + 1$
676.a.562432.1	676.a	\( 2^{2} \cdot 13^{2} \)	\( 2^{8} \cdot 13^{3} \)	$0$	$0$	$\Z/21\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$0$	2.60.2, 3.2160.20	✓	✓	$1$	\( 3 \cdot 7 \)	\(1.000000\)	\(6.723260\)	\(0.320155\)	$[1620,52953,29527389,71991296]$	$[405,4628,-8112,-6175936,562432]$	$[10896201253125/562432,5912281125/10816,-492075/208]$	$y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x$
676.b.17576.1	676.b	\( 2^{2} \cdot 13^{2} \)	\( - 2^{3} \cdot 13^{3} \)	$0$	$0$	$\Z/3\Z\oplus\Z/3\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathrm{M}_2(\Q)\)		$E_1$				$D_6$	$D_6$	$0$	$0$	2.120.4, 3.17280.1		✓	$1$	\( 3 \)	\(1.000000\)	\(7.177121\)	\(0.265819\)	$[1244,1249,129167,2249728]$	$[311,3978,72332,1667692,17576]$	$[2909390022551/17576,4602275343/676,10349147/26]$	$y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$