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-a2
28.1-a
$6$
$18$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{4} \cdot 7^{2} \)
$1.80374$
$(a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1.893869405$
$7.027708105$
3.033530572
\( -\frac{15625}{28} \)
\( \bigl[a\) , \( 0\) , \( 1\) , \( 5 a - 15\) , \( 30 a - 139\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(5a-15\right){x}+30a-139$
28.1-b2
28.1-b
$6$
$18$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{4} \cdot 7^{2} \)
$1.80374$
$(a+3), (2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$4$
\( 2^{2} \)
$1$
$35.33144352$
1.789507409
\( -\frac{15625}{28} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}$
196.1-a2
196.1-a
$6$
$18$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{4} \cdot 7^{8} \)
$2.93392$
$(a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$4$
\( 2^{2} \)
$1$
$5.955778371$
2.714895745
\( -\frac{15625}{28} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 2 a - 22\) , \( -11 a + 48\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-22\right){x}-11a+48$
196.1-b2
196.1-b
$6$
$18$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{4} \cdot 7^{8} \)
$2.93392$
$(a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$4$
\( 2^{2} \)
$1$
$5.955778371$
2.714895745
\( -\frac{15625}{28} \)
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -4 a - 19\) , \( 10 a + 37\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-4a-19\right){x}+10a+37$
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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.