| 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 |
| 4900.1-a1 |
4900.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 5^{10} \cdot 7^{2} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.394590828$ |
1.965320765 |
\( \frac{1367631}{2800} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( 12 \phi + 12\) , \( 55 \phi + 41\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(12\phi+12\right){x}+55\phi+41$ |
| 4900.1-a2 |
4900.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{14} \cdot 7^{4} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.394590828$ |
1.965320765 |
\( \frac{611960049}{122500} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( -88 \phi - 88\) , \( 375 \phi + 281\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-88\phi-88\right){x}+375\phi+281$ |
| 4900.1-a3 |
4900.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 5^{22} \cdot 7^{2} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.098647707$ |
1.965320765 |
\( \frac{74565301329}{5468750} \) |
\( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( -438 \phi - 438\) , \( -6345 \phi - 4759\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-438\phi-438\right){x}-6345\phi-4759$ |
| 4900.1-a4 |
4900.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 5^{10} \cdot 7^{8} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.394590828$ |
1.965320765 |
\( \frac{2121328796049}{120050} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( 1338 \phi - 2677\) , \( -33714 \phi + 59332\bigr] \) |
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(1338\phi-2677\right){x}-33714\phi+59332$ |
| 4900.1-b1 |
4900.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 5^{10} \cdot 7^{12} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$2.211195222$ |
1.977753131 |
\( -\frac{417267265}{235298} \) |
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -227 \phi - 227\) , \( 3019 \phi + 2321\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-227\phi-227\right){x}+3019\phi+2321$ |
| 4900.1-b2 |
4900.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 5^{10} \cdot 7^{4} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$2.211195222$ |
1.977753131 |
\( \frac{397535}{392} \) |
\( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( -23 \phi + 45\) , \( 76 \phi - 128\bigr] \) |
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-23\phi+45\right){x}+76\phi-128$ |
| 4900.1-c1 |
4900.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 5^{8} \cdot 7^{4} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \cdot 3 \cdot 11 \) |
$0.012846808$ |
$3.685488049$ |
2.794983082 |
\( -\frac{1026590625}{100352} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -180\) , \( 1047\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-180{x}+1047$ |
| 4900.1-d1 |
4900.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 5^{6} \cdot 7^{2} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.142886610$ |
1.405541621 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[\phi\) , \( -1\) , \( 1\) , \( 852 \phi - 1705\) , \( -17475 \phi + 30581\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}-{x}^{2}+\left(852\phi-1705\right){x}-17475\phi+30581$ |
| 4900.1-d2 |
4900.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{6} \cdot 7^{2} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.142886610$ |
1.405541621 |
\( -\frac{15625}{28} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -3 \phi - 3\) , \( -5 \phi - 4\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-3\phi-3\right){x}-5\phi-4$ |
| 4900.1-d3 |
4900.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{6} \cdot 7^{6} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$3.142886610$ |
1.405541621 |
\( \frac{9938375}{21952} \) |
\( \bigl[\phi\) , \( -1\) , \( 1\) , \( -23 \phi + 45\) , \( -115 \phi + 201\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-23\phi+45\right){x}-115\phi+201$ |
| 4900.1-d4 |
4900.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 5^{6} \cdot 7^{12} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$3.142886610$ |
1.405541621 |
\( \frac{4956477625}{941192} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -178 \phi - 178\) , \( 1395 \phi + 1046\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-178\phi-178\right){x}+1395\phi+1046$ |
| 4900.1-d5 |
4900.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 5^{6} \cdot 7^{4} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.142886610$ |
1.405541621 |
\( \frac{128787625}{98} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -53 \phi - 53\) , \( -245 \phi - 184\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-53\phi-53\right){x}-245\phi-184$ |
| 4900.1-d6 |
4900.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 5^{6} \cdot 7^{4} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.142886610$ |
1.405541621 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -13653 \phi - 13653\) , \( 1102915 \phi + 827186\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-13653\phi-13653\right){x}+1102915\phi+827186$ |
| 4900.1-e1 |
4900.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{8} \cdot 7^{4} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.489837150$ |
1.332550857 |
\( \frac{7336753}{6272} a - \frac{1493917}{3136} \) |
\( \bigl[\phi + 1\) , \( 0\) , \( \phi + 1\) , \( 33 \phi - 5\) , \( 76 \phi - 30\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(33\phi-5\right){x}+76\phi-30$ |
| 4900.1-f1 |
4900.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{8} \cdot 7^{4} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.489837150$ |
1.332550857 |
\( -\frac{7336753}{6272} a + \frac{4348919}{6272} \) |
\( \bigl[\phi\) , \( -\phi + 1\) , \( \phi\) , \( -35 \phi + 30\) , \( -77 \phi + 47\bigr] \) |
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-35\phi+30\right){x}-77\phi+47$ |
| 4900.1-g1 |
4900.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{2} \cdot 7^{4} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$0.031126488$ |
$7.093471642$ |
2.764788988 |
\( \frac{7336753}{6272} a - \frac{1493917}{3136} \) |
\( \bigl[1\) , \( \phi - 1\) , \( \phi\) , \( 7 \phi - 8\) , \( -16 \phi + 25\bigr] \) |
${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(7\phi-8\right){x}-16\phi+25$ |
| 4900.1-h1 |
4900.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{2} \cdot 7^{4} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$0.031126488$ |
$7.093471642$ |
2.764788988 |
\( -\frac{7336753}{6272} a + \frac{4348919}{6272} \) |
\( \bigl[1\) , \( -\phi\) , \( \phi + 1\) , \( -8 \phi - 1\) , \( 15 \phi + 9\bigr] \) |
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}-\phi{x}^{2}+\left(-8\phi-1\right){x}+15\phi+9$ |
| 4900.1-i1 |
4900.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{22} \cdot 5^{2} \cdot 7^{4} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.940068646$ |
0.840822958 |
\( -\frac{1026590625}{100352} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( 36 \phi - 72\) , \( 160 \phi - 272\bigr] \) |
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(36\phi-72\right){x}+160\phi-272$ |
| 4900.1-j1 |
4900.1-j |
$2$ |
$3$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 5^{4} \cdot 7^{12} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.653095700$ |
$0.802120939$ |
2.811337089 |
\( -\frac{417267265}{235298} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -45\) , \( -185\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-45{x}-185$ |
| 4900.1-j2 |
4900.1-j |
$2$ |
$3$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4900.1 |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 5^{4} \cdot 7^{4} \) |
$1.67175$ |
$(-2a+1), (2), (7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.217698566$ |
$7.219088453$ |
2.811337089 |
\( \frac{397535}{392} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 5\) , \( 5\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+5{x}+5$ |
*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.
