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
1396.1-a1
1396.1-a
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1396.1
\( 2^{2} \cdot 349 \)
\( 2^{2} \cdot 349 \)
$0.94606$
$(-20a+3), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$0.053939470$
$7.436372097$
0.926333044
\( \frac{281690}{349} a + \frac{1060217}{698} \)
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -a - 1\) , \( -a\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}-a$
1396.1-b1
1396.1-b
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1396.1
\( 2^{2} \cdot 349 \)
\( 2^{14} \cdot 349 \)
$0.94606$
$(-20a+3), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 7 \)
$0.016615231$
$3.688579680$
0.990747484
\( -\frac{21811087}{44672} a - \frac{45732957}{44672} \)
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -2 a - 1\) , \( -6 a + 1\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-1\right){x}-6a+1$
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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.