| 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 |
| 64.1-a2 |
64.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
64.1 |
\( 2^{6} \) |
\( - 2^{16} \) |
$0.56516$ |
$(2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$19.17933979$ |
0.536078844 |
\( -548896 a + 889584 \) |
\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( 4 \phi\) , \( 4\bigr] \) |
${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+4\phi{x}+4$ |
| 256.1-a2 |
256.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{16} \) |
$0.79925$ |
$(2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$17.18960052$ |
0.960927881 |
\( -548896 a + 889584 \) |
\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( 6 \phi - 5\) , \( -3 \phi + 7\bigr] \) |
${y}^2={x}^{3}+\left(\phi+1\right){x}^{2}+\left(6\phi-5\right){x}-3\phi+7$ |
| 256.1-b2 |
256.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{16} \) |
$0.79925$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8.594800260$ |
0.960927881 |
\( -548896 a + 889584 \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( 6 \phi - 5\) , \( 3 \phi - 7\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(6\phi-5\right){x}+3\phi-7$ |
| 256.1-c2 |
256.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{16} \) |
$0.79925$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$7.703142267$ |
0.861237487 |
\( -548896 a + 889584 \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( 4 \phi\) , \( -4\bigr] \) |
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+4\phi{x}-4$ |
| 1600.1-f2 |
1600.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{16} \cdot 5^{6} \) |
$1.26373$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.586422053$ |
$3.444949950$ |
1.806917001 |
\( -548896 a + 889584 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 25 \phi - 28\) , \( 55 \phi - 92\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(25\phi-28\right){x}+55\phi-92$ |
| 4096.1-a2 |
4096.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{28} \) |
$1.59850$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.851571133$ |
1.722474975 |
\( -548896 a + 889584 \) |
\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( 17 \phi - 2\) , \( -2 \phi - 13\bigr] \) |
${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(17\phi-2\right){x}-2\phi-13$ |
| 4096.1-m2 |
4096.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{28} \) |
$1.59850$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.289812848$ |
$8.594800260$ |
2.227913972 |
\( -548896 a + 889584 \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( 21 \phi - 22\) , \( -44 \phi + 57\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(21\phi-22\right){x}-44\phi+57$ |
| 4096.1-x2 |
4096.1-x |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{28} \) |
$1.59850$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.159251393$ |
$4.297400130$ |
2.227913972 |
\( -548896 a + 889584 \) |
\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( 21 \phi - 22\) , \( 44 \phi - 57\bigr] \) |
${y}^2={x}^{3}+\left(\phi+1\right){x}^{2}+\left(21\phi-22\right){x}+44\phi-57$ |
| 4096.1-y2 |
4096.1-y |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{28} \) |
$1.59850$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$9.589669897$ |
2.144315377 |
\( -548896 a + 889584 \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( 17 \phi - 2\) , \( 2 \phi + 13\bigr] \) |
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(17\phi-2\right){x}+2\phi+13$ |
*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.
