| 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-b4 |
1800.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{8} \) |
$1.16409$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.531575020$ |
1.531575020 |
\( \frac{868327204}{5625} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 50\) , \( -144 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+50{x}-144i$ |
| 16200.2-c4 |
16200.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16200.2 |
\( 2^{3} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 5^{8} \) |
$2.01626$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.510525006$ |
2.042100027 |
\( \frac{868327204}{5625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 450\) , \( 3888 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+450{x}+3888i$ |
| 18000.2-a4 |
18000.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.2 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{14} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.684941171$ |
1.369882343 |
\( \frac{868327204}{5625} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -200 i - 150\) , \( -1584 i - 288\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-200i-150\right){x}-1584i-288$ |
| 18000.3-b4 |
18000.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{14} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.684941171$ |
1.369882343 |
\( \frac{868327204}{5625} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 200 i - 150\) , \( 1584 i - 288\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(200i-150\right){x}+1584i-288$ |
| 45000.3-e4 |
45000.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
45000.3 |
\( 2^{3} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{20} \) |
$2.60299$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.800649340$ |
$0.306315004$ |
3.924014493 |
\( \frac{868327204}{5625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 1252\) , \( -16749 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1252\right){x}-16749i$ |
| 57600.2-a4 |
57600.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57600.2 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{8} \) |
$2.76869$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.871666361$ |
$0.765787510$ |
5.340089699 |
\( \frac{868327204}{5625} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 200\) , \( -1152 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+200{x}-1152i$ |
*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.
