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-a1
196.1-a
$6$
$18$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{36} \cdot 7^{2} \)
$1.10892$
$(2), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \cdot 3^{2} \)
$0.210429933$
$0.875417135$
0.999766831
\( -\frac{548347731625}{1835008} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$
196.1-a2
196.1-a
$6$
$18$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{4} \cdot 7^{2} \)
$1.10892$
$(2), (7)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \)
$1.893869405$
$7.878754216$
0.999766831
\( -\frac{15625}{28} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}$
196.1-a3
196.1-a
$6$
$18$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{12} \cdot 7^{6} \)
$1.10892$
$(2), (7)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3Cs.1.1
$1$
\( 2 \cdot 3^{2} \)
$0.631289801$
$2.626251405$
0.999766831
\( \frac{9938375}{21952} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
196.1-a4
196.1-a
$6$
$18$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{6} \cdot 7^{12} \)
$1.10892$
$(2), (7)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3Cs.1.1
$1$
\( 2 \cdot 3^{2} \)
$1.262579603$
$1.313125702$
0.999766831
\( \frac{4956477625}{941192} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$
196.1-a5
196.1-a
$6$
$18$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{2} \cdot 7^{4} \)
$1.10892$
$(2), (7)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \)
$3.787738810$
$3.939377108$
0.999766831
\( \frac{128787625}{98} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$
196.1-a6
196.1-a
$6$
$18$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{18} \cdot 7^{4} \)
$1.10892$
$(2), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \cdot 3^{2} \)
$0.420859867$
$0.437708567$
0.999766831
\( \frac{2251439055699625}{25088} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
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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.