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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
3969.d.250047.1	3969.d	\( 3^{4} \cdot 7^{2} \)	\( - 3^{6} \cdot 7^{3} \)	$0$	$2$	$\Z/2\Z\oplus\Z/6\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{RM}\)	✓	$J(E_1)$		✓		$C_2$	$C_2$	$4$	$2$	2.180.3, 3.1920.1	✓	✓	$1$	\( 2^{3} \)	\(1.000000\)	\(13.559050\)	\(0.753281\)	$[452,-15543,-660459,131712]$	$[339,10617,-211009,-46063185,250047]$	$[\frac{18424351793}{1029},\frac{5106412483}{3087},-\frac{2694373921}{27783}]$	$y^2 + (x^2 + x + 1)y = -3x^5 + 5x^4 - 4x^3 + x$

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