Genus 2 curves in isogeny class 1170.a of discriminant 10530

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
1170.a.10530.1	1170.a	\( 2 \cdot 3^{2} \cdot 5 \cdot 13 \)	\( - 2 \cdot 3^{4} \cdot 5 \cdot 13 \)	$0$	$4$	$\Z/2\Z\oplus\Z/6\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.90.6, 3.720.4	✓	✓	$4$	\( 3 \)	\(1.000000\)	\(5.542030\)	\(0.461836\)	$[507196,192673,32552199279,1347840]$	$[126799,669908072,4718980180980,37396285759331459,10530]$	$[32777750301275239538233999/10530,682861614668954802420364/5265,7205289570406928666]$	$y^2 + (x^2 + x)y = 15x^6 + 28x^5 + 62x^4 + 59x^3 + 62x^2 + 28x + 15$