| 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-a1 |
4800.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4800.1 |
\( 2^{6} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{16} \) |
$1.28828$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.382893755$ |
1.768510500 |
\( -\frac{27995042}{1171875} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -2400\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-80{x}-2400$ |
| 4800.1-a2 |
4800.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4800.1 |
\( 2^{6} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{16} \cdot 5^{2} \) |
$1.28828$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.765787510$ |
1.768510500 |
\( \frac{54607676}{32805} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 80\) , \( 80\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+80{x}+80$ |
| 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 |
\( \frac{3631696}{2025} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -20\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-20{x}$ |
| 4800.1-a4 |
4800.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4800.1 |
\( 2^{6} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{8} \) |
$1.28828$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.765787510$ |
1.768510500 |
\( \frac{868327204}{5625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -200\) , \( -1152\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-200{x}-1152$ |
| 4800.1-a5 |
4800.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4800.1 |
\( 2^{6} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$1.28828$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.063150040$ |
1.768510500 |
\( \frac{24918016}{45} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-15{x}+18$ |
| 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 |
\( \frac{1770025017602}{75} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3200\) , \( -70752\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3200{x}-70752$ |
| 4800.1-b1 |
4800.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4800.1 |
\( 2^{6} \cdot 3 \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 5^{2} \) |
$1.28828$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.481586885$ |
2.010095125 |
\( \frac{21296}{15} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 4 a - 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(4a-4\right){x}$ |
| 4800.1-b2 |
4800.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4800.1 |
\( 2^{6} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{4} \) |
$1.28828$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.740793442$ |
2.010095125 |
\( \frac{470596}{225} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -16 a + 16\) , \( -16\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-16a+16\right){x}-16$ |
| 4800.1-b3 |
4800.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4800.1 |
\( 2^{6} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{8} \) |
$1.28828$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.870396721$ |
2.010095125 |
\( \frac{136835858}{1875} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -136 a + 136\) , \( 560\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-136a+136\right){x}+560$ |
| 4800.1-b4 |
4800.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4800.1 |
\( 2^{6} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{2} \) |
$1.28828$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.870396721$ |
2.010095125 |
\( \frac{546718898}{405} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -216 a + 216\) , \( -1296\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-216a+216\right){x}-1296$ |
*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.
