| 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 |
| 300.1-a4 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.808889283$ |
1.634533048 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$ |
| 300.1-j4 |
300.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$2.168446869$ |
$5.367489134$ |
2.539863122 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 342 a - 960\) , \( -4308 a + 12021\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(342a-960\right){x}-4308a+12021$ |
| 900.1-e4 |
900.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{30} \cdot 5^{2} \) |
$2.24289$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.241776282$ |
1.956782763 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 205 a - 617\) , \( 2325 a - 6394\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(205a-617\right){x}+2325a-6394$ |
| 900.1-f4 |
900.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{30} \cdot 5^{2} \) |
$2.24289$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.241776282$ |
1.956782763 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -206 a - 411\) , \( -2325 a - 4069\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-206a-411\right){x}-2325a-4069$ |
*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.
