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Base field	Conductor norm	Rank*	Torsion order	CM discriminant

Base field degree/signature	Bad $p$	$\Q$-curves	Torsion structure	CM

Analytic order of Ш*	Cyclic isogeny degree	Isogeny class size	Reduction	Galois image

j-invariant	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
1089.1-e4	1089.1-e	$4$	$4$	$\Q(\sqrt{53}) $	$2$	$[2, 0]$	1089.1	$ 3^{2} \cdot 11^{2} $	$ 3^{6} \cdot 11^{8} $	$3.73709$	$(a+1), (a-2), (3)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$ 2^{4} \cdot 3 $	$0.723354634$	$8.936252827$	5.327457962	$ \frac{347873904937}{395307} $	$ \bigl[1$ , $ 1$ , $ 0$ , $ -146$ , $ 621\bigr] $	${y}^2+{x}{y}={x}^{3}+{x}^{2}-146{x}+621$

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*The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.