| 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-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 |
\( \frac{136835858}{1875} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -136 a + 136\) , \( 560\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-136a+136\right){x}+560$ |
| 19200.1-a3 |
19200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{8} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.333808752$ |
$0.870396721$ |
2.683949384 |
\( \frac{136835858}{1875} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -136\) , \( -560\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-136{x}-560$ |
| 57600.1-c3 |
57600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{8} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.502523781$ |
2.321057923 |
\( \frac{136835858}{1875} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -408 a\) , \( 3360 a - 1680\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-408a{x}+3360a-1680$ |
| 57600.1-r3 |
57600.1-r |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{8} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.502523781$ |
2.321057923 |
\( \frac{136835858}{1875} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 410 a - 409\) , \( -3769 a + 2089\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(410a-409\right){x}-3769a+2089$ |
| 120000.1-a3 |
120000.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
120000.1 |
\( 2^{6} \cdot 3 \cdot 5^{4} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{20} \) |
$2.88068$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.174079344$ |
1.608076100 |
\( \frac{136835858}{1875} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3408\) , \( 76812\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3408{x}+76812$ |
*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.
