| 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 |
| 4800.1-a6 |
4800.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4800.1 |
\( 2^{6} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{4} \) |
$1.28828$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.382893755$ |
1.768510500 |
\( \frac{1770025017602}{75} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3200\) , \( -70752\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3200{x}-70752$ |
| 19200.1-c6 |
19200.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.382893755$ |
1.768510500 |
\( \frac{1770025017602}{75} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3200\) , \( 70752\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3200{x}+70752$ |
| 57600.1-h6 |
57600.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.221063812$ |
1.021050013 |
\( \frac{1770025017602}{75} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 9602 a - 9601\) , \( 414911 a - 202655\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(9602a-9601\right){x}+414911a-202655$ |
| 57600.1-i6 |
57600.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.221063812$ |
1.021050013 |
\( \frac{1770025017602}{75} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -9600 a\) , \( -424512 a + 212256\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-9600a{x}-424512a+212256$ |
| 120000.1-c6 |
120000.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
120000.1 |
\( 2^{6} \cdot 3 \cdot 5^{4} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{16} \) |
$2.88068$ |
$(-2a+1), (2), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$7.547184459$ |
$0.076578751$ |
5.338909986 |
\( \frac{1770025017602}{75} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -80008\) , \( -8683988\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-80008{x}-8683988$ |
*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.
