| 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 |
| 48.1-a1 |
48.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{10} \cdot 3^{16} \) |
$1.15227$ |
$(-a+2), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$2.325279868$ |
1.898583062 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 6\) , \( -18\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+6{x}-18$ |
| 48.1-a2 |
48.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.15227$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.60223895$ |
1.898583062 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -14 a + 35\) , \( -67 a + 164\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-14a+35\right){x}-67a+164$ |
| 48.1-a3 |
48.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$1.15227$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$37.20447790$ |
1.898583062 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+{x}$ |
| 48.1-a4 |
48.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$1.15227$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$9.301119475$ |
1.898583062 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -4\) , \( -10\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-4{x}-10$ |
| 48.1-a5 |
48.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.15227$ |
$(-a+2), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$37.20447790$ |
1.898583062 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -14\) , \( 12\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-14{x}+12$ |
| 48.1-a6 |
48.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$1.15227$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.325279868$ |
1.898583062 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -94\) , \( -442\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-94{x}-442$ |
| 48.1-b1 |
48.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{10} \cdot 3^{16} \) |
$1.15227$ |
$(-a+2), (a+3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$5.683508517$ |
1.160141318 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -80 a + 193\) , \( -4455 a + 10911\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-80a+193\right){x}-4455a+10911$ |
| 48.1-b2 |
48.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.15227$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11.36701703$ |
1.160141318 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+{x}$ |
| 48.1-b3 |
48.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$1.15227$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$22.73403407$ |
1.160141318 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 20 a - 52\) , \( 99 a - 244\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(20a-52\right){x}+99a-244$ |
| 48.1-b4 |
48.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$1.15227$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$22.73403407$ |
1.160141318 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 120 a - 297\) , \( -891 a + 2181\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(120a-297\right){x}-891a+2181$ |
| 48.1-b5 |
48.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.15227$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.683508517$ |
1.160141318 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -320 a - 787\) , \( -5445 a - 13339\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-320a-787\right){x}-5445a-13339$ |
| 48.1-b6 |
48.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$1.15227$ |
$(-a+2), (a+3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$22.73403407$ |
1.160141318 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -1920 a - 4707\) , \( 68607 a + 168051\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1920a-4707\right){x}+68607a+168051$ |
*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.
