Genus 2 curves of conductor 2500

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	mod-$\ell$ images	Locally solvable	Square Ш*	Analytic Ш*	Tamagawa	Regulator	Real period	Leading coefficient	Igusa-Clebsch invariants	Igusa invariants	G2-invariants	Equation
2500.a.50000.1	2500.a	\( 2^{2} \cdot 5^{4} \)	\( 2^{4} \cdot 5^{5} \)	$0$	$0$	$\Z/15\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q \times \Q\)	✓	$J(E_1)$				$C_2^2$	$C_2^2$	$4$	$0$	2.60.2, 3.8640.9	✓	✓	$1$	\( 3 \cdot 5 \)	\(1.000000\)	\(10.235464\)	\(0.682364\)	$[100,625,21385,2048]$	$[125,0,-10000,-312500,50000]$	$[9765625/16,0,-3125]$	$y^2 + (x^3 + 1)y = x^5 + 2x^3 + x$
2500.a.400000.1	2500.a	\( 2^{2} \cdot 5^{4} \)	\( - 2^{7} \cdot 5^{5} \)	$0$	$0$	$\Z/5\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q \times \Q\)	✓	$J(E_1)$				$C_2^2$	$C_2^2$	$0$	$0$	2.60.2, 3.2880.2		✓	$1$	\( 5 \)	\(1.000000\)	\(3.411821\)	\(0.682364\)	$[860,36865,8199455,16384]$	$[1075,9750,107500,5125000,400000]$	$[459401384375/128,1937983125/64,9938375/32]$	$y^2 + (x^3 + 1)y = -2x^6 - 2x^5 + 2x^3 - 2x - 2$