| 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-a3 |
1800.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{8} \) |
$1.16409$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.222905284$ |
$1.740793442$ |
1.552128233 |
\( \frac{136835858}{1875} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 34\) , \( 70 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+34{x}+70i$ |
| 16200.2-d3 |
16200.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16200.2 |
\( 2^{3} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{14} \cdot 5^{8} \) |
$2.01626$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.374384071$ |
$0.580264480$ |
3.475868462 |
\( \frac{136835858}{1875} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 306\) , \( 2196 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+306\right){x}+2196i$ |
| 18000.2-g3 |
18000.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.2 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{14} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.280527545$ |
$0.778506494$ |
3.494280255 |
\( \frac{136835858}{1875} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -136 i - 102\) , \( 770 i + 140\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-136i-102\right){x}+770i+140$ |
| 18000.3-f3 |
18000.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
18000.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{14} \) |
$2.07008$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.280527545$ |
$0.778506494$ |
3.494280255 |
\( \frac{136835858}{1875} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 136 i - 102\) , \( -770 i + 140\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(136i-102\right){x}-770i+140$ |
| 45000.3-o3 |
45000.3-o |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
45000.3 |
\( 2^{3} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{10} \cdot 3^{2} \cdot 5^{20} \) |
$2.60299$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.348158688$ |
2.785269508 |
\( \frac{136835858}{1875} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 852\) , \( -9602 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i+852\right){x}-9602i$ |
| 57600.2-bb3 |
57600.2-bb |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57600.2 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{8} \) |
$2.76869$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.870396721$ |
3.481586885 |
\( \frac{136835858}{1875} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 136\) , \( -560 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+136{x}-560i$ |
*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.
