LMFDB - Elliptic curves over 4.4.18432.1 of conductor 7.4

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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
7.4-a1	7.4-a	$1$	$1$	4.4.18432.1	$4$	$[4, 0]$	7.4	$ 7 $	$ 7^{5} $	$15.47256$	$(-1/3a^3+1/3a^2+3a-3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	$ 1 $	$1$	$312.4324334$	2.301282211	$ \frac{1940359378}{50421} a^{3} - \frac{6297971513}{50421} a^{2} - \frac{994429675}{16807} a + \frac{3499312361}{16807} $	$ \bigl[\frac{1}{3} a^{2} - 1$ , $ \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1$ , $ \frac{1}{3} a^{2} + a - 2$ , $ -a^{3} + \frac{8}{3} a^{2} + 13 a - 18$ , $ \frac{7}{3} a^{3} - \frac{5}{3} a^{2} - 21 a + 25\bigr] $	${y}^2+\left(\frac{1}{3}a^{2}-1\right){x}{y}+\left(\frac{1}{3}a^{2}+a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){x}^{2}+\left(-a^{3}+\frac{8}{3}a^{2}+13a-18\right){x}+\frac{7}{3}a^{3}-\frac{5}{3}a^{2}-21a+25$
7.4-b1	7.4-b	$1$	$1$	4.4.18432.1	$4$	$[4, 0]$	7.4	$ 7 $	$ 7^{5} $	$15.47256$	$(-1/3a^3+1/3a^2+3a-3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	$ 1 $	$1$	$186.2904708$	1.372158908	$ \frac{1940359378}{50421} a^{3} - \frac{6297971513}{50421} a^{2} - \frac{994429675}{16807} a + \frac{3499312361}{16807} $	$ \bigl[\frac{1}{3} a^{2} + a - 1$ , $ \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + 3$ , $ \frac{1}{3} a^{2} - 1$ , $ \frac{8}{3} a^{3} - \frac{13}{3} a^{2} - 16 a + 12$ , $ \frac{1}{3} a^{3} + \frac{43}{3} a^{2} - 32 a - 50\bigr] $	${y}^2+\left(\frac{1}{3}a^{2}+a-1\right){x}{y}+\left(\frac{1}{3}a^{2}-1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-4a+3\right){x}^{2}+\left(\frac{8}{3}a^{3}-\frac{13}{3}a^{2}-16a+12\right){x}+\frac{1}{3}a^{3}+\frac{43}{3}a^{2}-32a-50$

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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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