Genus 2 curves of conductor 12500

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
12500.a.12500.1	12500.a	\( 2^{2} \cdot 5^{5} \)	\( 2^{2} \cdot 5^{5} \)	$0$	$0$	$\Z/5\Z$	\(\mathsf{RM}\)	\(\Q\)		$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$		✓	✓	$C_2$	$C_2$	$3$	$1$	2.36.1, 3.36.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(25.011388\)	\(1.000456\)	$[60,2025,67995,-512]$	$[75,-1875,-73125,-2250000,-12500]$	$[-759375/4,253125/4,131625/4]$	$y^2 + (x^3 + 1)y = x^6 + 2x^3 - x$
12500.b.50000.1	12500.b	\( 2^{2} \cdot 5^{5} \)	\( 2^{4} \cdot 5^{5} \)	$0$	$0$	$\Z/5\Z$	\(\mathsf{RM}\)	\(\Q\)		$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$		✓	✓	$C_2$	$C_2$	$3$	$1$	2.36.1, 3.36.1	✓	✓	$1$	\( 5 \)	\(1.000000\)	\(5.925134\)	\(1.185027\)	$[420,225,26865,2048]$	$[525,11250,322500,10687500,50000]$	$[12762815625/16,260465625/8,7111125/4]$	$y^2 + (x^3 + 1)y = x^5 - 3x^3 + 3x - 2$