Genus 2 curves of conductor 249

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
249.a.249.1	249.a	\( 3 \cdot 83 \)	\( 3 \cdot 83 \)	$0$	$1$	$\Z/14\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.60.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(25.783703\)	\(0.131550\)	$[108,57,2259,-31872]$	$[27,28,32,20,-249]$	$[-4782969/83,-183708/83,-7776/83]$	$y^2 + (x^3 + 1)y = x^2 + x$
249.a.6723.1	249.a	\( 3 \cdot 83 \)	\( - 3^{4} \cdot 83 \)	$0$	$1$	$\Z/28\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$6$	$2$	2.30.3	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(25.783703\)	\(0.131550\)	$[1932,87897,65765571,860544]$	$[483,6058,-161212,-28641190,6723]$	$[324526850403/83,25281736298/249,-4178776252/747]$	$y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$