Genus 2 curves of conductor 10000

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	Locally solvable	Square Ш*	Analytic Ш*	Tamagawa	Regulator	Real period	Leading coefficient	Igusa-Clebsch invariants	Igusa invariants	G2-invariants	Equation
10000.a.160000.1	10000.a	\( 2^{4} \cdot 5^{4} \)	\( - 2^{8} \cdot 5^{4} \)	$0$	$0$	$\Z/5\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2$	$C_2$	$2$	$0$	✓	✓	$1$	\( 5 \)	\(1.000000\)	\(8.650088\)	\(1.730018\)	$[612,11325,1916325,20000]$	$[612,8056,110704,712928,160000]$	$[335364543972/625,7213296078/625,161966871/625]$	$y^2 + xy = x^6 - 2x^5 + 2x^4 - x^3 + 2x^2 - 3x + 2$
10000.b.800000.1	10000.b	\( 2^{4} \cdot 5^{4} \)	\( 2^{8} \cdot 5^{5} \)	$0$	$1$	$\Z/10\Z$	\(\mathsf{CM}\)	\(\Q\)		$F_{ac}$		✓	✓	$C_2$	$C_{10}$	$4$	$2$	✓	✓	$1$	\( 2 \cdot 5 \)	\(1.000000\)	\(10.314071\)	\(1.031407\)	$[0,0,0,1]$	$[0,0,0,0,800000]$	$[0,0,0]$	$y^2 = x^5 + 1$