| 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 |
| 1280.1-a1 |
1280.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{22} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.498444490$ |
1.340249496 |
\( -\frac{1565563717889316}{5} a + \frac{2533135307076378}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 173 \phi - 547\) , \( 3764 \phi - 4110\bigr] \) |
${y}^2={x}^{3}+\left(173\phi-547\right){x}+3764\phi-4110$ |
| 1280.1-a2 |
1280.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{16} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$11.98755592$ |
1.340249496 |
\( -\frac{237035808}{5} a + \frac{383532624}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 \phi - 7\) , \( -16 \phi + 6\bigr] \) |
${y}^2={x}^{3}+\left(8\phi-7\right){x}-16\phi+6$ |
| 1280.1-a3 |
1280.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.996888981$ |
1.340249496 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13 \phi + 13\) , \( 68 \phi + 34\bigr] \) |
${y}^2={x}^{3}+\left(13\phi+13\right){x}+68\phi+34$ |
| 1280.1-a4 |
1280.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$11.98755592$ |
1.340249496 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7 \phi - 7\) , \( 12 \phi + 6\bigr] \) |
${y}^2={x}^{3}+\left(-7\phi-7\right){x}+12\phi+6$ |
| 1280.1-a5 |
1280.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$23.97511185$ |
1.340249496 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 \phi - 4\) , \( -2 \phi + 3\bigr] \) |
${y}^2={x}^{3}+\left(2\phi-4\right){x}-2\phi+3$ |
| 1280.1-a6 |
1280.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$5.993777963$ |
1.340249496 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -107 \phi - 107\) , \( 852 \phi + 426\bigr] \) |
${y}^2={x}^{3}+\left(-107\phi-107\right){x}+852\phi+426$ |
| 1280.1-a7 |
1280.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{16} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.993777963$ |
1.340249496 |
\( \frac{237035808}{5} a + \frac{146496816}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 \phi + 1\) , \( -16 \phi + 10\bigr] \) |
${y}^2={x}^{3}+\left(-8\phi+1\right){x}-16\phi+10$ |
| 1280.1-a8 |
1280.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{22} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.996888981$ |
1.340249496 |
\( \frac{1565563717889316}{5} a + \frac{967571589187062}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -173 \phi - 374\) , \( 3764 \phi + 346\bigr] \) |
${y}^2={x}^{3}+\left(-173\phi-374\right){x}+3764\phi+346$ |
| 1280.1-b1 |
1280.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{22} \cdot 5^{8} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$6.484547005$ |
1.449988790 |
\( -\frac{1613607658}{625} a + \frac{522073008}{125} \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( 60 \phi - 144\) , \( -276 \phi + 676\bigr] \) |
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(60\phi-144\right){x}-276\phi+676$ |
| 1280.1-b2 |
1280.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{8} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12.96909401$ |
1.449988790 |
\( \frac{2816}{5} a + \frac{1792}{5} \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+{x}$ |
| 1280.1-b3 |
1280.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{2} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$12.96909401$ |
1.449988790 |
\( -\frac{53328}{5} a + \frac{97888}{5} \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( -4\) , \( 4 \phi - 4\bigr] \) |
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}-4{x}+4\phi-4$ |
| 1280.1-b4 |
1280.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{20} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.242273502$ |
1.449988790 |
\( -\frac{1444495316}{5} a + \frac{2337509148}{5} \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( 20 \phi - 64\) , \( 108 \phi - 236\bigr] \) |
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(20\phi-64\right){x}+108\phi-236$ |
| 1280.1-b5 |
1280.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{20} \cdot 5^{4} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$12.96909401$ |
1.449988790 |
\( \frac{22755876}{25} a + \frac{14144708}{25} \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( -20 \phi - 24\) , \( 76 \phi + 52\bigr] \) |
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-20\phi-24\right){x}+76\phi+52$ |
| 1280.1-b6 |
1280.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{22} \cdot 5^{2} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.484547005$ |
1.449988790 |
\( \frac{9285883494578}{5} a + \frac{5738991619552}{5} \) |
\( \bigl[0\) , \( \phi\) , \( 0\) , \( -165 \phi + 136\) , \( -379 \phi + 1125\bigr] \) |
${y}^2={x}^{3}+\phi{x}^{2}+\left(-165\phi+136\right){x}-379\phi+1125$ |
| 1280.1-c1 |
1280.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{22} \cdot 5^{8} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.804604675$ |
1.254257341 |
\( -\frac{1613607658}{625} a + \frac{522073008}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -24 \phi - 84\) , \( -524 \phi - 124\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-24\phi-84\right){x}-524\phi-124$ |
| 1280.1-c2 |
1280.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{8} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$11.21841870$ |
1.254257341 |
\( \frac{2816}{5} a + \frac{1792}{5} \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( \phi + 1\) , \( -1\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(\phi+1\right){x}-1$ |
| 1280.1-c3 |
1280.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{2} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$11.21841870$ |
1.254257341 |
\( -\frac{53328}{5} a + \frac{97888}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 \phi - 4\) , \( -4 \phi - 4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-4\phi-4\right){x}-4\phi-4$ |
| 1280.1-c4 |
1280.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{20} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.609209351$ |
1.254257341 |
\( -\frac{1444495316}{5} a + \frac{2337509148}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -24 \phi - 44\) , \( 148 \phi + 20\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-24\phi-44\right){x}+148\phi+20$ |
| 1280.1-c5 |
1280.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{20} \cdot 5^{4} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$5.609209351$ |
1.254257341 |
\( \frac{22755876}{25} a + \frac{14144708}{25} \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( 6 \phi - 29\) , \( -33 \phi + 33\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(6\phi-29\right){x}-33\phi+33$ |
| 1280.1-c6 |
1280.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{22} \cdot 5^{2} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.402302337$ |
1.254257341 |
\( \frac{9285883494578}{5} a + \frac{5738991619552}{5} \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( -194 \phi - 29\) , \( -1113 \phi - 367\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-194\phi-29\right){x}-1113\phi-367$ |
| 1280.1-d1 |
1280.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{12} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.141031885$ |
1.436247851 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( 36 \phi - 72\) , \( -280 \phi + 420\bigr] \) |
${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(36\phi-72\right){x}-280\phi+420$ |
| 1280.1-d2 |
1280.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.423095656$ |
1.436247851 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( \phi\) , \( 0\) , \( 4 \phi + 4\) , \( 8 \phi + 4\bigr] \) |
${y}^2={x}^{3}+\phi{x}^{2}+\left(4\phi+4\right){x}+8\phi+4$ |
| 1280.1-d3 |
1280.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{3} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$8.564127542$ |
1.436247851 |
\( -\frac{170403887082176}{25} a + \frac{275719281184688}{25} \) |
\( \bigl[0\) , \( \phi\) , \( 0\) , \( 59 \phi - 216\) , \( -887 \phi + 1049\bigr] \) |
${y}^2={x}^{3}+\phi{x}^{2}+\left(59\phi-216\right){x}-887\phi+1049$ |
| 1280.1-d4 |
1280.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1$ |
$25.69238262$ |
1.436247851 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( \phi\) , \( 0\) , \( -\phi - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\phi{x}^{2}+\left(-\phi-1\right){x}$ |
| 1280.1-d5 |
1280.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$6.423095656$ |
1.436247851 |
\( -\frac{13352896}{5} a + \frac{21733168}{5} \) |
\( \bigl[0\) , \( \phi\) , \( 0\) , \( -6 \phi - 11\) , \( -19 \phi - 18\bigr] \) |
${y}^2={x}^{3}+\phi{x}^{2}+\left(-6\phi-11\right){x}-19\phi-18$ |
| 1280.1-d6 |
1280.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$8.564127542$ |
1.436247851 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( 41 \phi - 82\) , \( -232 \phi + 348\bigr] \) |
${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(41\phi-82\right){x}-232\phi+348$ |
| 1280.1-d7 |
1280.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$25.69238262$ |
1.436247851 |
\( \frac{13352896}{5} a + \frac{8380272}{5} \) |
\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( 6 \phi - 17\) , \( -19 \phi + 37\bigr] \) |
${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(6\phi-17\right){x}-19\phi+37$ |
| 1280.1-d8 |
1280.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{3} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.141031885$ |
1.436247851 |
\( \frac{170403887082176}{25} a + \frac{105315394102512}{25} \) |
\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( -59 \phi - 157\) , \( -887 \phi - 162\bigr] \) |
${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-59\phi-157\right){x}-887\phi-162$ |
| 1280.1-e1 |
1280.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{8} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.347404686$ |
$20.93652055$ |
1.626391824 |
\( -\frac{2816}{5} a + \frac{4608}{5} \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( \phi + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(\phi+1\right){x}$ |
| 1280.1-e2 |
1280.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{22} \cdot 5^{2} \) |
$1.19516$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.173702343$ |
$5.234130138$ |
1.626391824 |
\( -\frac{9285883494578}{5} a + 3004975022826 \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( 196 \phi - 224\) , \( -1308 \phi + 1704\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(196\phi-224\right){x}-1308\phi+1704$ |
| 1280.1-e3 |
1280.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{20} \cdot 5^{4} \) |
$1.19516$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.347404686$ |
$10.46826027$ |
1.626391824 |
\( -\frac{22755876}{25} a + \frac{36900584}{25} \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( -4 \phi - 24\) , \( -28 \phi + 24\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-4\phi-24\right){x}-28\phi+24$ |
| 1280.1-e4 |
1280.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{2} \) |
$1.19516$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.173702343$ |
$20.93652055$ |
1.626391824 |
\( \frac{53328}{5} a + 8912 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 \phi - 8\) , \( -4 \phi + 8\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(4\phi-8\right){x}-4\phi+8$ |
| 1280.1-e5 |
1280.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{22} \cdot 5^{8} \) |
$1.19516$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.694809372$ |
$2.617065069$ |
1.626391824 |
\( \frac{1613607658}{625} a + \frac{996757382}{625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 24 \phi - 108\) , \( -524 \phi + 648\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(24\phi-108\right){x}-524\phi+648$ |
| 1280.1-e6 |
1280.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{20} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.347404686$ |
$10.46826027$ |
1.626391824 |
\( \frac{1444495316}{5} a + \frac{893013832}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 24 \phi - 68\) , \( 148 \phi - 168\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(24\phi-68\right){x}+148\phi-168$ |
| 1280.1-f1 |
1280.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{12} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$5.171827352$ |
1.156455752 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -36\) , \( 140\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-36{x}+140$ |
| 1280.1-f2 |
1280.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$5.171827352$ |
1.156455752 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4\) , \( -4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+4{x}-4$ |
| 1280.1-f3 |
1280.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{3} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$10.34365470$ |
1.156455752 |
\( -\frac{170403887082176}{25} a + \frac{275719281184688}{25} \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( -98 \phi - 157\) , \( 563 \phi + 725\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-98\phi-157\right){x}+563\phi+725$ |
| 1280.1-f4 |
1280.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1$ |
$20.68730941$ |
1.156455752 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-{x}$ |
| 1280.1-f5 |
1280.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$10.34365470$ |
1.156455752 |
\( -\frac{13352896}{5} a + \frac{21733168}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 5 \phi - 16\) , \( 17 \phi - 16\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(5\phi-16\right){x}+17\phi-16$ |
| 1280.1-f6 |
1280.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1$ |
$20.68730941$ |
1.156455752 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-41{x}+116$ |
| 1280.1-f7 |
1280.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$10.34365470$ |
1.156455752 |
\( \frac{13352896}{5} a + \frac{8380272}{5} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 \phi - 11\) , \( -17 \phi + 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-5\phi-11\right){x}-17\phi+1$ |
| 1280.1-f8 |
1280.1-f |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{3} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$10.34365470$ |
1.156455752 |
\( \frac{170403887082176}{25} a + \frac{105315394102512}{25} \) |
\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( 100 \phi - 256\) , \( -464 \phi + 1032\bigr] \) |
${y}^2={x}^{3}+\left(\phi+1\right){x}^{2}+\left(100\phi-256\right){x}-464\phi+1032$ |
| 1280.1-g1 |
1280.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{8} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12.96909401$ |
1.449988790 |
\( -\frac{2816}{5} a + \frac{4608}{5} \) |
\( \bigl[0\) , \( \phi\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\phi{x}^{2}+{x}$ |
| 1280.1-g2 |
1280.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{22} \cdot 5^{2} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.484547005$ |
1.449988790 |
\( -\frac{9285883494578}{5} a + 3004975022826 \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( 165 \phi - 29\) , \( 379 \phi + 746\bigr] \) |
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(165\phi-29\right){x}+379\phi+746$ |
| 1280.1-g3 |
1280.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{20} \cdot 5^{4} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$12.96909401$ |
1.449988790 |
\( -\frac{22755876}{25} a + \frac{36900584}{25} \) |
\( \bigl[0\) , \( \phi\) , \( 0\) , \( 20 \phi - 44\) , \( -76 \phi + 128\bigr] \) |
${y}^2={x}^{3}+\phi{x}^{2}+\left(20\phi-44\right){x}-76\phi+128$ |
| 1280.1-g4 |
1280.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{2} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$12.96909401$ |
1.449988790 |
\( \frac{53328}{5} a + 8912 \) |
\( \bigl[0\) , \( \phi\) , \( 0\) , \( -4\) , \( -4 \phi\bigr] \) |
${y}^2={x}^{3}+\phi{x}^{2}-4{x}-4\phi$ |
| 1280.1-g5 |
1280.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{22} \cdot 5^{8} \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$6.484547005$ |
1.449988790 |
\( \frac{1613607658}{625} a + \frac{996757382}{625} \) |
\( \bigl[0\) , \( \phi\) , \( 0\) , \( -60 \phi - 84\) , \( 276 \phi + 400\bigr] \) |
${y}^2={x}^{3}+\phi{x}^{2}+\left(-60\phi-84\right){x}+276\phi+400$ |
| 1280.1-g6 |
1280.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{20} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.242273502$ |
1.449988790 |
\( \frac{1444495316}{5} a + \frac{893013832}{5} \) |
\( \bigl[0\) , \( \phi\) , \( 0\) , \( -20 \phi - 44\) , \( -108 \phi - 128\bigr] \) |
${y}^2={x}^{3}+\phi{x}^{2}+\left(-20\phi-44\right){x}-108\phi-128$ |
| 1280.1-h1 |
1280.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( - 2^{22} \cdot 5^{8} \) |
$1.19516$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.694809372$ |
$2.617065069$ |
1.626391824 |
\( -\frac{1613607658}{625} a + \frac{522073008}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24 \phi - 84\) , \( 524 \phi + 124\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-24\phi-84\right){x}+524\phi+124$ |
| 1280.1-h2 |
1280.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{8} \cdot 5 \) |
$1.19516$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.347404686$ |
$20.93652055$ |
1.626391824 |
\( \frac{2816}{5} a + \frac{1792}{5} \) |
\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( \phi + 1\) , \( 1\bigr] \) |
${y}^2={x}^{3}+\left(\phi+1\right){x}^{2}+\left(\phi+1\right){x}+1$ |
*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.
