Genus 2 curves of conductor 449012

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
449012.a.898024.1	449012.a	\( 2^{2} \cdot 112253 \)	\( - 2^{3} \cdot 112253 \)	$0$	$3$	$\Z/3\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$3$	✓	✓	$C_2$	$C_2$	$0$	$0$	3.80.1			$8$	\( 3 \)	\(1.000000\)	\(1.363736\)	\(3.636630\)	$[60428,225918169,3418701707075,114947072]$	$[15107,95970,602044,-28790548,898024]$	$[786848544941745592307/898024,165439872520613355/449012,34349838510439/224506]$	$y^2 + (x^2 + x + 1)y = -x^6 + x^5 - 5x^4 + 14x^3 - 12x^2 + 27x - 38$