Genus 2 curve search results

Results (5 matches)

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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
3125.a.3125.1	3125.a	\( 5^{5} \)	\( 5^{5} \)	$0$	$0$	$\Z/5\Z$	\(\mathsf{CM}\)	\(\Q\)		$F_{ac}$		✓	✓	$C_2$	$C_{10}$	$3$	$1$	2.36.1, 3.1296.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(17.957841\)	\(0.718314\)	$[0,0,0,4]$	$[0,0,0,0,3125]$	$[0,0,0]$	$y^2 + y = x^5$
10000.b.800000.1	10000.b	\( 2^{4} \cdot 5^{4} \)	\( 2^{8} \cdot 5^{5} \)	$0$	$1$	$\Z/10\Z$	\(\mathsf{CM}\)	\(\Q\)		$F_{ac}$		✓	✓	$C_2$	$C_{10}$	$4$	$2$	2.180.2, 3.1296.1	✓	✓	$1$	\( 2 \cdot 5 \)	\(1.000000\)	\(10.314071\)	\(1.031407\)	$[0,0,0,1]$	$[0,0,0,0,800000]$	$[0,0,0]$	$y^2 = x^5 + 1$
50000.a.200000.1	50000.a	\( 2^{4} \cdot 5^{5} \)	\( 2^{6} \cdot 5^{5} \)	$1$	$1$	$\Z/5\Z$	\(\mathsf{CM}\)	\(\Q\)		$F_{ac}$		✓	✓	$C_2$	$C_{10}$	$5$	$1$	2.36.1, 3.1296.1	✓	✓	$1$	\( 5 \)	\(0.821052\)	\(11.847756\)	\(1.945524\)	$[0,0,0,8]$	$[0,0,0,0,200000]$	$[0,0,0]$	$y^2 + y = 2x^5$
50625.a.253125.1	50625.a	\( 3^{4} \cdot 5^{4} \)	\( 3^{4} \cdot 5^{5} \)	$1$	$1$	$\mathsf{trivial}$	\(\mathsf{CM}\)	\(\Q\)		$F_{ac}$		✓	✓	$C_2$	$C_{10}$	$3$	$1$	2.36.1, 3.6480.5	✓	✓	$1$	\( 2 \)	\(0.189560\)	\(5.175122\)	\(1.961993\)	$[0,0,0,324]$	$[0,0,0,0,253125]$	$[0,0,0]$	$y^2 + y = x^5 - 1$
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	✓	✓	$1$	\( 2 \)	\(1.207711\)	\(4.612593\)	\(2.785339\)	$[0,0,0,1]$	$[0,0,0,0,800000]$	$[0,0,0]$	$y^2 = x^5 - 1$

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