Genus 2 curves of conductor 494206

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
494206.a.988412.1	494206.a	\( 2 \cdot 109 \cdot 2267 \)	\( - 2^{2} \cdot 109 \cdot 2267 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$17$	$1$	2.6.1	✓	✓	$1$	\( 2 \)	\(0.058748\)	\(14.923765\)	\(1.753491\)	$[724,29737,4593493,-126516736]$	$[181,126,12224,549167,-988412]$	$[-194264244901/988412,-373573683/494206,-100117616/247103]$	$y^2 + (x^3 + 1)y = x^5 + 3x^4 - 3x^2 - x$