Genus 2 curves in isogeny class 1300.a of discriminant 130000

Results (unique match)

 

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
1300.a.130000.1	1300.a	\( 2^{2} \cdot 5^{2} \cdot 13 \)	\( - 2^{4} \cdot 5^{4} \cdot 13 \)	$1$	$2$	$\Z/6\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$6$	$0$	2.90.1, 3.720.4	✓	✓	$1$	\( 2^{2} \cdot 3 \)	\(0.093879\)	\(7.601599\)	\(0.237876\)	$[4600,9904,15140164,520000]$	$[2300,218766,27536704,3868964111,130000]$	$[6436343000000/13,266172592200/13,1120532032]$	$y^2 + (x^3 + x)y = 2x^4 + 9x^2 + 13$