Genus 2 curves of conductor 75625

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
75625.a.75625.1	75625.a	\( 5^{4} \cdot 11^{2} \)	\( 5^{4} \cdot 11^{2} \)	$0$	$2$	$\Z/5\Z$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$0$	$0$	✓	✓	$4$	\( 1 \)	\(1.000000\)	\(18.948154\)	\(3.031705\)	$[6428,1809025,4688688575,-9680000]$	$[1607,32226,-21867176,-9044766727,-75625]$	$[-10717151840024807/75625,-133737756368718/75625,56470866794024/75625]$	$y^2 + (x^3 + x + 1)y = x^6 + 5x^5 + 7x^4 - 10x^2 - 4x + 4$
75625.b.75625.1	75625.b	\( 5^{4} \cdot 11^{2} \)	\( 5^{4} \cdot 11^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$4$	$0$	✓	✓	$1$	\( 1 \)	\(0.133569\)	\(11.284721\)	\(1.507286\)	$[8388,-50775,-142234875,9680000]$	$[2097,185341,22088889,2992278488,75625]$	$[40550120800150257/75625,1709097320540493/75625,97133879288601/75625]$	$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 6x^3 + 11x - 7$