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
36.1-a1
36.1-a
$4$
$6$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{6} \)
$1.07231$
$(-a+2), (a+3)$
0
$\Z/2\Z$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \)
$1$
$5.898343969$
1.203994421
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 198 a - 485\bigr] \)
${y}^2={x}^{3}+198a-485$
36.1-a2
36.1-a
$4$
$6$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{6} \)
$1.07231$
$(-a+2), (a+3)$
0
$\Z/6\Z$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3 \)
$1$
$17.69503190$
1.203994421
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \)
${y}^2={x}^{3}+1$
36.1-a3
36.1-a
$4$
$6$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{6} \)
$1.07231$
$(-a+2), (a+3)$
0
$\Z/2\Z$
$\textsf{potential}$
$-12$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3B.1.2
$1$
\( 2 \)
$1$
$11.79668793$
1.203994421
\( 54000 \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -6\) , \( -6\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-6{x}-6$
36.1-a4
36.1-a
$4$
$6$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
36.1
\( 2^{2} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{6} \)
$1.07231$
$(-a+2), (a+3)$
0
$\Z/6\Z$
$\textsf{potential}$
$-12$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$35.39006381$
1.203994421
\( 54000 \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( -75 a - 183\) , \( 507 a + 1242\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-75a-183\right){x}+507a+1242$
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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.