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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
4096.b.65536.1	4096.b	\( 2^{12} \)	\( - 2^{16} \)	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$	\(\mathrm{M}_2(\mathsf{CM})\)	\(\mathsf{CM}\)	✓	$J(C_2)$		✓		$C_4$	$GL(2,3)$	$4$	$4$	2.360.2, 3.6480.22	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(12.689987\)	\(0.793124\)	$[20,-20,-40,8]$	$[80,480,-1280,-83200,65536]$	$[50000,3750,-125]$	$y^2 = x^5 - x$
5184.a.46656.1	5184.a	\( 2^{6} \cdot 3^{4} \)	\( - 2^{6} \cdot 3^{6} \)	$0$	$1$	$\Z/6\Z$	\(\mathrm{M}_2(\mathsf{CM})\)	\(\mathsf{CM}\)	✓	$J(C_2)$		✓		$C_2$	$D_6$	$2$	$0$	2.180.4, 3.8640.16	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(14.110203\)	\(0.783900\)	$[76,252,5160,24]$	$[228,654,-644,-143637,46656]$	$[\frac{39617584}{3},\frac{1495262}{9},-\frac{58121}{81}]$	$y^2 + x^3y = x^3 + 2$

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