Genus 2 curves of conductor 588

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
588.a.18816.1	588.a	\( 2^{2} \cdot 3 \cdot 7^{2} \)	\( - 2^{7} \cdot 3 \cdot 7^{2} \)	$0$	$1$	$\Z/24\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$6$	$0$	2.45.1, 3.720.4	✓	✓	$1$	\( 2^{3} \)	\(1.000000\)	\(20.658150\)	\(0.286919\)	$[748,11545,2902787,2408448]$	$[187,976,-192,-247120,18816]$	$[228669389707/18816,398891383/1176,-34969/98]$	$y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8$