Genus 2 curves of conductor 1497

Results (displaying both matches)

 

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
1497.a.1497.1	1497.a	\( 3 \cdot 499 \)	\( 3 \cdot 499 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$4$	$0$		✓	✓	$1$	\( 1 \)	\(0.021772\)	\(12.141842\)	\(0.264354\)	$[356,2065,274969,191616]$	$[89,244,-60,-16219,1497]$	$[5584059449/1497,172012436/1497,-158420/499]$	$y^2 + (x^3 + x + 1)y = -x^4 + x^3 - 2x^2 + x - 1$
1497.b.13473.1	1497.b	\( 3 \cdot 499 \)	\( 3^{3} \cdot 499 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$10$	$0$		✓	✓	$1$	\( 3 \)	\(0.002757\)	\(24.920459\)	\(0.206128\)	$[92,36025,3650051,-1724544]$	$[23,-1479,-41077,-783053,-13473]$	$[-6436343/13473,5998331/4491,21729733/13473]$	$y^2 + (x^3 + x + 1)y = -2x^5 + 3x^4 - x^2$