| 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 |
| 1800.2-a2 |
1800.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{4} \) |
$1.16409$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.111452642$ |
$3.481586885$ |
1.552128233 |
\( \frac{470596}{225} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 4\) , \( -2 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+4{x}-2i$ |
| 16200.2-d2 |
16200.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16200.2 |
\( 2^{3} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 5^{4} \) |
$2.01626$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.748768142$ |
$1.160528961$ |
3.475868462 |
\( \frac{470596}{225} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 36\) , \( -18 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+36\right){x}-18i$ |
| 18000.2-g2 |
18000.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.2 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{10} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.561055090$ |
$1.557012989$ |
3.494280255 |
\( \frac{470596}{225} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -16 i - 12\) , \( -22 i - 4\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-16i-12\right){x}-22i-4$ |
| 18000.3-f2 |
18000.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{10} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.561055090$ |
$1.557012989$ |
3.494280255 |
\( \frac{470596}{225} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 16 i - 12\) , \( 22 i - 4\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(16i-12\right){x}+22i-4$ |
| 45000.3-o2 |
45000.3-o |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
45000.3 |
\( 2^{3} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{16} \) |
$2.60299$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.696317377$ |
2.785269508 |
\( \frac{470596}{225} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 102\) , \( 148 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i+102\right){x}+148i$ |
| 57600.2-bb2 |
57600.2-bb |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57600.2 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{4} \) |
$2.76869$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.740793442$ |
3.481586885 |
\( \frac{470596}{225} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 16\) , \( 16 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+16{x}+16i$ |
*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.
