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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
8192.a.32768.1	8192.a	\( 2^{13} \)	\( 2^{15} \)	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q\)		$J(E_4)$		✓		$C_2$	$D_4$	$4$	$4$	2.360.2, 3.270.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(16.855414\)	\(1.053463\)	$[67,82,1930,4]$	$[268,2118,-124,-1129789,32768]$	$[\frac{1350125107}{32},\frac{318508017}{256},-\frac{139159}{512}]$	$y^2 = x^5 - 3x^3 + 2x$
16384.a.32768.1	16384.a	\( 2^{14} \)	\( 2^{15} \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q\)		$J(E_4)$		✓		$C_2$	$D_4$	$2$	$2$	2.180.3, 3.270.1	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(8.427707\)	\(1.053463\)	$[67,82,1930,4]$	$[268,2118,-124,-1129789,32768]$	$[\frac{1350125107}{32},\frac{318508017}{256},-\frac{139159}{512}]$	$y^2 = x^5 + 3x^3 + 2x$

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