Genus 2 curves in isogeny class 1164.b of discriminant 670464

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
1164.b.670464.1	1164.b	\( 2^{2} \cdot 3 \cdot 97 \)	\( 2^{8} \cdot 3^{3} \cdot 97 \)	$0$	$0$	$\Z/21\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3,7$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.6.1, 3.80.1	✓	✓	$1$	\( 3 \cdot 7 \)	\(1.000000\)	\(8.941486\)	\(0.425785\)	$[372,4521,1271253,85819392]$	$[93,172,-10928,-261472,670464]$	$[257662359/24832,1281013/6208,-656363/4656]$	$y^2 + (x^2 + x + 1)y = 2x^5 - 2x^4 + x^3 - x^2$