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
338.1-d2
338.1-d
$2$
$7$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
338.1
\( 2 \cdot 13^{2} \)
\( 2^{14} \cdot 13^{2} \)
$1.87704$
$(-a+2), (13)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$7$
7B.1.1
$1$
\( 2 \cdot 7 \)
$1$
$18.89430030$
1.101937971
\( -\frac{2146689}{1664} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3{x}+3$
338.1-e2
338.1-e
$2$
$7$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
338.1
\( 2 \cdot 13^{2} \)
\( 2^{14} \cdot 13^{2} \)
$1.87704$
$(-a+2), (13)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$7$
7B.6.1
$1$
\( 2 \)
$0.625224564$
$3.254622356$
1.661464272
\( -\frac{2146689}{1664} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -53 a - 127\) , \( -592 a - 1451\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-53a-127\right){x}-592a-1451$
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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.