| 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 |
| 2916.1-a1 |
2916.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$39.86878607$ |
1.981095907 |
\( -\frac{132651}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 2916.1-a2 |
2916.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{22} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$0.492207235$ |
1.981095907 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -123\) , \( -667\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-123{x}-667$ |
| 2916.1-a3 |
2916.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$4.429865119$ |
1.981095907 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 12\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+12{x}+8$ |
| 2916.1-b1 |
2916.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{10} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$14.80474561$ |
2.206961172 |
\( -295397215188 a - \frac{365131038423}{2} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( -31 \phi - 29\) , \( 55 \phi + 112\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(-31\phi-29\right){x}+55\phi+112$ |
| 2916.1-b2 |
2916.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$14.80474561$ |
2.206961172 |
\( -3591 a - \frac{17415}{8} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( -\phi + 1\) , \( \phi - 2\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(-\phi+1\right){x}+\phi-2$ |
| 2916.1-b3 |
2916.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.644971735$ |
2.206961172 |
\( \frac{1918701}{2} a - \frac{3101139}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 27 \phi - 2\) , \( -26\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(27\phi-2\right){x}-26$ |
| 2916.1-c1 |
2916.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{14} \cdot 3^{22} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$4.122959226$ |
1.843843419 |
\( -\frac{446631}{128} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( 89 \phi - 179\) , \( -713 \phi + 1268\bigr] \) |
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(89\phi-179\right){x}-713\phi+1268$ |
| 2916.1-d1 |
2916.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.644971735$ |
2.206961172 |
\( -\frac{1918701}{2} a - 591219 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -27 \phi + 25\) , \( -26\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-27\phi+25\right){x}-26$ |
| 2916.1-d2 |
2916.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{10} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$14.80474561$ |
2.206961172 |
\( 295397215188 a - \frac{955925468799}{2} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( 31 \phi - 60\) , \( -86 \phi + 227\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(31\phi-60\right){x}-86\phi+227$ |
| 2916.1-d3 |
2916.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$14.80474561$ |
2.206961172 |
\( 3591 a - \frac{46143}{8} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( \phi\) , \( -2 \phi - 1\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\phi{x}-2\phi-1$ |
| 2916.1-e1 |
2916.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{22} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$3.521410481$ |
1.574822642 |
\( 6591 a + \frac{6591}{2} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -21 \phi - 21\) , \( 56 \phi + 15\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-21\phi-21\right){x}+56\phi+15$ |
| 2916.1-f1 |
2916.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{14} \cdot 3^{10} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1.755143231$ |
0.784923915 |
\( -\frac{446631}{128} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( 10 \phi - 20\) , \( 26 \phi - 44\bigr] \) |
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(10\phi-20\right){x}+26\phi-44$ |
| 2916.1-g1 |
2916.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{22} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$3.521410481$ |
1.574822642 |
\( -6591 a + \frac{19773}{2} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( 22 \phi - 44\) , \( -78 \phi + 114\bigr] \) |
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(22\phi-44\right){x}-78\phi+114$ |
| 2916.1-h1 |
2916.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{8} \cdot 3^{10} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.032222051$ |
$12.37762825$ |
2.140360212 |
\( -\frac{13323039}{8} a + \frac{43132233}{16} \) |
\( \bigl[1\) , \( -1\) , \( \phi\) , \( 16 \phi - 21\) , \( -33 \phi + 55\bigr] \) |
${y}^2+{x}{y}+\phi{y}={x}^{3}-{x}^{2}+\left(16\phi-21\right){x}-33\phi+55$ |
| 2916.1-i1 |
2916.1-i |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{22} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$0.267419514$ |
2.152685568 |
\( -\frac{7211641251}{4} a - \frac{3537268269}{4} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( -1089 \phi - 1642\) , \( -30205 \phi - 30617\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-1089\phi-1642\right){x}-30205\phi-30617$ |
| 2916.1-i2 |
2916.1-i |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{12} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$2.406775632$ |
2.152685568 |
\( -\frac{38259}{32} a + \frac{64017}{64} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( -9 \phi - 22\) , \( -73 \phi - 53\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-9\phi-22\right){x}-73\phi-53$ |
| 2916.1-i3 |
2916.1-i |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$21.66098069$ |
2.152685568 |
\( -\frac{92495547}{2} a + \frac{299324565}{4} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( 6 \phi - 7\) , \( -2 \phi + 9\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(6\phi-7\right){x}-2\phi+9$ |
| 2916.1-j1 |
2916.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{12} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$2.406775632$ |
2.152685568 |
\( \frac{38259}{32} a - \frac{12501}{64} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( 9 \phi - 30\) , \( 64 \phi - 95\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(9\phi-30\right){x}+64\phi-95$ |
| 2916.1-j2 |
2916.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$21.66098069$ |
2.152685568 |
\( \frac{92495547}{2} a + \frac{114333471}{4} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( -6 \phi\) , \( 8 \phi + 8\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}-6\phi{x}+8\phi+8$ |
| 2916.1-j3 |
2916.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{22} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$0.267419514$ |
2.152685568 |
\( \frac{7211641251}{4} a - 2687227380 \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( 1089 \phi - 2730\) , \( 29116 \phi - 58091\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(1089\phi-2730\right){x}+29116\phi-58091$ |
| 2916.1-k1 |
2916.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{8} \cdot 3^{10} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.032222051$ |
$12.37762825$ |
2.140360212 |
\( \frac{13323039}{8} a + \frac{16486155}{16} \) |
\( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( -17 \phi - 5\) , \( 32 \phi + 22\bigr] \) |
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(-17\phi-5\right){x}+32\phi+22$ |
| 2916.1-l1 |
2916.1-l |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{6} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.422386824$ |
$18.70526296$ |
2.355580333 |
\( \frac{8235}{4} a + \frac{22815}{8} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( -2 \phi\) , \( 2 \phi + 1\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}-2\phi{x}+2\phi+1$ |
| 2916.1-l2 |
2916.1-l |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1.267160474$ |
$2.078362551$ |
2.355580333 |
\( \frac{868995}{2} a + \frac{526365}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 27 \phi - 56\) , \( 108 \phi - 188\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(27\phi-56\right){x}+108\phi-188$ |
| 2916.1-l3 |
2916.1-l |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{10} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.267160474$ |
$18.70526296$ |
2.355580333 |
\( \frac{140981980695}{2} a + 43565801820 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 27 \phi - 86\) , \( -144 \phi + 348\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(27\phi-86\right){x}-144\phi+348$ |
| 2916.1-m1 |
2916.1-m |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{10} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.267160474$ |
$18.70526296$ |
2.355580333 |
\( -\frac{140981980695}{2} a + \frac{228113584335}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -27 \phi - 59\) , \( 144 \phi + 204\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-27\phi-59\right){x}+144\phi+204$ |
| 2916.1-m2 |
2916.1-m |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1.267160474$ |
$2.078362551$ |
2.355580333 |
\( -\frac{868995}{2} a + 697680 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -27 \phi - 29\) , \( -108 \phi - 80\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-27\phi-29\right){x}-108\phi-80$ |
| 2916.1-m3 |
2916.1-m |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{6} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.422386824$ |
$18.70526296$ |
2.355580333 |
\( -\frac{8235}{4} a + \frac{39285}{8} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( 2 \phi - 2\) , \( 1\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(2\phi-2\right){x}+1$ |
| 2916.1-n1 |
2916.1-n |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{10} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.044196980$ |
$16.11783287$ |
1.911461221 |
\( -6591 a + \frac{19773}{2} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( 2 \phi - 5\) , \( 2 \phi - 4\bigr] \) |
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(2\phi-5\right){x}+2\phi-4$ |
| 2916.1-o1 |
2916.1-o |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$23.79028099$ |
1.182148566 |
\( -\frac{1918701}{2} a - 591219 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 \phi + 3\) , \( \phi\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-3\phi+3\right){x}+\phi$ |
| 2916.1-o2 |
2916.1-o |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{22} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$0.293707172$ |
1.182148566 |
\( 295397215188 a - \frac{955925468799}{2} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( 279 \phi - 543\) , \( 2305 \phi - 5873\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(279\phi-543\right){x}+2305\phi-5873$ |
| 2916.1-o3 |
2916.1-o |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$2.643364555$ |
1.182148566 |
\( 3591 a - \frac{46143}{8} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( 9 \phi - 3\) , \( 37 \phi + 13\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(9\phi-3\right){x}+37\phi+13$ |
| 2916.1-p1 |
2916.1-p |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{6} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$4.212638865$ |
1.883949373 |
\( \frac{8235}{4} a + \frac{22815}{8} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( -18 \phi - 3\) , \( -17 \phi - 14\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-18\phi-3\right){x}-17\phi-14$ |
| 2916.1-p2 |
2916.1-p |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$37.91374978$ |
1.883949373 |
\( \frac{868995}{2} a + \frac{526365}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 \phi - 6\) , \( -5 \phi + 9\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(3\phi-6\right){x}-5\phi+9$ |
| 2916.1-p3 |
2916.1-p |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{22} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$0.468070985$ |
1.883949373 |
\( \frac{140981980695}{2} a + 43565801820 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 243 \phi - 771\) , \( 3645 \phi - 8632\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(243\phi-771\right){x}+3645\phi-8632$ |
| 2916.1-q1 |
2916.1-q |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{10} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$0.044196980$ |
$16.11783287$ |
1.911461221 |
\( 6591 a + \frac{6591}{2} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( -2 \phi - 2\) , \( -5 \phi - 3\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-2\phi-2\right){x}-5\phi-3$ |
| 2916.1-r1 |
2916.1-r |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{22} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$0.293707172$ |
1.182148566 |
\( -295397215188 a - \frac{365131038423}{2} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( -279 \phi - 265\) , \( -2584 \phi - 3833\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-279\phi-265\right){x}-2584\phi-3833$ |
| 2916.1-r2 |
2916.1-r |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$2.643364555$ |
1.182148566 |
\( -3591 a - \frac{17415}{8} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( -9 \phi + 5\) , \( -46 \phi + 55\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-9\phi+5\right){x}-46\phi+55$ |
| 2916.1-r3 |
2916.1-r |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$23.79028099$ |
1.182148566 |
\( \frac{1918701}{2} a - \frac{3101139}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 \phi\) , \( -\phi + 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+3\phi{x}-\phi+1$ |
| 2916.1-s1 |
2916.1-s |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{10} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.616375716$ |
$17.26115040$ |
2.114694993 |
\( -\frac{7211641251}{4} a - \frac{3537268269}{4} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( -121 \phi - 182\) , \( 937 \phi + 972\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(-121\phi-182\right){x}+937\phi+972$ |
| 2916.1-s2 |
2916.1-s |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{12} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.205458572$ |
$17.26115040$ |
2.114694993 |
\( -\frac{38259}{32} a + \frac{64017}{64} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( -\phi - 2\) , \( \phi\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(-\phi-2\right){x}+\phi$ |
| 2916.1-s3 |
2916.1-s |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.616375716$ |
$1.917905600$ |
2.114694993 |
\( -\frac{92495547}{2} a + \frac{299324565}{4} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( 59 \phi - 62\) , \( 157 \phi - 316\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(59\phi-62\right){x}+157\phi-316$ |
| 2916.1-t1 |
2916.1-t |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{8} \cdot 3^{22} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.444460438$ |
1.291964692 |
\( \frac{13323039}{8} a + \frac{16486155}{16} \) |
\( \bigl[1\) , \( -1\) , \( \phi\) , \( -149 \phi - 42\) , \( -736 \phi - 566\bigr] \) |
${y}^2+{x}{y}+\phi{y}={x}^{3}-{x}^{2}+\left(-149\phi-42\right){x}-736\phi-566$ |
| 2916.1-u1 |
2916.1-u |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.061975282$ |
1.424789353 |
\( -\frac{132651}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -29\) , \( -53\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-29{x}-53$ |
| 2916.1-u2 |
2916.1-u |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{10} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$9.557777544$ |
1.424789353 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-14{x}+29$ |
| 2916.1-u3 |
2916.1-u |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$9.557777544$ |
1.424789353 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}-1$ |
| 2916.1-v1 |
2916.1-v |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{8} \cdot 3^{22} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.444460438$ |
1.291964692 |
\( -\frac{13323039}{8} a + \frac{43132233}{16} \) |
\( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( 148 \phi - 191\) , \( 735 \phi - 1302\bigr] \) |
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(148\phi-191\right){x}+735\phi-1302$ |
| 2916.1-w1 |
2916.1-w |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{22} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$0.468070985$ |
1.883949373 |
\( -\frac{140981980695}{2} a + \frac{228113584335}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -243 \phi - 528\) , \( -3645 \phi - 4987\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-243\phi-528\right){x}-3645\phi-4987$ |
| 2916.1-w2 |
2916.1-w |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{2} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$37.91374978$ |
1.883949373 |
\( -\frac{868995}{2} a + 697680 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 \phi - 3\) , \( 5 \phi + 4\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-3\phi-3\right){x}+5\phi+4$ |
| 2916.1-w3 |
2916.1-w |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{6} \cdot 3^{18} \) |
$1.46832$ |
$(2), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$4.212638865$ |
1.883949373 |
\( -\frac{8235}{4} a + \frac{39285}{8} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( 18 \phi - 22\) , \( 35 \phi - 53\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(18\phi-22\right){x}+35\phi-53$ |
| 2916.1-x1 |
2916.1-x |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2916.1 |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{12} \cdot 3^{6} \) |
$1.46832$ |
$(2), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.205458572$ |
$17.26115040$ |
2.114694993 |
\( \frac{38259}{32} a - \frac{12501}{64} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( \phi - 3\) , \( -2 \phi + 4\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(\phi-3\right){x}-2\phi+4$ |
*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.
