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
56.1-b5
56.1-b
$6$
$8$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
56.1
\( 2^{3} \cdot 7 \)
\( 2^{10} \cdot 7^{2} \)
$1.82928$
$(-a+4), (-2a+7)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1.933057233$
$24.47471212$
3.161100443
\( \frac{1443468546}{7} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 8970 a - 33563\) , \( -881050 a + 3296587\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(8970a-33563\right){x}-881050a+3296587$
56.1-d5
56.1-d
$6$
$8$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
56.1
\( 2^{3} \cdot 7 \)
\( 2^{10} \cdot 7^{2} \)
$1.82928$
$(-a+4), (-2a+7)$
$2$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$8.090838387$
$2.636293528$
2.850317744
\( \frac{1443468546}{7} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -75\) , \( -361\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-75{x}-361$
112.1-b5
112.1-b
$6$
$8$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
112.1
\( 2^{4} \cdot 7 \)
\( 2^{10} \cdot 7^{2} \)
$2.17539$
$(-a+4), (-2a+7)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$16$
\( 2^{3} \)
$1$
$2.636293528$
2.818316330
\( \frac{1443468546}{7} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 8970 a - 33556\) , \( 907960 a - 3397272\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(8970a-33556\right){x}+907960a-3397272$
112.1-e5
112.1-e
$6$
$8$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
112.1
\( 2^{4} \cdot 7 \)
\( 2^{10} \cdot 7^{2} \)
$2.17539$
$(-a+4), (-2a+7)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$2.786954333$
$24.47471212$
2.278732990
\( \frac{1443468546}{7} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -68\) , \( 140\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-68{x}+140$
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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.