Genus 2 curves of conductor 5618

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
5618.a.11236.1	5618.a	\( 2 \cdot 53^{2} \)	\( - 2^{2} \cdot 53^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$12$	$0$	2.60.2, 3.90.1	✓	✓	$1$	\( 2 \)	\(0.006408\)	\(23.498592\)	\(0.301139\)	$[84,7305,129381,-1438208]$	$[21,-286,0,-20449,-11236]$	$[-4084101/11236,1324323/5618,0]$	$y^2 + (x^3 + 1)y = -x^5 + x^4 + x^2 - x$