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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
169.a.169.1	169.a	\( 13^{2} \)	\( - 13^{2} \)	$0$	$0$	$\Z/19\Z$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_6$		✓		$C_6$	$D_6$	$6$	$0$	2.40.3, 3.480.12	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(32.667031\)	\(0.090490\)	$[4,793,3757,-21632]$	$[1,-33,-43,-283,-169]$	$[-1/169,33/169,43/169]$	$y^2 + (x^3 + x + 1)y = x^5 + x^4$

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