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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

Base change of	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

j-invariant

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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
605.1-b1	605.1-b	$1$	$1$	$\Q(\sqrt{-55}) $	$2$	$[0, 1]$	605.1	$ 5 \cdot 11^{2} $	$ 5^{22} \cdot 11^{4} $	$3.28669$	$(5,a+2), (11,a+5)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓					$1$	$ 2 \cdot 3 \cdot 5 $	$0.341202911$	$1.618785171$	8.937207628	$ -\frac{1459161}{3125} $	$ \bigl[1$ , $ -1$ , $ 0$ , $ -292$ , $ 4241\bigr] $	${y}^2+{x}{y}={x}^3-{x}^2-292{x}+4241$

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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.