Genus 2 curves in isogeny class 8649.b of discriminant 700569

Results (unique match)

  Download displayed columns for results to

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
8649.b.700569.1	8649.b	\( 3^{2} \cdot 31^{2} \)	\( 3^{6} \cdot 31^{2} \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_6$		✓		$C_6$	$D_6$	$3$	$3$	2.240.1, 3.480.12	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(5.541100\)	\(1.385275\)	$[1132,73377,21088959,369024]$	$[849,2517,-2507,-2115933,700569]$	$[\frac{1815232161643}{2883},\frac{19016091893}{8649},-\frac{200783123}{77841}]$	$y^2 + (x^2 + x)y = 9x^5 + 2x^4 - 21x^3 - 22x^2 - 8x - 1$

  Download displayed columns for results to