Genus 2 curves in isogeny class 882.a of discriminant 63504

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
882.a.63504.1	882.a	\( 2 \cdot 3^{2} \cdot 7^{2} \)	\( 2^{4} \cdot 3^{4} \cdot 7^{2} \)	$0$	$2$	$\Z/2\Z\oplus\Z/8\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$2$	2.360.1, 3.90.1	✓	✓	$1$	\( 2^{3} \)	\(1.000000\)	\(12.542623\)	\(0.391957\)	$[548,6049,662961,8128512]$	$[137,530,6336,146783,63504]$	$[48261724457/63504,681408545/31752,825836/441]$	$y^2 + (x^2 + x)y = x^5 + x^4 + x^3 + 3x^2 + 3x + 1$