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
28.1-a4
28.1-a
$6$
$18$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{6} \cdot 7^{12} \)
$1.80374$
$(a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3Cs
$1$
\( 2 \cdot 3 \)
$1.262579603$
$7.027708105$
3.033530572
\( \frac{4956477625}{941192} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -321 a - 1235\) , \( 4940 a + 19211\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-321a-1235\right){x}+4940a+19211$
28.1-b4
28.1-b
$6$
$18$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{6} \cdot 7^{12} \)
$1.80374$
$(a+3), (2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3Cs.1.1
$4$
\( 2^{2} \cdot 3^{2} \)
$1$
$3.925715946$
1.789507409
\( \frac{4956477625}{941192} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$
196.1-a4
196.1-a
$6$
$18$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{6} \cdot 7^{18} \)
$2.93392$
$(a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3Cs
$4$
\( 2^{2} \cdot 3 \)
$1$
$1.985259457$
2.714895745
\( \frac{4956477625}{941192} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 247 a - 1247\) , \( 4154 a - 20287\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(247a-1247\right){x}+4154a-20287$
196.1-b4
196.1-b
$6$
$18$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{6} \cdot 7^{18} \)
$2.93392$
$(a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3Cs
$4$
\( 2^{2} \cdot 3 \)
$1$
$1.985259457$
2.714895745
\( \frac{4956477625}{941192} \)
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -249 a - 999\) , \( -4155 a - 16133\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-249a-999\right){x}-4155a-16133$
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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.