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Conductor	Absolute discriminant	Rational points*	Weierstrass points	Torsion order

Bad \(p\)	2-Selmer rank	Analytic rank*	Analytic Ш*	Torsion

\(\Q\)-end algebra	\(\mathrm{ST}(X)\)	\(\mathrm{Aut}(X)\)	Square Ш*	\(\overline{\Q}\)-simple

\(\overline{\Q}\)-end algebra	\(\mathrm{ST}^0(X)\)	\(\mathrm{Aut}(X_{\overline{\Q}})\)	Locally solvable	$\GL_2$-type

Galois image	Nonmax$\ \ell$

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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	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(25.783703\)	\(0.131550\)	$[108,57,2259,-31872]$	$[27,28,32,20,-249]$	$[-\frac{4782969}{83},-\frac{183708}{83},-\frac{7776}{83}]$	$y^2 + (x^3 + 1)y = x^2 + x$
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	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(25.783703\)	\(0.131550\)	$[1932,87897,65765571,860544]$	$[483,6058,-161212,-28641190,6723]$	$[\frac{324526850403}{83},\frac{25281736298}{249},-\frac{4178776252}{747}]$	$y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$

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