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
49.1-a1
49.1-a
$2$
$2$
4.4.2624.1
$4$
$[4, 0]$
49.1
\( 7^{2} \)
\( 7^{6} \)
$7.44552$
$(-a^3+3a^2+a-3), (-a^2+a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$0.007510917$
$1331.429247$
1.561777484
\( -\frac{13298986880}{2401} a^{3} + \frac{42933262144}{2401} a^{2} - \frac{1833696512}{343} a - \frac{10829641152}{2401} \)
\( \bigl[a^{2} - a - 1\) , \( a^{3} - 2 a^{2} - 2 a\) , \( a + 1\) , \( -2 a^{2} + 5 a\) , \( -2 a^{3} + 7 a^{2} - 4 a - 1\bigr] \)
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a\right){x}^{2}+\left(-2a^{2}+5a\right){x}-2a^{3}+7a^{2}-4a-1$
343.3-c1
343.3-c
$2$
$2$
4.4.2624.1
$4$
$[4, 0]$
343.3
\( 7^{3} \)
\( 7^{12} \)
$9.49581$
$(-a^3+3a^2+a-3), (-a^2+a+2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.206533754$
$109.8637801$
3.543673082
\( -\frac{13298986880}{2401} a^{3} + \frac{42933262144}{2401} a^{2} - \frac{1833696512}{343} a - \frac{10829641152}{2401} \)
\( \bigl[a^{2} - a - 1\) , \( a^{3} - a^{2} - 3 a - 1\) , \( a^{2} - 2 a\) , \( 3 a^{3} - 10 a^{2} + 7 a + 4\) , \( -2 a^{3} + 12 a^{2} - 17 a - 8\bigr] \)
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a-1\right){x}^{2}+\left(3a^{3}-10a^{2}+7a+4\right){x}-2a^{3}+12a^{2}-17a-8$
343.4-a2
343.4-a
$2$
$2$
4.4.2624.1
$4$
$[4, 0]$
343.4
\( 7^{3} \)
\( 7^{12} \)
$9.49581$
$(-a^3+3a^2+a-3), (-a^2+a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$63.72703149$
2.488122560
\( -\frac{13298986880}{2401} a^{3} + \frac{42933262144}{2401} a^{2} - \frac{1833696512}{343} a - \frac{10829641152}{2401} \)
\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - a + 2\) , \( a + 1\) , \( -6 a^{3} + 13 a^{2} + 16 a - 11\) , \( -31 a^{3} + 55 a^{2} + 94 a - 25\bigr] \)
${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+2\right){x}^{2}+\left(-6a^{3}+13a^{2}+16a-11\right){x}-31a^{3}+55a^{2}+94a-25$
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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.