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-b3
196.1-b
$6$
$18$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{12} \cdot 7^{6} \)
$1.20552$
$(2), (7)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3Cs.1.1
$1$
\( 2 \cdot 3^{2} \)
$1$
$3.925715946$
0.544398851
\( \frac{9938375}{21952} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
1764.2-h3
1764.2-h
$6$
$18$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1764.2
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \)
\( 2^{12} \cdot 3^{6} \cdot 7^{6} \)
$2.08802$
$(-a), (2), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3Cs
$1$
\( 2^{2} \cdot 3 \)
$1$
$3.032533911$
2.523220734
\( \frac{9938375}{21952} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 4 a + 13\) , \( 23 a + 17\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a+13\right){x}+23a+17$
1764.3-h3
1764.3-h
$6$
$18$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
1764.3
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \)
\( 2^{12} \cdot 3^{6} \cdot 7^{6} \)
$2.08802$
$(-a+1), (2), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3Cs
$1$
\( 2^{2} \cdot 3 \)
$1$
$3.032533911$
2.523220734
\( \frac{9938375}{21952} \)
\( \bigl[a\) , \( -1\) , \( 1\) , \( -5 a + 18\) , \( -23 a + 40\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-5a+18\right){x}-23a+40$
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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.