Genus 2 curves of conductor 160000

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
160000.a.800000.1	160000.a	\( 2^{8} \cdot 5^{4} \)	\( 2^{8} \cdot 5^{5} \)	$1$	$1$	$\Z/3\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$0$	2.15.2, 3.720.4	✓	✓	$1$	\( 3 \)	\(1.783187\)	\(3.388529\)	\(2.014127\)	$[760,10,1390,32]$	$[3800,601500,127040000,30237437500,800000]$	$[990439600000,41256885000,2293072000]$	$y^2 + xy = -x^6 + 5x^4 - 9x^2 + 5$
160000.b.800000.1	160000.b	\( 2^{8} \cdot 5^{4} \)	\( - 2^{8} \cdot 5^{5} \)	$1$	$2$	$\Z/3\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.15.2, 3.720.4			$2$	\( 3 \)	\(0.841394\)	\(4.913231\)	\(2.755974\)	$[760,10,1390,32]$	$[3800,601500,127040000,30237437500,800000]$	$[990439600000,41256885000,2293072000]$	$y^2 + xy = -x^6 - 5x^4 - 9x^2 - 5$
160000.c.800000.1	160000.c	\( 2^{8} \cdot 5^{4} \)	\( 2^{8} \cdot 5^{5} \)	$1$	$2$	$\Z/2\Z$	\(\mathsf{CM}\)	\(\Q\)		$F_{ac}$		✓	✓	$C_2$	$C_{10}$	$2$	$2$	2.180.2, 3.1296.1	✓	✓	$1$	\( 2 \)	\(1.207711\)	\(4.612593\)	\(2.785339\)	$[0,0,0,1]$	$[0,0,0,0,800000]$	$[0,0,0]$	$y^2 = x^5 - 1$