| 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 |
| 2268.1-a1 |
2268.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2268.1 |
\( 2^{2} \cdot 3^{4} \cdot 7 \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{3} \) |
$1.06810$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$3.432415362$ |
1.321137289 |
\( \frac{1192725}{1372} a - \frac{2098143}{2744} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a\) , \( -3 a + 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3a{x}-3a+3$ |
| 2268.1-a2 |
2268.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2268.1 |
\( 2^{2} \cdot 3^{4} \cdot 7 \) |
\( 2^{2} \cdot 3^{10} \cdot 7^{9} \) |
$1.06810$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$1.144138454$ |
1.321137289 |
\( -\frac{50481832659}{80707214} a + \frac{60742004649}{80707214} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 27 a\) , \( 63 a - 81\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+27a{x}+63a-81$ |
| 2268.1-a3 |
2268.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2268.1 |
\( 2^{2} \cdot 3^{4} \cdot 7 \) |
\( 2^{18} \cdot 3^{10} \cdot 7 \) |
$1.06810$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$1.144138454$ |
1.321137289 |
\( \frac{457190997}{1792} a + \frac{610173645}{3584} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a + 105\) , \( -465 a + 192\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-3a+105\right){x}-465a+192$ |
| 2268.1-a4 |
2268.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2268.1 |
\( 2^{2} \cdot 3^{4} \cdot 7 \) |
\( 2^{2} \cdot 3^{6} \cdot 7 \) |
$1.06810$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$3.432415362$ |
1.321137289 |
\( \frac{43477641}{14} a - \frac{4669083}{7} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3 a - 17\) , \( 6 a - 22\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3a-17\right){x}+6a-22$ |
| 2268.1-a5 |
2268.1-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2268.1 |
\( 2^{2} \cdot 3^{4} \cdot 7 \) |
\( 2^{2} \cdot 3^{10} \cdot 7 \) |
$1.06810$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$9$ |
\( 1 \) |
$1$ |
$1.144138454$ |
1.321137289 |
\( \frac{13989364197}{7} a + \frac{2196790845}{14} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -303 a + 30\) , \( -2091 a + 1329\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-303a+30\right){x}-2091a+1329$ |
*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.
