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-a2
11.1-a
$4$
$4$
4.4.18625.1
$4$
$[4, 0]$
11.1
\( 11 \)
\( 11^{4} \)
$16.45738$
$(1/6a^3-7/3a-11/6)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.300288744$
$351.7147644$
3.095576241
\( -\frac{1060007393}{87846} a^{3} + \frac{746018190}{14641} a^{2} + \frac{411434192}{43923} a - \frac{13361296451}{87846} \)
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{6}\) , \( a + 1\) , \( \frac{47}{6} a^{3} + 17 a^{2} - \frac{155}{3} a - \frac{547}{6}\) , \( \frac{611}{3} a^{3} + 320 a^{2} - \frac{6034}{3} a - \frac{9808}{3}\bigr] \)
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{35}{6}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{6}\right){x}^{2}+\left(\frac{47}{6}a^{3}+17a^{2}-\frac{155}{3}a-\frac{547}{6}\right){x}+\frac{611}{3}a^{3}+320a^{2}-\frac{6034}{3}a-\frac{9808}{3}$
11.1-b3
11.1-b
$4$
$4$
4.4.18625.1
$4$
$[4, 0]$
11.1
\( 11 \)
\( 11^{4} \)
$16.45738$
$(1/6a^3-7/3a-11/6)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.652535562$
$756.7063129$
3.618123622
\( -\frac{1060007393}{87846} a^{3} + \frac{746018190}{14641} a^{2} + \frac{411434192}{43923} a - \frac{13361296451}{87846} \)
\( \bigl[a\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{4}{3} a - \frac{49}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{35}{6}\) , \( \frac{1}{2} a^{3} - 5 a + \frac{11}{2}\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{7}{3} a - \frac{55}{6}\bigr] \)
${y}^2+a{x}{y}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{35}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+a^{2}+\frac{4}{3}a-\frac{49}{6}\right){x}^{2}+\left(\frac{1}{2}a^{3}-5a+\frac{11}{2}\right){x}-\frac{1}{6}a^{3}+a^{2}+\frac{7}{3}a-\frac{55}{6}$
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Pari/GP
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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.