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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
25.1-c6	25.1-c	$6$	$8$	4.4.9225.1	$4$	$[4, 0]$	25.1	$ 5^{2} $	$ 5^{2} $	$12.83407$	$(1/2a^3-3a-1/2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$ 1 $	$0.755755172$	$290.8077153$	2.288252076	$ -\frac{540595195}{4} a^{3} - \frac{730667933}{5} a^{2} + \frac{10473423273}{10} a + \frac{24675440989}{20} $	$ \bigl[1$ , $ \frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}$ , $ \frac{1}{4} a^{3} + a^{2} - \frac{1}{2} a - \frac{19}{4}$ , $ \frac{1}{4} a^{3} - a^{2} - \frac{5}{2} a + \frac{25}{4}$ , $ -\frac{3}{2} a^{3} + 9 a - \frac{11}{2}\bigr] $	${y}^2+{x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{1}{2}a-\frac{19}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{1}{4}\right){x}^{2}+\left(\frac{1}{4}a^{3}-a^{2}-\frac{5}{2}a+\frac{25}{4}\right){x}-\frac{3}{2}a^{3}+9a-\frac{11}{2}$
25.1-d4	25.1-d	$6$	$8$	4.4.9225.1	$4$	$[4, 0]$	25.1	$ 5^{2} $	$ 5^{2} $	$12.83407$	$(1/2a^3-3a-1/2)$	$1$	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$ 1 $	$2.939676283$	$1324.943058$	2.534507336	$ -\frac{540595195}{4} a^{3} - \frac{730667933}{5} a^{2} + \frac{10473423273}{10} a + \frac{24675440989}{20} $	$ \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}$ , $ -\frac{1}{4} a^{3} + a^{2} + \frac{1}{2} a - \frac{17}{4}$ , $ a^{2} - 4$ , $ -\frac{5}{2} a^{3} + 7 a + \frac{15}{2}$ , $ -\frac{17}{4} a^{3} - 2 a^{2} + \frac{33}{2} a + \frac{51}{4}\bigr] $	${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+a^{2}+\frac{1}{2}a-\frac{17}{4}\right){x}^{2}+\left(-\frac{5}{2}a^{3}+7a+\frac{15}{2}\right){x}-\frac{17}{4}a^{3}-2a^{2}+\frac{33}{2}a+\frac{51}{4}$

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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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