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
196.1-b6
196.1-b
$6$
$18$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{18} \cdot 7^{4} \)
$1.20552$
$(2), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \cdot 3^{2} \)
$1$
$0.436190660$
0.544398851
\( \frac{2251439055699625}{25088} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
1764.2-h6
1764.2-h
$6$
$18$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1764.2
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \)
\( 2^{18} \cdot 3^{6} \cdot 7^{4} \)
$2.08802$
$(-a), (2), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$9$
\( 2^{2} \)
$1$
$1.010844637$
2.523220734
\( \frac{2251439055699625}{25088} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -2731 a - 8192\) , \( 220583 a + 165437\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2731a-8192\right){x}+220583a+165437$
1764.3-h6
1764.3-h
$6$
$18$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1764.3
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \)
\( 2^{18} \cdot 3^{6} \cdot 7^{4} \)
$2.08802$
$(-a+1), (2), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$9$
\( 2^{2} \)
$1$
$1.010844637$
2.523220734
\( \frac{2251439055699625}{25088} \)
\( \bigl[a\) , \( -1\) , \( 1\) , \( 2730 a - 10922\) , \( -220583 a + 386020\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(2730a-10922\right){x}-220583a+386020$
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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.