Genus 2 curves in isogeny class 4400.b of discriminant 352000

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
4400.b.352000.1	4400.b	\( 2^{4} \cdot 5^{2} \cdot 11 \)	\( - 2^{8} \cdot 5^{3} \cdot 11 \)	$1$	$2$	$\Z/3\Z\oplus\Z/6\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$10$	$0$	2.90.1, 3.5760.3	✓	✓	$1$	\( 3^{3} \)	\(0.365679\)	\(17.627207\)	\(0.537158\)	$[154,1876,128326,1375]$	$[308,-1050,-416900,-32376925,352000]$	$[984285148/125,-871563/10,-2247091/20]$	$y^2 = x^6 - 2x^4 - 3x^3 + x^2 + 3x + 1$