| 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-a3 |
4800.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4800.1 |
\( 2^{6} \cdot 3 \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 5^{4} \) |
$1.28828$ |
$(-2a+1), (2), (5)$ |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.531575020$ |
1.768510500 |
\( \frac{3631696}{2025} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -20\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-20{x}$ |
| 19200.1-c3 |
19200.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.531575020$ |
1.768510500 |
\( \frac{3631696}{2025} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -20\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-20{x}$ |
| 57600.1-h3 |
57600.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{14} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$0.884255250$ |
1.021050013 |
\( \frac{3631696}{2025} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 62 a - 61\) , \( -61 a + 61\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(62a-61\right){x}-61a+61$ |
| 57600.1-i3 |
57600.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{14} \cdot 5^{4} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$0.884255250$ |
1.021050013 |
\( \frac{3631696}{2025} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -60 a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-60a{x}$ |
| 120000.1-c3 |
120000.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
120000.1 |
\( 2^{6} \cdot 3 \cdot 5^{4} \) |
\( 2^{16} \cdot 3^{8} \cdot 5^{16} \) |
$2.88068$ |
$(-2a+1), (2), (5)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.886796114$ |
$0.306315004$ |
5.338909986 |
\( \frac{3631696}{2025} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -508\) , \( 1012\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-508{x}+1012$ |
*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.
