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
11.1-a1
11.1-a
$4$
$4$
4.4.18625.1
$4$
$[4, 0]$
11.1
\( 11 \)
\( 11 \)
$16.45738$
$(1/6a^3-7/3a-11/6)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1.201154978$
$351.7147644$
3.095576241
\( -\frac{9077631989}{66} a^{3} - \frac{2221371056}{11} a^{2} + \frac{47094365738}{33} a + \frac{150783937729}{66} \)
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( a^{2} - 7\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( \frac{59}{3} a^{3} + 85 a^{2} - \frac{544}{3} a - \frac{2368}{3}\) , \( \frac{917}{3} a^{3} + 78 a^{2} - \frac{8992}{3} a - \frac{3031}{3}\bigr] \)
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{35}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(\frac{59}{3}a^{3}+85a^{2}-\frac{544}{3}a-\frac{2368}{3}\right){x}+\frac{917}{3}a^{3}+78a^{2}-\frac{8992}{3}a-\frac{3031}{3}$
11.1-b4
11.1-b
$4$
$4$
4.4.18625.1
$4$
$[4, 0]$
11.1
\( 11 \)
\( 11 \)
$16.45738$
$(1/6a^3-7/3a-11/6)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$0.652535562$
$756.7063129$
3.618123622
\( -\frac{9077631989}{66} a^{3} - \frac{2221371056}{11} a^{2} + \frac{47094365738}{33} a + \frac{150783937729}{66} \)
\( \bigl[a\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{7}{6}\) , \( -2 a^{3} + 8 a^{2} + 19 a - 63\) , \( -\frac{22}{3} a^{3} + 22 a^{2} + \frac{218}{3} a - \frac{607}{3}\bigr] \)
${y}^2+a{x}{y}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{7}{6}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){x}^{2}+\left(-2a^{3}+8a^{2}+19a-63\right){x}-\frac{22}{3}a^{3}+22a^{2}+\frac{218}{3}a-\frac{607}{3}$
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Pari/GP
SageMath
Magma
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CSV
*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.