| 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 |
| 268.3-b1 |
268.3-b |
$2$ |
$11$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
268.3 |
\( 2^{2} \cdot 67 \) |
\( 2^{22} \cdot 67 \) |
$0.95658$ |
$(a), (-a+1), (-6a+1)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{2} \) |
$1$ |
$2.762336240$ |
2.088129922 |
\( \frac{4432109}{68608} a + \frac{1557205}{137216} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2 a - 2\) , \( -5 a + 7\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-2\right){x}-5a+7$ |
| 268.4-b1 |
268.4-b |
$2$ |
$11$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
268.4 |
\( 2^{2} \cdot 67 \) |
\( 2^{22} \cdot 67 \) |
$0.95658$ |
$(a), (-a+1), (6a-5)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{2} \) |
$1$ |
$2.762336240$ |
2.088129922 |
\( -\frac{4432109}{68608} a + \frac{10421423}{137216} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( a - 3\) , \( 4 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(a-3\right){x}+4a+3$ |
| 4338.3-b2 |
4338.3-b |
$2$ |
$11$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4338.3 |
\( 2 \cdot 3^{2} \cdot 241 \) |
\( 2^{11} \cdot 3^{22} \cdot 241 \) |
$2.05119$ |
$(a), (-a-1), (a-1), (-6a+13)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{3} \) |
$1$ |
$0.597215219$ |
4.645244245 |
\( \frac{1560085565819}{2732315328} a + \frac{699337828027}{227692944} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -66 a + 123\) , \( -163 a - 355\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-66a+123\right){x}-163a-355$ |
| 4338.4-b2 |
4338.4-b |
$2$ |
$11$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4338.4 |
\( 2 \cdot 3^{2} \cdot 241 \) |
\( 2^{11} \cdot 3^{22} \cdot 241 \) |
$2.05119$ |
$(a), (-a-1), (a-1), (6a+13)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{3} \) |
$1$ |
$0.597215219$ |
4.645244245 |
\( -\frac{1560085565819}{2732315328} a + \frac{699337828027}{227692944} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 62 a + 122\) , \( 286 a - 483\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(62a+122\right){x}+286a-483$ |
| 46.1-b2 |
46.1-b |
$2$ |
$11$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
46.1 |
\( 2 \cdot 23 \) |
\( 2^{11} \cdot 23 \) |
$0.65822$ |
$(a), (-a+5)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$27.80343496$ |
0.893636245 |
\( \frac{4758131}{1472} a - \frac{998961}{184} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -2 a - 3\) , \( 2 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-2a-3\right){x}+2a+3$ |
| 46.2-b2 |
46.2-b |
$2$ |
$11$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
46.2 |
\( 2 \cdot 23 \) |
\( 2^{11} \cdot 23 \) |
$0.65822$ |
$(a), (-a-5)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$27.80343496$ |
0.893636245 |
\( -\frac{4758131}{1472} a - \frac{998961}{184} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( a - 3\) , \( -2 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-3\right){x}-2a+3$ |
| 828.1-d2 |
828.1-d |
$2$ |
$11$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
828.1 |
\( 2^{2} \cdot 3^{2} \cdot 23 \) |
\( 2^{22} \cdot 3^{22} \cdot 23 \) |
$1.72829$ |
$(-a), (-a+1), (-3a-1), (2)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{3} \) |
$1$ |
$0.981956226$ |
2.995802213 |
\( \frac{23317935850638647}{4172166144} a - \frac{107391930667615985}{8344332288} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 297 a - 401\) , \( -16497 a - 13044\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(297a-401\right){x}-16497a-13044$ |
| 828.2-d1 |
828.2-d |
$2$ |
$11$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
828.2 |
\( 2^{2} \cdot 3^{2} \cdot 23 \) |
\( 2^{22} \cdot 3^{22} \cdot 23 \) |
$1.72829$ |
$(-a), (-a+1), (3a-4), (2)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{3} \) |
$1$ |
$0.981956226$ |
2.995802213 |
\( -\frac{23317935850638647}{4172166144} a - \frac{60756058966338691}{8344332288} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -297 a - 104\) , \( 16497 a - 29541\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-297a-104\right){x}+16497a-29541$ |
| 172.1-f2 |
172.1-f |
$2$ |
$11$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
172.1 |
\( 2^{2} \cdot 43 \) |
\( 2^{22} \cdot 43 \) |
$1.33427$ |
$(-a+2), (-a-1), (-4a+7)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{2} \) |
$1$ |
$13.26552063$ |
3.217361338 |
\( \frac{522287779}{44032} a - \frac{2679429217}{88064} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -10 a - 16\) , \( 167 a + 261\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-10a-16\right){x}+167a+261$ |
| 172.2-f1 |
172.2-f |
$2$ |
$11$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
172.2 |
\( 2^{2} \cdot 43 \) |
\( 2^{22} \cdot 43 \) |
$1.33427$ |
$(-a+2), (-a-1), (4a+3)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{2} \) |
$1$ |
$13.26552063$ |
3.217361338 |
\( -\frac{522287779}{44032} a - \frac{1634853659}{88064} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 11 a - 27\) , \( -179 a + 455\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11a-27\right){x}-179a+455$ |
| 92.1-e2 |
92.1-e |
$2$ |
$11$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
92.1 |
\( 2^{2} \cdot 23 \) |
\( - 2^{22} \cdot 23 \) |
$3.37505$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{2} \) |
$1$ |
$63.53752536$ |
3.574265051 |
\( -\frac{10742213}{47104} a^{2} + \frac{5274879}{23552} a + \frac{19013567}{23552} \) |
\( \bigl[1\) , \( a^{2} - 3\) , \( a + 1\) , \( a + 2\) , \( 2 a^{2} + 2 a - 3\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(a+2\right){x}+2a^{2}+2a-3$ |
| 258.2-c2 |
258.2-c |
$2$ |
$11$ |
3.3.404.1 |
$3$ |
$[3, 0]$ |
258.2 |
\( 2 \cdot 3 \cdot 43 \) |
\( - 2^{11} \cdot 3^{11} \cdot 43 \) |
$4.53175$ |
$(a+1), (a^2-2a-2), (-2a^2+2a+7)$ |
$0 \le r \le 1$ |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
|
\( 11^{2} \) |
$1$ |
$43.67983372$ |
5.811112058 |
\( \frac{2689846261}{60938568} a^{2} - \frac{4920631609}{40625712} a - \frac{3250035487}{121877136} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 2\) , \( a^{2} - a - 3\) , \( -3 a^{2} + a + 14\) , \( -145 a^{2} + 194 a + 716\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-3a^{2}+a+14\right){x}-145a^{2}+194a+716$ |
| 12.1-c2 |
12.1-c |
$2$ |
$11$ |
3.3.1436.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{22} \cdot 3^{11} \) |
$5.12365$ |
$(a+2), (a+1), (-a^2+3a+3)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{3} \) |
$1$ |
$18.97498806$ |
5.508038618 |
\( -\frac{68915170505}{362797056} a^{2} - \frac{3447025613}{30233088} a + \frac{105325093363}{362797056} \) |
\( \bigl[a^{2} - a - 7\) , \( a^{2} - 2 a - 6\) , \( a\) , \( -487 a^{2} + 568 a + 4428\) , \( -35927 a^{2} + 46510 a + 337128\bigr] \) |
${y}^2+\left(a^{2}-a-7\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-487a^{2}+568a+4428\right){x}-35927a^{2}+46510a+337128$ |
| 109.1-a2 |
109.1-a |
$2$ |
$11$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
109.1 |
\( 109 \) |
\( 109 \) |
$4.32500$ |
$(-a^3+a^2+5a)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2755.971058$ |
0.845902442 |
\( \frac{3718291}{109} a^{3} - \frac{9007348}{109} a^{2} + \frac{1282551}{109} a + \frac{2463928}{109} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( a^{2} - a\) , \( -a^{2} + 1\) , \( -a^{2} + a + 1\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-3\right){x}^{2}+\left(-a^{2}+1\right){x}-a^{2}+a+1$ |
| 109.4-a1 |
109.4-a |
$2$ |
$11$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
109.4 |
\( 109 \) |
\( 109 \) |
$4.32500$ |
$(-2a^3+2a^2+7a-3)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2755.971058$ |
0.845902442 |
\( \frac{7148367}{109} a^{3} - \frac{1859310}{109} a^{2} - \frac{23015867}{109} a - \frac{9973167}{109} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 2 a^{2} - 2\) , \( a^{3} - 2 a\) , \( -3 a^{3} + 4 a^{2} + a - 2\) , \( -2 a^{3} + 3 a^{2} - 1\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}-2\right){x}^{2}+\left(-3a^{3}+4a^{2}+a-2\right){x}-2a^{3}+3a^{2}-1$ |
| 356.1-a2 |
356.1-a |
$2$ |
$11$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
356.1 |
\( 2^{2} \cdot 89 \) |
\( - 2^{22} \cdot 89 \) |
$7.44955$ |
$(-a^3+1/2a^2+5a), (1/2a^3-2a)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$695.7631500$ |
1.581279886 |
\( -\frac{9295265473}{2848} a^{3} - \frac{9777302469}{1424} a^{2} + \frac{18982583669}{5696} a + \frac{12851484651}{2848} \) |
\( \bigl[\frac{1}{2} a^{3} - a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( \frac{3}{2} a^{2} + 12 a + 1\) , \( -\frac{1}{2} a^{3} + 7 a^{2} + 8 a + 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a\right){x}^{2}+\left(\frac{3}{2}a^{2}+12a+1\right){x}-\frac{1}{2}a^{3}+7a^{2}+8a+5$ |
| 356.2-a1 |
356.2-a |
$2$ |
$11$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
356.2 |
\( 2^{2} \cdot 89 \) |
\( - 2^{22} \cdot 89 \) |
$7.44955$ |
$(1/2a^3+1/2a^2-a-3), (1/2a^3-2a)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$695.7631500$ |
1.581279886 |
\( -\frac{92560602007}{11392} a^{3} + \frac{9777302469}{1424} a^{2} + \frac{240500744129}{5696} a - \frac{104476144977}{2848} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( \frac{1}{2} a^{3} - a + 1\) , \( \frac{3}{2} a^{3} + 3 a^{2} - 11 a - 12\) , \( -3 a^{3} - a^{2} + 12 a + 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(\frac{3}{2}a^{3}+3a^{2}-11a-12\right){x}-3a^{3}-a^{2}+12a+9$ |
| 356.3-a1 |
356.3-a |
$2$ |
$11$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
356.3 |
\( 2^{2} \cdot 89 \) |
\( - 2^{22} \cdot 89 \) |
$7.44955$ |
$(1/2a^3-1/2a^2-a+3), (1/2a^3-2a)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$695.7631500$ |
1.581279886 |
\( \frac{92560602007}{11392} a^{3} + \frac{9777302469}{1424} a^{2} - \frac{240500744129}{5696} a - \frac{104476144977}{2848} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( -\frac{3}{2} a^{3} + \frac{7}{2} a^{2} + 14 a - 12\) , \( 6 a^{3} + 3 a^{2} - 23 a + 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{3}{2}a^{3}+\frac{7}{2}a^{2}+14a-12\right){x}+6a^{3}+3a^{2}-23a+14$ |
| 356.4-a2 |
356.4-a |
$2$ |
$11$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
356.4 |
\( 2^{2} \cdot 89 \) |
\( - 2^{22} \cdot 89 \) |
$7.44955$ |
$(1/2a^3-a^2-3a+1), (1/2a^3-2a)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$695.7631500$ |
1.581279886 |
\( \frac{9295265473}{2848} a^{3} - \frac{9777302469}{1424} a^{2} - \frac{18982583669}{5696} a + \frac{12851484651}{2848} \) |
\( \bigl[\frac{1}{2} a^{3} - a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a\) , \( \frac{1}{2} a^{2} + a\) , \( \frac{7}{2} a^{3} + a^{2} - 15 a + 2\) , \( \frac{5}{2} a^{3} - \frac{5}{2} a^{2} - 11 a + 18\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a\right){x}^{2}+\left(\frac{7}{2}a^{3}+a^{2}-15a+2\right){x}+\frac{5}{2}a^{3}-\frac{5}{2}a^{2}-11a+18$ |
| 129.2-d2 |
129.2-d |
$2$ |
$11$ |
4.4.1957.1 |
$4$ |
$[4, 0]$ |
129.2 |
\( 3 \cdot 43 \) |
\( - 3^{11} \cdot 43 \) |
$7.25701$ |
$(a^3-4a), (a-3)$ |
$1$ |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$0.210757626$ |
$1296.268258$ |
2.245691418 |
\( \frac{1797414937694}{7617321} a^{3} - \frac{2025883730947}{7617321} a^{2} - \frac{1047556662304}{2539107} a - \frac{605709398558}{7617321} \) |
\( \bigl[-a^{3} + a^{2} + 3 a - 1\) , \( -a^{3} + 3 a + 1\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{3} + a^{2} - 3 a - 7\) , \( 2 a^{3} - 3 a^{2} - 6 a + 7\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+3a-1\right){x}{y}+\left(-a^{3}+a^{2}+3a\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(a^{3}+a^{2}-3a-7\right){x}+2a^{3}-3a^{2}-6a+7$ |
| 597.1-d2 |
597.1-d |
$2$ |
$11$ |
4.4.1957.1 |
$4$ |
$[4, 0]$ |
597.1 |
\( 3 \cdot 199 \) |
\( 3^{11} \cdot 199 \) |
$8.78882$ |
$(a^3-4a), (-3a^3+a^2+9a+1)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$655.0531666$ |
1.346134492 |
\( -\frac{75804690804830}{35252253} a^{3} - \frac{155220621957059}{35252253} a^{2} - \frac{5836788500090}{11750751} a + \frac{36043119422093}{35252253} \) |
\( \bigl[a^{2} - 1\) , \( -2 a^{3} + a^{2} + 6 a - 1\) , \( a^{3} - 4 a - 1\) , \( -3 a + 3\) , \( -4 a^{3} + 2 a^{2} + 12 a + 4\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-2a^{3}+a^{2}+6a-1\right){x}^{2}+\left(-3a+3\right){x}-4a^{3}+2a^{2}+12a+4$ |
| 1058.1-b1 |
1058.1-b |
$2$ |
$11$ |
\(\Q(\zeta_{16})^+\) |
$4$ |
$[4, 0]$ |
1058.1 |
\( 2 \cdot 23^{2} \) |
\( 2^{22} \cdot 23^{2} \) |
$9.65749$ |
$(a), (-a^2+7)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 2 \cdot 11 \) |
$1$ |
$773.0309958$ |
3.105769654 |
\( \frac{4758131}{1472} a^{2} - \frac{8753975}{736} \) |
\( \bigl[a^{2} - 1\) , \( -1\) , \( 1\) , \( -2 a^{2} + 1\) , \( 2 a^{2} - 1\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-2a^{2}+1\right){x}+2a^{2}-1$ |
| 1058.2-b2 |
1058.2-b |
$2$ |
$11$ |
\(\Q(\zeta_{16})^+\) |
$4$ |
$[4, 0]$ |
1058.2 |
\( 2 \cdot 23^{2} \) |
\( 2^{22} \cdot 23^{2} \) |
$9.65749$ |
$(a), (-a^2-3)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 2 \cdot 11 \) |
$1$ |
$773.0309958$ |
3.105769654 |
\( -\frac{4758131}{1472} a^{2} + \frac{762287}{736} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + 1\) , \( 1\) , \( a^{2} - 5\) , \( -2 a^{2} + 7\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(a^{2}-5\right){x}-2a^{2}+7$ |
| 46.1-b2 |
46.1-b |
$2$ |
$11$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
46.1 |
\( 2 \cdot 23 \) |
\( 2^{11} \cdot 23 \) |
$6.92189$ |
$(a^3-4a+1), (a^3-a^2-4a+1)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$903.8888112$ |
1.711910627 |
\( \frac{434109501}{92} a^{3} + \frac{222189605}{92} a^{2} - \frac{3233114731}{184} a - \frac{1672205729}{184} \) |
\( \bigl[a\) , \( -a^{2} - a + 2\) , \( a^{3} - 4 a + 1\) , \( a^{3} - 3 a + 2\) , \( 3 a^{3} + 7 a^{2} + a - 3\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(a^{3}-3a+2\right){x}+3a^{3}+7a^{2}+a-3$ |
| 46.2-b1 |
46.2-b |
$2$ |
$11$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
46.2 |
\( 2 \cdot 23 \) |
\( 2^{11} \cdot 23 \) |
$6.92189$ |
$(a^3-4a+1), (-a^3-a^2+3a)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$903.8888112$ |
1.711910627 |
\( \frac{239761277}{184} a^{3} - \frac{222189605}{92} a^{2} - \frac{45413053}{92} a + \frac{105311111}{184} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a + 1\) , \( a^{3} - 3 a + 2\) , \( 13 a^{3} - 7 a^{2} - 49 a + 25\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(a^{3}-3a+2\right){x}+13a^{3}-7a^{2}-49a+25$ |
| 46.3-b1 |
46.3-b |
$2$ |
$11$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
46.3 |
\( 2 \cdot 23 \) |
\( 2^{11} \cdot 23 \) |
$6.92189$ |
$(a^3-4a+1), (-a^2+a+3)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$903.8888112$ |
1.711910627 |
\( -\frac{239761277}{184} a^{3} - \frac{222189605}{92} a^{2} + \frac{45413053}{92} a + \frac{105311111}{184} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a + 1\) , \( -2 a^{3} + 7 a + 2\) , \( -13 a^{3} - 7 a^{2} + 48 a + 25\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(-2a^{3}+7a+2\right){x}-13a^{3}-7a^{2}+48a+25$ |
| 46.4-b2 |
46.4-b |
$2$ |
$11$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
46.4 |
\( 2 \cdot 23 \) |
\( 2^{11} \cdot 23 \) |
$6.92189$ |
$(a^3-4a+1), (a^3+a^2-4a-1)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$903.8888112$ |
1.711910627 |
\( -\frac{434109501}{92} a^{3} + \frac{222189605}{92} a^{2} + \frac{3233114731}{184} a - \frac{1672205729}{184} \) |
\( \bigl[a\) , \( -a^{2} + a + 2\) , \( a^{3} - 4 a + 1\) , \( -a^{3} + 2 a + 2\) , \( -4 a^{3} + 7 a^{2} + 3 a - 3\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-a^{3}+2a+2\right){x}-4a^{3}+7a^{2}+3a-3$ |
| 1058.3-d2 |
1058.3-d |
$2$ |
$11$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1058.3 |
\( 2 \cdot 23^{2} \) |
\( 2^{22} \cdot 23^{2} \) |
$10.24331$ |
$(a^3-4a+1), (-a^2+a+3), (a^3+a^2-4a-1)$ |
$0 \le r \le 1$ |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$11$ |
11B.1.1 |
|
\( 2 \cdot 11 \) |
$1$ |
$773.0309958$ |
5.586721508 |
\( -\frac{4758131}{1472} a^{3} + \frac{14274393}{1472} a - \frac{998961}{184} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 3 a - 1\) , \( 1\) , \( a^{3} - 3 a - 3\) , \( -2 a^{3} + 6 a + 3\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}+\left(a^{3}-3a-3\right){x}-2a^{3}+6a+3$ |
| 1058.6-d2 |
1058.6-d |
$2$ |
$11$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
1058.6 |
\( 2 \cdot 23^{2} \) |
\( 2^{22} \cdot 23^{2} \) |
$10.24331$ |
$(a^3-4a+1), (a^3-a^2-4a+1), (-a^3-a^2+3a)$ |
$0 \le r \le 1$ |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$11$ |
11B.1.1 |
|
\( 2 \cdot 11 \) |
$1$ |
$773.0309958$ |
5.586721508 |
\( \frac{4758131}{1472} a^{3} - \frac{14274393}{1472} a - \frac{998961}{184} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -1\) , \( 1\) , \( -2 a^{3} + 6 a - 3\) , \( 2 a^{3} - 6 a + 3\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-2a^{3}+6a-3\right){x}+2a^{3}-6a+3$ |
| 115.1-d2 |
115.1-d |
$2$ |
$11$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
115.1 |
\( 5 \cdot 23 \) |
\( 5^{11} \cdot 23 \) |
$10.48597$ |
$(a^3-a^2-5a), (a^3-2a^2-5a)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$730.6024422$ |
1.024248730 |
\( -\frac{7365468008421}{359375} a^{3} - \frac{387513656342}{71875} a^{2} + \frac{2536101691117}{71875} a - \frac{2965958283079}{359375} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 3\) , \( a^{3} - a^{2} - 4 a\) , \( 29 a^{3} - 18 a^{2} - 149 a - 99\) , \( -117 a^{3} + 76 a^{2} + 605 a + 347\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(29a^{3}-18a^{2}-149a-99\right){x}-117a^{3}+76a^{2}+605a+347$ |
| 115.2-d2 |
115.2-d |
$2$ |
$11$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
115.2 |
\( 5 \cdot 23 \) |
\( 5^{11} \cdot 23 \) |
$10.48597$ |
$(a^3-a^2-5a), (a^3-a^2-4a-4)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$730.6024422$ |
1.024248730 |
\( \frac{33449867876651}{359375} a^{3} - \frac{4829366317304}{71875} a^{2} - \frac{33837381532993}{71875} a - \frac{90296475618806}{359375} \) |
\( \bigl[1\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( a^{3} - a^{2} - 4 a\) , \( -8 a^{3} - 3 a^{2} + 21 a - 7\) , \( 20 a^{3} + 21 a^{2} - 25 a + 5\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-1\right){x}^{2}+\left(-8a^{3}-3a^{2}+21a-7\right){x}+20a^{3}+21a^{2}-25a+5$ |
| 178.1-b1 |
178.1-b |
$2$ |
$11$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
178.1 |
\( 2 \cdot 89 \) |
\( 2^{11} \cdot 89 \) |
$14.45906$ |
$(a^2-a-2), (-2a-1)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$982.8161949$ |
1.055311378 |
\( -\frac{65768939}{178} a^{3} - \frac{227533053}{356} a^{2} + \frac{499038965}{712} a + \frac{618580065}{712} \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{3} - 4 a + 1\) , \( -5 a^{3} + 6 a^{2} + 21 a - 24\) , \( 6 a^{3} - 8 a^{2} - 26 a + 34\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(-5a^{3}+6a^{2}+21a-24\right){x}+6a^{3}-8a^{2}-26a+34$ |
| 178.2-b1 |
178.2-b |
$2$ |
$11$ |
4.4.7168.1 |
$4$ |
$[4, 0]$ |
178.2 |
\( 2 \cdot 89 \) |
\( 2^{11} \cdot 89 \) |
$14.45906$ |
$(a^2-a-2), (2a-1)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$982.8161949$ |
1.055311378 |
\( \frac{65768939}{178} a^{3} - \frac{227533053}{356} a^{2} - \frac{499038965}{712} a + \frac{618580065}{712} \) |
\( \bigl[a\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{3} - 4 a + 1\) , \( 5 a^{3} + 6 a^{2} - 22 a - 24\) , \( -7 a^{3} - 8 a^{2} + 30 a + 34\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(5a^{3}+6a^{2}-22a-24\right){x}-7a^{3}-8a^{2}+30a+34$ |
| 92.2-f2 |
92.2-f |
$2$ |
$11$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
92.2 |
\( 2^{2} \cdot 23 \) |
\( 2^{22} \cdot 23^{2} \) |
$15.96302$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1), (1/2a^3-3/2a^2-3a+9)$ |
$1$ |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 2 \cdot 11^{2} \) |
$0.141460746$ |
$773.0309958$ |
8.618266439 |
\( -\frac{4758131}{2944} a^{2} + \frac{4758131}{2944} a + \frac{762287}{736} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 1\) , \( 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 5\) , \( -a^{2} + a + 7\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+1\right){x}^{2}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-5\right){x}-a^{2}+a+7$ |
| 4.1-c1 |
4.1-c |
$2$ |
$11$ |
4.4.11348.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{22} \) |
$11.32024$ |
$(a), (-a-1)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11^{2} \) |
$1$ |
$305.8508628$ |
2.871111419 |
\( \frac{96026345973}{2048} a^{3} - \frac{26829847203}{2048} a^{2} - \frac{500046449383}{2048} a - \frac{265678036177}{2048} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{2} + 2 a + 2\) , \( a^{2} - 2\) , \( -a^{3} + 5 a^{2} - 6 a - 5\) , \( 4 a^{3} - 15 a^{2} + 9 a + 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-a^{3}+5a^{2}-6a-5\right){x}+4a^{3}-15a^{2}+9a+1$ |
| 3.1-a2 |
3.1-a |
$2$ |
$11$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{11} \) |
$14.43250$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
$0 \le r \le 1$ |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
|
\( 11 \) |
$1$ |
$317.9283472$ |
2.780221650 |
\( -\frac{73343}{729} a^{3} + \frac{24131}{729} a^{2} + \frac{615892}{729} a + \frac{18719}{27} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( a\) , \( a^{2} - 4\) , \( -\frac{7}{3} a^{3} + \frac{2}{3} a^{2} + 22 a + 9\) , \( -\frac{10}{3} a^{3} + \frac{5}{3} a^{2} + 32 a + 7\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+a{x}^{2}+\left(-\frac{7}{3}a^{3}+\frac{2}{3}a^{2}+22a+9\right){x}-\frac{10}{3}a^{3}+\frac{5}{3}a^{2}+32a+7$ |
| 121.1-a1 |
121.1-a |
$2$ |
$11$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{4} \) |
$17.46636$ |
$(a^2+a-2)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.1[5] |
$1$ |
\( 1 \) |
$1$ |
$17090.60992$ |
1.16731165 |
\( -24729001 \) |
\( \bigl[a^{4} - 3 a^{2} + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( a^{2} + a - 1\) , \( -15 a^{4} + 38 a^{3} - 10 a^{2} - 19 a\) , \( 94 a^{4} - 262 a^{3} + 77 a^{2} + 174 a - 46\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+2a\right){x}^{2}+\left(-15a^{4}+38a^{3}-10a^{2}-19a\right){x}+94a^{4}-262a^{3}+77a^{2}+174a-46$ |
| 121.1-b1 |
121.1-b |
$2$ |
$11$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{3} \) |
$17.46636$ |
$(a^2+a-2)$ |
$1$ |
$\Z/11\Z$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.1[5] |
$1$ |
\( 2 \) |
$0.089785156$ |
$28099.20145$ |
1.72316863 |
\( -32768 \) |
\( \bigl[0\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( 9 a^{4} - 16 a^{3} - 23 a^{2} + 45 a - 10\) , \( -38 a^{4} + 67 a^{3} + 96 a^{2} - 188 a + 43\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){x}^{2}+\left(9a^{4}-16a^{3}-23a^{2}+45a-10\right){x}-38a^{4}+67a^{3}+96a^{2}-188a+43$ |
| 121.1-d2 |
121.1-d |
$2$ |
$11$ |
\(\Q(\zeta_{11})^+\) |
$5$ |
$[5, 0]$ |
121.1 |
\( 11^{2} \) |
\( - 11^{2} \) |
$17.46636$ |
$(a^2+a-2)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.1[5] |
$1$ |
\( 1 \) |
$1$ |
$16148.59853$ |
1.10297101 |
\( -121 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 4 a - 5\) , \( a^{4} - 3 a^{2}\) , \( -3 a^{4} + 2 a^{3} + 9 a^{2} - 5 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{4}-3a^{2}\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+4a-5\right){x}^{2}+\left(-3a^{4}+2a^{3}+9a^{2}-5a\right){x}+a^{4}-2a^{3}-3a^{2}+6a+1$ |
| 215.1-a1 |
215.1-a |
$2$ |
$11$ |
5.5.24217.1 |
$5$ |
$[5, 0]$ |
215.1 |
\( 5 \cdot 43 \) |
\( 5^{11} \cdot 43 \) |
$23.79264$ |
$(2a^4-a^3-9a^2+2a+3), (3a^4-a^3-14a^2+3a+6)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$3214.638961$ |
1.87792978 |
\( \frac{184085714199821838}{2099609375} a^{4} - \frac{133057170602456514}{2099609375} a^{3} - \frac{824254054347329148}{2099609375} a^{2} + \frac{411684322153514106}{2099609375} a + \frac{254688629703915571}{2099609375} \) |
\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 3\) , \( 3 a^{4} - 2 a^{3} - 14 a^{2} + 6 a + 6\) , \( a^{4} - 4 a^{2} + a + 1\) , \( -34 a^{4} + 13 a^{3} + 163 a^{2} - 30 a - 87\) , \( 51 a^{4} - 20 a^{3} - 248 a^{2} + 44 a + 137\bigr] \) |
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-2a-3\right){x}{y}+\left(a^{4}-4a^{2}+a+1\right){y}={x}^{3}+\left(3a^{4}-2a^{3}-14a^{2}+6a+6\right){x}^{2}+\left(-34a^{4}+13a^{3}+163a^{2}-30a-87\right){x}+51a^{4}-20a^{3}-248a^{2}+44a+137$ |
| 96.1-b2 |
96.1-b |
$2$ |
$11$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{5} \cdot 3^{11} \) |
$26.94600$ |
$(a^2-1), (2)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$4027.885871$ |
1.91670770 |
\( \frac{4635347349833}{354294} a^{4} - \frac{4301816705935}{118098} a^{3} - \frac{2171808483433}{118098} a^{2} + \frac{15742451548358}{177147} a - \frac{11062613396675}{354294} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( -2 a^{4} + 3 a^{3} + 6 a^{2} - 7 a - 2\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( 6 a^{4} - 5 a^{3} - 23 a^{2} + 3 a + 6\) , \( -9 a^{4} + 5 a^{3} + 34 a^{2} + 3 a - 6\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a+1\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+6a^{2}-7a-2\right){x}^{2}+\left(6a^{4}-5a^{3}-23a^{2}+3a+6\right){x}-9a^{4}+5a^{3}+34a^{2}+3a-6$ |
| 134.1-d1 |
134.1-d |
$2$ |
$11$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
134.1 |
\( 2 \cdot 67 \) |
\( - 2^{11} \cdot 67 \) |
$41.63435$ |
$(a^2-2), (a^4-5a^2-2a+5)$ |
$1$ |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$0.678030025$ |
$5646.711968$ |
6.09563702 |
\( -\frac{12513491203}{137216} a^{4} + \frac{33846362449}{137216} a^{3} + \frac{4537858261}{137216} a^{2} - \frac{44786598571}{137216} a + \frac{14496755279}{137216} \) |
\( \bigl[a^{2} - 1\) , \( a^{4} - 5 a^{2} + 2\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -8 a^{4} + 17 a^{3} + 22 a^{2} - 47 a + 15\) , \( -470 a^{4} + 1008 a^{3} + 1201 a^{2} - 2785 a + 825\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{4}-5a^{2}+2\right){x}^{2}+\left(-8a^{4}+17a^{3}+22a^{2}-47a+15\right){x}-470a^{4}+1008a^{3}+1201a^{2}-2785a+825$ |
| 86.1-c1 |
86.1-c |
$2$ |
$11$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
86.1 |
\( 2 \cdot 43 \) |
\( 2^{11} \cdot 43 \) |
$39.84779$ |
$(-a^3+3a), (-a^3+4a-2)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 11 \) |
$1$ |
$10128.90380$ |
3.22369508 |
\( \frac{10735647001}{88064} a^{4} - \frac{15875335341}{88064} a^{3} - \frac{38204684869}{88064} a^{2} + \frac{57838817481}{88064} a - \frac{6696919893}{88064} \) |
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{2} + a + 1\) , \( a^{4} - 3 a^{2} + a\) , \( a^{4} - 4 a^{3} - 3 a^{2} + 9 a - 1\) , \( -a^{4} + a^{2} + 1\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(a^{4}-3a^{2}+a\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(a^{4}-4a^{3}-3a^{2}+9a-1\right){x}-a^{4}+a^{2}+1$ |
| 659.1-a2 |
659.1-a |
$2$ |
$11$ |
6.6.300125.1 |
$6$ |
$[6, 0]$ |
659.1 |
\( 659 \) |
\( 659 \) |
$84.08079$ |
$(a^4-a^3-6a^2+a-1)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$115648.4677$ |
1.74463 |
\( \frac{403485475}{659} a^{5} - \frac{414238319}{659} a^{4} - \frac{2738775928}{659} a^{3} + \frac{847996689}{659} a^{2} + \frac{2267626059}{659} a - \frac{1015901922}{659} \) |
\( \bigl[-5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 27 a - 8\) , \( 6 a^{5} - 2 a^{4} - 43 a^{3} - 17 a^{2} + 28 a + 7\) , \( -a^{5} + 8 a^{3} + 4 a^{2} - 6 a - 1\) , \( 54 a^{5} - 15 a^{4} - 389 a^{3} - 173 a^{2} + 254 a + 75\) , \( 67 a^{5} - 19 a^{4} - 482 a^{3} - 213 a^{2} + 315 a + 93\bigr] \) |
${y}^2+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-27a-8\right){x}{y}+\left(-a^{5}+8a^{3}+4a^{2}-6a-1\right){y}={x}^{3}+\left(6a^{5}-2a^{4}-43a^{3}-17a^{2}+28a+7\right){x}^{2}+\left(54a^{5}-15a^{4}-389a^{3}-173a^{2}+254a+75\right){x}+67a^{5}-19a^{4}-482a^{3}-213a^{2}+315a+93$ |
| 659.2-a2 |
659.2-a |
$2$ |
$11$ |
6.6.300125.1 |
$6$ |
$[6, 0]$ |
659.2 |
\( 659 \) |
\( 659 \) |
$84.08079$ |
$(-a^5+6a^3+7a^2+2a-4)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$115648.4677$ |
1.74463 |
\( -\frac{73991878}{659} a^{5} + \frac{276810831}{659} a^{4} + \frac{172193165}{659} a^{3} - \frac{1198901984}{659} a^{2} + \frac{461638070}{659} a + \frac{164848757}{659} \) |
\( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 19 a - 6\) , \( -7 a^{5} + 2 a^{4} + 50 a^{3} + 22 a^{2} - 30 a - 8\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 27 a - 7\) , \( -10 a^{5} + 3 a^{4} + 72 a^{3} + 32 a^{2} - 45 a - 14\) , \( -7 a^{5} + 3 a^{4} + 50 a^{3} + 18 a^{2} - 31 a - 9\bigr] \) |
${y}^2+\left(-4a^{5}+a^{4}+29a^{3}+14a^{2}-19a-6\right){x}{y}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-27a-7\right){y}={x}^{3}+\left(-7a^{5}+2a^{4}+50a^{3}+22a^{2}-30a-8\right){x}^{2}+\left(-10a^{5}+3a^{4}+72a^{3}+32a^{2}-45a-14\right){x}-7a^{5}+3a^{4}+50a^{3}+18a^{2}-31a-9$ |
| 659.3-a1 |
659.3-a |
$2$ |
$11$ |
6.6.300125.1 |
$6$ |
$[6, 0]$ |
659.3 |
\( 659 \) |
\( 659 \) |
$84.08079$ |
$(5a^5-2a^4-35a^3-11a^2+21a+2)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$115648.4677$ |
1.74463 |
\( -\frac{39173125}{659} a^{5} - \frac{59724405}{659} a^{4} + \frac{442335847}{659} a^{3} + \frac{305264178}{659} a^{2} - \frac{322851510}{659} a - \frac{102431212}{659} \) |
\( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 13 a^{2} - 18 a - 5\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 8\) , \( -8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 11\) , \( -2 a^{5} + 15 a^{3} + 10 a^{2} - 9 a - 3\) , \( 0\bigr] \) |
${y}^2+\left(-4a^{5}+a^{4}+29a^{3}+13a^{2}-18a-5\right){x}{y}+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-38a-11\right){y}={x}^{3}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-26a-8\right){x}^{2}+\left(-2a^{5}+15a^{3}+10a^{2}-9a-3\right){x}$ |
| 659.4-a2 |
659.4-a |
$2$ |
$11$ |
6.6.300125.1 |
$6$ |
$[6, 0]$ |
659.4 |
\( 659 \) |
\( 659 \) |
$84.08079$ |
$(2a^5-a^4-14a^3-4a^2+9a-1)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$115648.4677$ |
1.74463 |
\( -\frac{2741616006}{659} a^{5} + \frac{764786792}{659} a^{4} + \frac{19748932201}{659} a^{3} + \frac{8739365128}{659} a^{2} - \frac{12906633295}{659} a - \frac{3808072212}{659} \) |
\( \bigl[-6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 29 a - 7\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + a\) , \( -a^{5} + 8 a^{3} + 4 a^{2} - 6 a\) , \( 3 a^{5} - 2 a^{4} - 20 a^{3} - 3 a^{2} + 10 a + 4\) , \( a^{5} - a^{4} - 6 a^{3} + 2 a + 1\bigr] \) |
${y}^2+\left(-6a^{5}+2a^{4}+43a^{3}+17a^{2}-29a-7\right){x}{y}+\left(-a^{5}+8a^{3}+4a^{2}-6a\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+a^{2}+a\right){x}^{2}+\left(3a^{5}-2a^{4}-20a^{3}-3a^{2}+10a+4\right){x}+a^{5}-a^{4}-6a^{3}+2a+1$ |
| 659.5-a2 |
659.5-a |
$2$ |
$11$ |
6.6.300125.1 |
$6$ |
$[6, 0]$ |
659.5 |
\( 659 \) |
\( 659 \) |
$84.08079$ |
$(5a^5-2a^4-37a^3-10a^2+31a+3)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$115648.4677$ |
1.74463 |
\( \frac{2554288959}{659} a^{5} - \frac{583518151}{659} a^{4} - \frac{18340840768}{659} a^{3} - \frac{9021388012}{659} a^{2} + \frac{10968703012}{659} a + \frac{3290061833}{659} \) |
\( \bigl[-a^{5} + 8 a^{3} + 4 a^{2} - 6 a\) , \( a^{4} - a^{3} - 6 a^{2} - a + 3\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 19 a - 7\) , \( 2 a^{4} - 4 a^{3} - 8 a^{2} + 3 a + 4\) , \( -5 a^{5} + 3 a^{4} + 32 a^{3} + 12 a^{2} - 20 a - 6\bigr] \) |
${y}^2+\left(-a^{5}+8a^{3}+4a^{2}-6a\right){x}{y}+\left(-4a^{5}+a^{4}+29a^{3}+14a^{2}-19a-7\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}-a+3\right){x}^{2}+\left(2a^{4}-4a^{3}-8a^{2}+3a+4\right){x}-5a^{5}+3a^{4}+32a^{3}+12a^{2}-20a-6$ |
| 659.6-a1 |
659.6-a |
$2$ |
$11$ |
6.6.300125.1 |
$6$ |
$[6, 0]$ |
659.6 |
\( 659 \) |
\( 659 \) |
$84.08079$ |
$(2a^5-a^4-15a^3-3a^2+13a+1)$ |
0 |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$115648.4677$ |
1.74463 |
\( -\frac{102993425}{659} a^{5} + \frac{15883252}{659} a^{4} + \frac{716155483}{659} a^{3} + \frac{327664001}{659} a^{2} - \frac{468482336}{659} a - \frac{138998659}{659} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 9 a - 2\) , \( 3 a^{5} - 2 a^{4} - 20 a^{3} - 3 a^{2} + 12 a\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 8\) , \( -8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 41 a - 9\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 30 a - 10\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}+4a^{2}-9a-2\right){x}{y}+\left(-5a^{5}+a^{4}+37a^{3}+18a^{2}-26a-8\right){y}={x}^{3}+\left(3a^{5}-2a^{4}-20a^{3}-3a^{2}+12a\right){x}^{2}+\left(-8a^{5}+2a^{4}+58a^{3}+27a^{2}-41a-9\right){x}-6a^{5}+a^{4}+44a^{3}+23a^{2}-30a-10$ |
| 859.1-a1 |
859.1-a |
$2$ |
$11$ |
\(\Q(\zeta_{13})^+\) |
$6$ |
$[6, 0]$ |
859.1 |
\( 859 \) |
\( 859 \) |
$95.60847$ |
$(-2a^5+8a^3+2a^2-5a-4)$ |
$1$ |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
$1$ |
\( 1 \) |
$0.416738802$ |
$127184.0031$ |
4.31325 |
\( \frac{45538889}{859} a^{5} - \frac{105723117}{859} a^{4} - \frac{74076507}{859} a^{3} + \frac{211921154}{859} a^{2} + \frac{31322898}{859} a - \frac{84241502}{859} \) |
\( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 2 a\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a\) , \( a^{5} - 4 a^{3} + 3 a + 1\) , \( -3 a^{5} - 4 a^{4} + 9 a^{3} + 11 a^{2} - 2 a - 1\) , \( a^{5} - 2 a^{3} + 2 a^{2}\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+2a\right){x}{y}+\left(a^{5}-4a^{3}+3a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a\right){x}^{2}+\left(-3a^{5}-4a^{4}+9a^{3}+11a^{2}-2a-1\right){x}+a^{5}-2a^{3}+2a^{2}$ |
*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.
