| 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-a6 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$1.248395236$ |
1.634533048 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$ |
| 300.1-j6 |
300.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$1.70423$ |
$(-a+2), (-a), (-a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{3} \) |
$0.361407811$ |
$5.367489134$ |
2.539863122 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 1667 a - 4670\) , \( -55159 a + 153969\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1667a-4670\right){x}-55159a+153969$ |
| 900.1-e6 |
900.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 5^{12} \) |
$2.24289$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$1.494517521$ |
1.956782763 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 1000 a - 3002\) , \( 28413 a - 78136\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1000a-3002\right){x}+28413a-78136$ |
| 900.1-f6 |
900.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
900.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 5^{12} \) |
$2.24289$ |
$(-a+2), (-a), (-a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$1.494517521$ |
1.956782763 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -1001 a - 2001\) , \( -28413 a - 49723\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-1001a-2001\right){x}-28413a-49723$ |
*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.
