| 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-a2 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$11.23555713$ |
1.634533048 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$ |
| 300.1-j2 |
300.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$2.168446869$ |
$5.367489134$ |
2.539863122 |
\( \frac{357911}{2160} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -8 a + 20\) , \( 46 a - 131\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-8a+20\right){x}+46a-131$ |
| 900.1-e2 |
900.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \) |
$2.24289$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.483552565$ |
1.956782763 |
\( \frac{357911}{2160} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -5 a + 13\) , \( -27 a + 74\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a+13\right){x}-27a+74$ |
| 900.1-f2 |
900.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \) |
$2.24289$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.483552565$ |
1.956782763 |
\( \frac{357911}{2160} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 4 a + 9\) , \( 27 a + 47\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(4a+9\right){x}+27a+47$ |
*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.
