| 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 |
| 1.1-a1 |
1.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.29334$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 1 \) |
$1$ |
$153.7642850$ |
1.478502740 |
\( -\frac{47968256}{5} a^{3} - \frac{82358016}{5} a^{2} + \frac{125586176}{5} a - \frac{12910272}{5} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{17}{5}\) , \( \frac{2}{5} a^{3} - \frac{3}{5} a^{2} - \frac{22}{5} a + \frac{4}{5}\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{3}{5}\) , \( -a^{3} + a^{2} + 10 a - 2\) , \( \frac{11}{5} a^{3} - \frac{14}{5} a^{2} - \frac{111}{5} a + \frac{17}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{6}{5}a-\frac{17}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{3}{5}\right){y}={x}^{3}+\left(\frac{2}{5}a^{3}-\frac{3}{5}a^{2}-\frac{22}{5}a+\frac{4}{5}\right){x}^{2}+\left(-a^{3}+a^{2}+10a-2\right){x}+\frac{11}{5}a^{3}-\frac{14}{5}a^{2}-\frac{111}{5}a+\frac{17}{5}$ |
| 1.1-a2 |
1.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.29334$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 1 \) |
$1$ |
$153.7642850$ |
1.478502740 |
\( \frac{397131776}{5} a^{3} - \frac{441387264}{5} a^{2} - \frac{3966384896}{5} a + \frac{446935872}{5} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{17}{5}\) , \( \frac{2}{5} a^{3} - \frac{3}{5} a^{2} - \frac{22}{5} a + \frac{4}{5}\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{3}{5}\) , \( \frac{2}{5} a^{3} - \frac{3}{5} a^{2} - \frac{12}{5} a + \frac{9}{5}\) , \( -a^{2} - 2 a + 1\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{6}{5}a-\frac{17}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{3}{5}\right){y}={x}^{3}+\left(\frac{2}{5}a^{3}-\frac{3}{5}a^{2}-\frac{22}{5}a+\frac{4}{5}\right){x}^{2}+\left(\frac{2}{5}a^{3}-\frac{3}{5}a^{2}-\frac{12}{5}a+\frac{9}{5}\right){x}-a^{2}-2a+1$ |
| 1.1-a3 |
1.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.29334$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 1 \) |
$1$ |
$153.7642850$ |
1.478502740 |
\( -\frac{397131776}{5} a^{3} + \frac{750008064}{5} a^{2} + \frac{3657764096}{5} a - \frac{3563704512}{5} \) |
\( \bigl[\frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{8}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{4}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{17}{5} a - \frac{4}{5}\) , \( -2 a^{3} + 3 a^{2} + 20 a - 3\) , \( -\frac{3}{5} a^{3} + \frac{2}{5} a^{2} + \frac{43}{5} a - \frac{6}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{8}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{17}{5}a-\frac{4}{5}\right){y}={x}^{3}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{4}{5}\right){x}^{2}+\left(-2a^{3}+3a^{2}+20a-3\right){x}-\frac{3}{5}a^{3}+\frac{2}{5}a^{2}+\frac{43}{5}a-\frac{6}{5}$ |
| 1.1-a4 |
1.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.29334$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 1 \) |
$1$ |
$153.7642850$ |
1.478502740 |
\( \frac{47968256}{5} a^{3} - \frac{226262784}{5} a^{2} + \frac{183034624}{5} a - \frac{17650368}{5} \) |
\( \bigl[\frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{8}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{4}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{17}{5} a - \frac{4}{5}\) , \( -\frac{3}{5} a^{3} + \frac{2}{5} a^{2} + \frac{43}{5} a + \frac{29}{5}\) , \( -\frac{7}{5} a^{3} + \frac{13}{5} a^{2} + \frac{72}{5} a - \frac{49}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{8}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{17}{5}a-\frac{4}{5}\right){y}={x}^{3}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{4}{5}\right){x}^{2}+\left(-\frac{3}{5}a^{3}+\frac{2}{5}a^{2}+\frac{43}{5}a+\frac{29}{5}\right){x}-\frac{7}{5}a^{3}+\frac{13}{5}a^{2}+\frac{72}{5}a-\frac{49}{5}$ |
| 1.1-b1 |
1.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.29334$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$3, 5$ |
3Ns, 5B.1.2 |
$225$ |
\( 1 \) |
$1$ |
$0.541914270$ |
1.172410680 |
\( -23788477376 \) |
\( \bigl[\frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{8}{5}\) , \( a - 1\) , \( 1\) , \( -\frac{241}{5} a^{3} - \frac{536}{5} a^{2} + \frac{256}{5} a - \frac{177}{5}\) , \( -\frac{7111}{5} a^{3} - \frac{13036}{5} a^{2} + \frac{16341}{5} a - \frac{1997}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{8}{5}\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{241}{5}a^{3}-\frac{536}{5}a^{2}+\frac{256}{5}a-\frac{177}{5}\right){x}-\frac{7111}{5}a^{3}-\frac{13036}{5}a^{2}+\frac{16341}{5}a-\frac{1997}{5}$ |
| 1.1-b2 |
1.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$9.29334$ |
$\textsf{none}$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$3, 5$ |
3Ns, 5B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$338.6964188$ |
1.172410680 |
\( 64 \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{17}{5}\) , \( -a\) , \( 1\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{21}{5} a + \frac{22}{5}\) , \( \frac{1}{5} a^{3} - \frac{4}{5} a^{2} - \frac{1}{5} a + \frac{2}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{6}{5}a-\frac{17}{5}\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{21}{5}a+\frac{22}{5}\right){x}+\frac{1}{5}a^{3}-\frac{4}{5}a^{2}-\frac{1}{5}a+\frac{2}{5}$ |
| 4.1-a1 |
4.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$11.05171$ |
$(-2/5a^3+3/5a^2+17/5a-9/5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3Cs, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$815.4744629$ |
0.627288048 |
\( \frac{1331}{8} \) |
\( \bigl[-\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{9}{5}\) , \( \frac{2}{5} a^{3} - \frac{3}{5} a^{2} - \frac{22}{5} a + \frac{4}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{4}{5}\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{9}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{4}{5}\right){y}={x}^{3}+\left(\frac{2}{5}a^{3}-\frac{3}{5}a^{2}-\frac{22}{5}a+\frac{4}{5}\right){x}^{2}$ |
| 4.1-a2 |
4.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{60} \) |
$11.05171$ |
$(-2/5a^3+3/5a^2+17/5a-9/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3Cs, 5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$1.304759140$ |
0.627288048 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[-\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{9}{5}\) , \( \frac{2}{5} a^{3} - \frac{3}{5} a^{2} - \frac{22}{5} a + \frac{4}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{4}{5}\) , \( 30 a^{3} - 45 a^{2} - 330 a + 35\) , \( \frac{866}{5} a^{3} - \frac{1299}{5} a^{2} - \frac{9526}{5} a + \frac{1067}{5}\bigr] \) |
${y}^2+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{9}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{4}{5}\right){y}={x}^{3}+\left(\frac{2}{5}a^{3}-\frac{3}{5}a^{2}-\frac{22}{5}a+\frac{4}{5}\right){x}^{2}+\left(30a^{3}-45a^{2}-330a+35\right){x}+\frac{866}{5}a^{3}-\frac{1299}{5}a^{2}-\frac{9526}{5}a+\frac{1067}{5}$ |
| 4.1-a3 |
4.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$11.05171$ |
$(-2/5a^3+3/5a^2+17/5a-9/5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$815.4744629$ |
0.627288048 |
\( -\frac{461373}{5} a^{3} + \frac{1384119}{10} a^{2} + \frac{5075103}{5} a - \frac{9466337}{10} \) |
\( \bigl[1\) , \( 1\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{9}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{24}{5}\) , \( \frac{2}{5} a^{3} - \frac{3}{5} a^{2} - \frac{22}{5} a + \frac{14}{5}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{9}{5}\right){y}={x}^{3}+{x}^{2}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{24}{5}\right){x}+\frac{2}{5}a^{3}-\frac{3}{5}a^{2}-\frac{22}{5}a+\frac{14}{5}$ |
| 4.1-a4 |
4.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{20} \) |
$11.05171$ |
$(-2/5a^3+3/5a^2+17/5a-9/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$1.304759140$ |
0.627288048 |
\( \frac{1250637664527933}{80} a^{3} - \frac{3751912993583799}{160} a^{2} - \frac{13757014309807263}{80} a + \frac{1554618788036141}{80} \) |
\( \bigl[1\) , \( 1\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{9}{5}\) , \( \frac{58}{5} a^{3} - \frac{87}{5} a^{2} - \frac{638}{5} a + \frac{271}{5}\) , \( \frac{104}{5} a^{3} - \frac{156}{5} a^{2} - \frac{1144}{5} a - \frac{62}{5}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{9}{5}\right){y}={x}^{3}+{x}^{2}+\left(\frac{58}{5}a^{3}-\frac{87}{5}a^{2}-\frac{638}{5}a+\frac{271}{5}\right){x}+\frac{104}{5}a^{3}-\frac{156}{5}a^{2}-\frac{1144}{5}a-\frac{62}{5}$ |
| 4.1-a5 |
4.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{20} \) |
$11.05171$ |
$(-2/5a^3+3/5a^2+17/5a-9/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$1.304759140$ |
0.627288048 |
\( -\frac{1250637664527933}{80} a^{3} + \frac{3751912993583799}{160} a^{2} + \frac{13757014309807263}{80} a - \frac{25655428708070177}{160} \) |
\( \bigl[1\) , \( 1\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{4}{5}\) , \( -\frac{56}{5} a^{3} + \frac{84}{5} a^{2} + \frac{616}{5} a - \frac{387}{5}\) , \( -\frac{102}{5} a^{3} + \frac{153}{5} a^{2} + \frac{1122}{5} a - \frac{1249}{5}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{4}{5}\right){y}={x}^{3}+{x}^{2}+\left(-\frac{56}{5}a^{3}+\frac{84}{5}a^{2}+\frac{616}{5}a-\frac{387}{5}\right){x}-\frac{102}{5}a^{3}+\frac{153}{5}a^{2}+\frac{1122}{5}a-\frac{1249}{5}$ |
| 4.1-a6 |
4.1-a |
$6$ |
$45$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$11.05171$ |
$(-2/5a^3+3/5a^2+17/5a-9/5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$815.4744629$ |
0.627288048 |
\( \frac{461373}{5} a^{3} - \frac{1384119}{10} a^{2} - \frac{5075103}{5} a + \frac{572621}{5} \) |
\( \bigl[1\) , \( 1\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{4}{5}\) , \( \frac{4}{5} a^{3} - \frac{6}{5} a^{2} - \frac{44}{5} a + \frac{8}{5}\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{4}{5}\right){y}={x}^{3}+{x}^{2}+\left(\frac{4}{5}a^{3}-\frac{6}{5}a^{2}-\frac{44}{5}a+\frac{8}{5}\right){x}$ |
| 17.1-a1 |
17.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{10} \) |
$13.24274$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$242.4088719$ |
1.165427268 |
\( \frac{3801370127425654473}{10079969502245} a^{3} - \frac{7221424493129596622}{10079969502245} a^{2} - \frac{34967321138050896153}{10079969502245} a + \frac{34548459725185600066}{10079969502245} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{12}{5}\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{13}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{17}{5} a - \frac{9}{5}\) , \( -2 a^{3} + 10 a^{2} + 8 a - 8\) , \( \frac{76}{5} a^{3} - \frac{304}{5} a^{2} + \frac{159}{5} a + \frac{32}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{12}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{17}{5}a-\frac{9}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{13}{5}\right){x}^{2}+\left(-2a^{3}+10a^{2}+8a-8\right){x}+\frac{76}{5}a^{3}-\frac{304}{5}a^{2}+\frac{159}{5}a+\frac{32}{5}$ |
| 17.1-a2 |
17.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{2} \) |
$13.24274$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$242.4088719$ |
1.165427268 |
\( \frac{17250812019971382}{1445} a^{3} + \frac{29619513007034002}{1445} a^{2} - \frac{45161959121873127}{1445} a + \frac{4641055424640274}{1445} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{12}{5}\) , \( -1\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{3}{5}\) , \( -33 a^{3} + 71 a^{2} + 299 a - 381\) , \( -\frac{1403}{5} a^{3} + \frac{2787}{5} a^{2} + \frac{12803}{5} a - \frac{13911}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{12}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{3}{5}\right){y}={x}^{3}-{x}^{2}+\left(-33a^{3}+71a^{2}+299a-381\right){x}-\frac{1403}{5}a^{3}+\frac{2787}{5}a^{2}+\frac{12803}{5}a-\frac{13911}{5}$ |
| 17.1-a3 |
17.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$13.24274$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$484.8177438$ |
1.165427268 |
\( -\frac{3927595156}{85} a^{3} + \frac{18760072909}{85} a^{2} - \frac{15222416164}{85} a + \frac{1468800088}{85} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{12}{5}\) , \( -1\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{3}{5}\) , \( -a^{3} + 3 a^{2} + 12 a - 17\) , \( -\frac{36}{5} a^{3} + \frac{79}{5} a^{2} + \frac{341}{5} a - \frac{362}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{12}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{3}{5}\right){y}={x}^{3}-{x}^{2}+\left(-a^{3}+3a^{2}+12a-17\right){x}-\frac{36}{5}a^{3}+\frac{79}{5}a^{2}+\frac{341}{5}a-\frac{362}{5}$ |
| 17.1-a4 |
17.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{5} \) |
$13.24274$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$484.8177438$ |
1.165427268 |
\( \frac{8904033506}{7099285} a^{3} + \frac{25242669241}{7099285} a^{2} - \frac{23183713636}{7099285} a - \frac{5575147073}{7099285} \) |
\( \bigl[1\) , \( -\frac{3}{5} a^{3} + \frac{2}{5} a^{2} + \frac{33}{5} a - \frac{6}{5}\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{17}{5}\) , \( -\frac{17}{5} a^{3} + \frac{28}{5} a^{2} + \frac{157}{5} a - \frac{104}{5}\) , \( \frac{21}{5} a^{3} - \frac{49}{5} a^{2} - \frac{181}{5} a + \frac{267}{5}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{6}{5}a-\frac{17}{5}\right){y}={x}^{3}+\left(-\frac{3}{5}a^{3}+\frac{2}{5}a^{2}+\frac{33}{5}a-\frac{6}{5}\right){x}^{2}+\left(-\frac{17}{5}a^{3}+\frac{28}{5}a^{2}+\frac{157}{5}a-\frac{104}{5}\right){x}+\frac{21}{5}a^{3}-\frac{49}{5}a^{2}-\frac{181}{5}a+\frac{267}{5}$ |
| 17.1-b1 |
17.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{5} \) |
$13.24274$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$177.3048262$ |
1.704854098 |
\( -\frac{10821661047}{7099285} a^{3} - \frac{5675610622}{7099285} a^{2} + \frac{175127911387}{7099285} a - \frac{7164211504}{7099285} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{17}{5}\) , \( -\frac{3}{5} a^{3} + \frac{2}{5} a^{2} + \frac{33}{5} a - \frac{6}{5}\) , \( -\frac{4}{5} a^{3} + \frac{6}{5} a^{2} + \frac{39}{5} a - \frac{13}{5}\) , \( -\frac{3}{5} a^{3} + \frac{12}{5} a^{2} + \frac{43}{5} a - \frac{6}{5}\) , \( a^{3} - 6 a + 1\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{17}{5}\right){x}{y}+\left(-\frac{4}{5}a^{3}+\frac{6}{5}a^{2}+\frac{39}{5}a-\frac{13}{5}\right){y}={x}^{3}+\left(-\frac{3}{5}a^{3}+\frac{2}{5}a^{2}+\frac{33}{5}a-\frac{6}{5}\right){x}^{2}+\left(-\frac{3}{5}a^{3}+\frac{12}{5}a^{2}+\frac{43}{5}a-\frac{6}{5}\right){x}+a^{3}-6a+1$ |
| 17.1-b2 |
17.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( -17 \) |
$13.24274$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$177.3048262$ |
1.704854098 |
\( -\frac{5789959578}{85} a^{3} + \frac{6484492012}{85} a^{2} + \frac{57765231773}{85} a - \frac{7049815586}{85} \) |
\( \bigl[\frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{3}{5}\) , \( -\frac{1}{5} a^{3} - \frac{1}{5} a^{2} + \frac{16}{5} a + \frac{3}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{17}{5} a - \frac{9}{5}\) , \( -\frac{7}{5} a^{3} + \frac{13}{5} a^{2} + \frac{67}{5} a - \frac{39}{5}\) , \( -\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{46}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{3}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{17}{5}a-\frac{9}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}-\frac{1}{5}a^{2}+\frac{16}{5}a+\frac{3}{5}\right){x}^{2}+\left(-\frac{7}{5}a^{3}+\frac{13}{5}a^{2}+\frac{67}{5}a-\frac{39}{5}\right){x}-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{46}{5}$ |
| 17.1-c1 |
17.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{2} \) |
$13.24274$ |
$(a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$581.0603335$ |
0.310395477 |
\( \frac{3210711531231}{289} a^{3} - \frac{6063836627233}{289} a^{2} - \frac{29571918659584}{289} a + \frac{28813786374912}{289} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{1}{5} a^{3} - \frac{1}{5} a^{2} + \frac{16}{5} a + \frac{8}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{4}{5}\) , \( \frac{29}{5} a^{3} - \frac{31}{5} a^{2} - \frac{284}{5} a + \frac{43}{5}\) , \( \frac{127}{5} a^{3} - \frac{138}{5} a^{2} - \frac{1262}{5} a + \frac{144}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{4}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}-\frac{1}{5}a^{2}+\frac{16}{5}a+\frac{8}{5}\right){x}^{2}+\left(\frac{29}{5}a^{3}-\frac{31}{5}a^{2}-\frac{284}{5}a+\frac{43}{5}\right){x}+\frac{127}{5}a^{3}-\frac{138}{5}a^{2}-\frac{1262}{5}a+\frac{144}{5}$ |
| 17.1-c2 |
17.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$13.24274$ |
$(a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1162.120667$ |
0.310395477 |
\( -\frac{630546}{17} a^{3} + \frac{1197307}{17} a^{2} + \frac{5801040}{17} a - \frac{5692366}{17} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{1}{5} a^{3} - \frac{1}{5} a^{2} + \frac{16}{5} a + \frac{8}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{4}{5}\) , \( \frac{4}{5} a^{3} - \frac{6}{5} a^{2} - \frac{34}{5} a + \frac{43}{5}\) , \( \frac{7}{5} a^{3} - \frac{8}{5} a^{2} - \frac{62}{5} a + \frac{29}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{4}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}-\frac{1}{5}a^{2}+\frac{16}{5}a+\frac{8}{5}\right){x}^{2}+\left(\frac{4}{5}a^{3}-\frac{6}{5}a^{2}-\frac{34}{5}a+\frac{43}{5}\right){x}+\frac{7}{5}a^{3}-\frac{8}{5}a^{2}-\frac{62}{5}a+\frac{29}{5}$ |
| 17.1-c3 |
17.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$13.24274$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$14.34716872$ |
0.310395477 |
\( \frac{12505804884532}{4913} a^{3} - \frac{13623039948907}{4913} a^{2} - \frac{125268909832442}{4913} a + \frac{14111579527425}{4913} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{1}{5} a^{3} - \frac{1}{5} a^{2} + \frac{16}{5} a + \frac{8}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{4}{5}\) , \( \frac{154}{5} a^{3} - \frac{181}{5} a^{2} - \frac{1534}{5} a + \frac{218}{5}\) , \( \frac{1142}{5} a^{3} - \frac{1293}{5} a^{2} - \frac{11447}{5} a + \frac{1324}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{4}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}-\frac{1}{5}a^{2}+\frac{16}{5}a+\frac{8}{5}\right){x}^{2}+\left(\frac{154}{5}a^{3}-\frac{181}{5}a^{2}-\frac{1534}{5}a+\frac{218}{5}\right){x}+\frac{1142}{5}a^{3}-\frac{1293}{5}a^{2}-\frac{11447}{5}a+\frac{1324}{5}$ |
| 17.1-c4 |
17.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{6} \) |
$13.24274$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$7.173584364$ |
0.310395477 |
\( -\frac{1241199546225878340287683226}{24137569} a^{3} + \frac{1379516247722765785040555200}{24137569} a^{2} + \frac{12396581736100767502995556457}{24137569} a - \frac{1396863067472854518705564769}{24137569} \) |
\( \bigl[-\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{4}{5}\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{12}{5}\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{17}{5}\) , \( -25 a^{3} + 16 a^{2} + 143 a - 230\) , \( \frac{224}{5} a^{3} - \frac{3231}{5} a^{2} - \frac{7984}{5} a + \frac{6638}{5}\bigr] \) |
${y}^2+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{4}{5}\right){x}{y}+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{6}{5}a-\frac{17}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{12}{5}\right){x}^{2}+\left(-25a^{3}+16a^{2}+143a-230\right){x}+\frac{224}{5}a^{3}-\frac{3231}{5}a^{2}-\frac{7984}{5}a+\frac{6638}{5}$ |
| 17.2-a1 |
17.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{2} \) |
$13.24274$ |
$(4/5a^3-6/5a^2-39/5a+13/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$242.4088719$ |
1.165427268 |
\( -\frac{142823351287871138}{1445} a^{3} + \frac{158739295894815632}{1445} a^{2} + \frac{1426459891068770443}{1445} a - \frac{160735369090740316}{1445} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{12}{5}\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{13}{5}\) , \( 1\) , \( \frac{19}{5} a^{3} - \frac{121}{5} a^{2} + \frac{156}{5} a - \frac{32}{5}\) , \( \frac{163}{5} a^{3} - \frac{1032}{5} a^{2} + \frac{832}{5} a - \frac{44}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{12}{5}\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{13}{5}\right){x}^{2}+\left(\frac{19}{5}a^{3}-\frac{121}{5}a^{2}+\frac{156}{5}a-\frac{32}{5}\right){x}+\frac{163}{5}a^{3}-\frac{1032}{5}a^{2}+\frac{832}{5}a-\frac{44}{5}$ |
| 17.2-a2 |
17.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$13.24274$ |
$(4/5a^3-6/5a^2-39/5a+13/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$484.8177438$ |
1.165427268 |
\( \frac{32518231008}{85} a^{3} - \frac{61646026687}{85} a^{2} - \frac{299274578208}{85} a + \frac{294161819576}{85} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{12}{5}\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{13}{5}\) , \( 1\) , \( -\frac{1}{5} a^{3} + \frac{9}{5} a^{2} + \frac{51}{5} a - \frac{22}{5}\) , \( \frac{16}{5} a^{3} - \frac{29}{5} a^{2} - \frac{51}{5} a + \frac{42}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{12}{5}\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{13}{5}\right){x}^{2}+\left(-\frac{1}{5}a^{3}+\frac{9}{5}a^{2}+\frac{51}{5}a-\frac{22}{5}\right){x}+\frac{16}{5}a^{3}-\frac{29}{5}a^{2}-\frac{51}{5}a+\frac{42}{5}$ |
| 17.2-a3 |
17.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{10} \) |
$13.24274$ |
$(4/5a^3-6/5a^2-39/5a+13/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$242.4088719$ |
1.165427268 |
\( -\frac{461334641886496037}{10079969502245} a^{3} + \frac{2211371264820858968}{10079969502245} a^{2} - \frac{1773069202879846643}{10079969502245} a + \frac{172595243369773646}{10079969502245} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{12}{5}\) , \( -1\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{17}{5}\) , \( \frac{56}{5} a^{3} - \frac{99}{5} a^{2} - \frac{496}{5} a + \frac{462}{5}\) , \( -\frac{549}{5} a^{3} + \frac{1046}{5} a^{2} + \frac{5069}{5} a - \frac{4938}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{12}{5}\right){x}{y}+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{6}{5}a-\frac{17}{5}\right){y}={x}^{3}-{x}^{2}+\left(\frac{56}{5}a^{3}-\frac{99}{5}a^{2}-\frac{496}{5}a+\frac{462}{5}\right){x}-\frac{549}{5}a^{3}+\frac{1046}{5}a^{2}+\frac{5069}{5}a-\frac{4938}{5}$ |
| 17.2-a4 |
17.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{5} \) |
$13.24274$ |
$(4/5a^3-6/5a^2-39/5a+13/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$484.8177438$ |
1.165427268 |
\( -\frac{81783466038}{7099285} a^{3} + \frac{84076479557}{7099285} a^{2} + \frac{824857471488}{7099285} a - \frac{27681700021}{7099285} \) |
\( \bigl[1\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{22}{5}\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{17}{5}\) , \( \frac{6}{5} a^{3} - \frac{14}{5} a^{2} - \frac{31}{5} a + \frac{37}{5}\) , \( -a^{3} + 5 a^{2} + a - 5\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{6}{5}a-\frac{17}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{22}{5}\right){x}^{2}+\left(\frac{6}{5}a^{3}-\frac{14}{5}a^{2}-\frac{31}{5}a+\frac{37}{5}\right){x}-a^{3}+5a^{2}+a-5$ |
| 17.2-b1 |
17.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{5} \) |
$13.24274$ |
$(4/5a^3-6/5a^2-39/5a+13/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$177.3048262$ |
1.704854098 |
\( -\frac{38166891189}{7099285} a^{3} + \frac{79158438976}{7099285} a^{2} + \frac{363746163209}{7099285} a - \frac{349298769068}{7099285} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{17}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{14}{5}\) , \( -\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{21}{5} a^{3} + \frac{29}{5} a^{2} + \frac{211}{5} a - \frac{52}{5}\) , \( \frac{9}{5} a^{3} - \frac{6}{5} a^{2} - \frac{79}{5} a - \frac{7}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{17}{5}\right){x}{y}+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){y}={x}^{3}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{14}{5}\right){x}^{2}+\left(-\frac{21}{5}a^{3}+\frac{29}{5}a^{2}+\frac{211}{5}a-\frac{52}{5}\right){x}+\frac{9}{5}a^{3}-\frac{6}{5}a^{2}-\frac{79}{5}a-\frac{7}{5}$ |
| 17.2-b2 |
17.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( -17 \) |
$13.24274$ |
$(4/5a^3-6/5a^2-39/5a+13/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$177.3048262$ |
1.704854098 |
\( \frac{709857174}{85} a^{3} + \frac{1135661594}{85} a^{2} - \frac{1884105329}{85} a + \frac{194886248}{85} \) |
\( \bigl[\frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{3}{5}\) , \( -\frac{4}{5} a^{3} + \frac{6}{5} a^{2} + \frac{39}{5} a - \frac{23}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{17}{5} a - \frac{9}{5}\) , \( \frac{1}{5} a^{3} - \frac{4}{5} a^{2} + \frac{4}{5} a + \frac{22}{5}\) , \( -\frac{1}{5} a^{3} - \frac{1}{5} a^{2} + \frac{16}{5} a - \frac{12}{5}\bigr] \) |
${y}^2+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{3}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{17}{5}a-\frac{9}{5}\right){y}={x}^{3}+\left(-\frac{4}{5}a^{3}+\frac{6}{5}a^{2}+\frac{39}{5}a-\frac{23}{5}\right){x}^{2}+\left(\frac{1}{5}a^{3}-\frac{4}{5}a^{2}+\frac{4}{5}a+\frac{22}{5}\right){x}-\frac{1}{5}a^{3}-\frac{1}{5}a^{2}+\frac{16}{5}a-\frac{12}{5}$ |
| 17.2-c1 |
17.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17^{3} \) |
$13.24274$ |
$(4/5a^3-6/5a^2-39/5a+13/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$14.34716872$ |
0.310395477 |
\( -\frac{7193420678544}{24565} a^{3} - \frac{14888205871639}{24565} a^{2} + \frac{17652907976934}{24565} a + \frac{13590263576257}{24565} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{9}{5}\) , \( -\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{13}{5} a^{3} - \frac{28}{5} a^{2} - \frac{2}{5} a - \frac{76}{5}\) , \( -27 a^{3} - 60 a^{2} + 28 a - 24\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){x}{y}+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){y}={x}^{3}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{9}{5}\right){x}^{2}+\left(-\frac{13}{5}a^{3}-\frac{28}{5}a^{2}-\frac{2}{5}a-\frac{76}{5}\right){x}-27a^{3}-60a^{2}+28a-24$ |
| 17.2-c2 |
17.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{2} \) |
$13.24274$ |
$(4/5a^3-6/5a^2-39/5a+13/5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$581.0603335$ |
0.310395477 |
\( -\frac{1938997758127}{1445} a^{3} + \frac{9147343289123}{1445} a^{2} - \frac{7400565580388}{1445} a + \frac{713965990966}{1445} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{9}{5}\) , \( -\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{8}{5} a^{3} + \frac{2}{5} a^{2} + \frac{68}{5} a - \frac{41}{5}\) , \( -\frac{22}{5} a^{3} - \frac{27}{5} a^{2} + \frac{77}{5} a - \frac{24}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){x}{y}+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){y}={x}^{3}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{9}{5}\right){x}^{2}+\left(-\frac{8}{5}a^{3}+\frac{2}{5}a^{2}+\frac{68}{5}a-\frac{41}{5}\right){x}-\frac{22}{5}a^{3}-\frac{27}{5}a^{2}+\frac{77}{5}a-\frac{24}{5}$ |
| 17.2-c3 |
17.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$13.24274$ |
$(4/5a^3-6/5a^2-39/5a+13/5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1162.120667$ |
0.310395477 |
\( \frac{381182}{85} a^{3} - \frac{1829213}{85} a^{2} + \frac{1481828}{85} a + \frac{15174}{85} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{9}{5}\) , \( -\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{38}{5} a - \frac{31}{5}\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{16}{5} a - \frac{17}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){x}{y}+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){y}={x}^{3}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{9}{5}\right){x}^{2}+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{38}{5}a-\frac{31}{5}\right){x}-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{16}{5}a-\frac{17}{5}$ |
| 17.2-c4 |
17.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{6} \) |
$13.24274$ |
$(4/5a^3-6/5a^2-39/5a+13/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$7.173584364$ |
0.310395477 |
\( \frac{749587644870392160801298542}{120687845} a^{3} + \frac{1287033890774670385752900382}{120687845} a^{2} - \frac{1962397731654842567969488817}{120687845} a + \frac{201665273832168517002410229}{120687845} \) |
\( \bigl[1\) , \( -\frac{3}{5} a^{3} + \frac{2}{5} a^{2} + \frac{33}{5} a + \frac{4}{5}\) , \( 1\) , \( \frac{1921}{5} a^{3} - \frac{9144}{5} a^{2} + \frac{7694}{5} a - \frac{923}{5}\) , \( -19895 a^{3} + 93813 a^{2} - 75771 a + 7205\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{3}{5}a^{3}+\frac{2}{5}a^{2}+\frac{33}{5}a+\frac{4}{5}\right){x}^{2}+\left(\frac{1921}{5}a^{3}-\frac{9144}{5}a^{2}+\frac{7694}{5}a-\frac{923}{5}\right){x}-19895a^{3}+93813a^{2}-75771a+7205$ |
| 17.3-a1 |
17.3-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( - 17^{10} \) |
$13.24274$ |
$(-4/5a^3+6/5a^2+39/5a-28/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$242.4088719$ |
1.165427268 |
\( \frac{461334641886496037}{10079969502245} a^{3} + \frac{827367339161370857}{10079969502245} a^{2} - \frac{1265669401102383182}{10079969502245} a + \frac{149562663424289934}{10079969502245} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{26}{5}\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{16}{5} a - \frac{8}{5}\) , \( 0\) , \( -\frac{58}{5} a^{3} + \frac{67}{5} a^{2} + \frac{568}{5} a - \frac{66}{5}\) , \( \frac{624}{5} a^{3} - \frac{691}{5} a^{2} - \frac{6239}{5} a + \frac{693}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{26}{5}\right){x}{y}={x}^{3}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{16}{5}a-\frac{8}{5}\right){x}^{2}+\left(-\frac{58}{5}a^{3}+\frac{67}{5}a^{2}+\frac{568}{5}a-\frac{66}{5}\right){x}+\frac{624}{5}a^{3}-\frac{691}{5}a^{2}-\frac{6239}{5}a+\frac{693}{5}$ |
| 17.3-a2 |
17.3-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( - 17^{2} \) |
$13.24274$ |
$(-4/5a^3+6/5a^2+39/5a-28/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$242.4088719$ |
1.165427268 |
\( \frac{142823351287871138}{1445} a^{3} - \frac{269730757968797782}{1445} a^{2} - \frac{1315468428994788293}{1445} a + \frac{1281640466584974621}{1445} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{26}{5}\) , \( \frac{3}{5} a^{3} - \frac{7}{5} a^{2} - \frac{28}{5} a + \frac{26}{5}\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{12}{5}\) , \( -\frac{1}{5} a^{3} - \frac{111}{5} a^{2} - \frac{84}{5} a + \frac{138}{5}\) , \( -\frac{154}{5} a^{3} - \frac{454}{5} a^{2} + \frac{434}{5} a + \frac{107}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{26}{5}\right){x}{y}+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{6}{5}a-\frac{12}{5}\right){y}={x}^{3}+\left(\frac{3}{5}a^{3}-\frac{7}{5}a^{2}-\frac{28}{5}a+\frac{26}{5}\right){x}^{2}+\left(-\frac{1}{5}a^{3}-\frac{111}{5}a^{2}-\frac{84}{5}a+\frac{138}{5}\right){x}-\frac{154}{5}a^{3}-\frac{454}{5}a^{2}+\frac{434}{5}a+\frac{107}{5}$ |
| 17.3-a3 |
17.3-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( 17 \) |
$13.24274$ |
$(-4/5a^3+6/5a^2+39/5a-28/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$484.8177438$ |
1.165427268 |
\( -\frac{32518231008}{85} a^{3} + \frac{35908666337}{85} a^{2} + \frac{325011938558}{85} a - \frac{34240554311}{85} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{26}{5}\) , \( \frac{3}{5} a^{3} - \frac{7}{5} a^{2} - \frac{28}{5} a + \frac{26}{5}\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{12}{5}\) , \( \frac{19}{5} a^{3} - \frac{41}{5} a^{2} - \frac{179}{5} a + \frac{153}{5}\) , \( \frac{13}{5} a^{3} - \frac{47}{5} a^{2} - \frac{143}{5} a + \frac{181}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{26}{5}\right){x}{y}+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{6}{5}a-\frac{12}{5}\right){y}={x}^{3}+\left(\frac{3}{5}a^{3}-\frac{7}{5}a^{2}-\frac{28}{5}a+\frac{26}{5}\right){x}^{2}+\left(\frac{19}{5}a^{3}-\frac{41}{5}a^{2}-\frac{179}{5}a+\frac{153}{5}\right){x}+\frac{13}{5}a^{3}-\frac{47}{5}a^{2}-\frac{143}{5}a+\frac{181}{5}$ |
| 17.3-a4 |
17.3-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( 17^{5} \) |
$13.24274$ |
$(-4/5a^3+6/5a^2+39/5a-28/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$484.8177438$ |
1.165427268 |
\( \frac{81783466038}{7099285} a^{3} - \frac{161273918557}{7099285} a^{2} - \frac{747660032488}{7099285} a + \frac{799468784986}{7099285} \) |
\( \bigl[-\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{17}{5} a - \frac{4}{5}\) , \( \frac{1}{5} a^{3} - \frac{4}{5} a^{2} - \frac{11}{5} a + \frac{22}{5}\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{3}{5}\) , \( -\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{1}{5} a + \frac{28}{5}\) , \( -\frac{186}{5} a^{3} + \frac{879}{5} a^{2} - \frac{729}{5} a + \frac{83}{5}\bigr] \) |
${y}^2+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{17}{5}a-\frac{4}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{3}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-\frac{4}{5}a^{2}-\frac{11}{5}a+\frac{22}{5}\right){x}^{2}+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{1}{5}a+\frac{28}{5}\right){x}-\frac{186}{5}a^{3}+\frac{879}{5}a^{2}-\frac{729}{5}a+\frac{83}{5}$ |
| 17.3-b1 |
17.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( - 17^{5} \) |
$13.24274$ |
$(-4/5a^3+6/5a^2+39/5a-28/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$177.3048262$ |
1.704854098 |
\( \frac{38166891189}{7099285} a^{3} - \frac{35342234591}{7099285} a^{2} - \frac{407562367594}{7099285} a + \frac{55438941928}{7099285} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{9}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{4}{5}\) , \( \frac{19}{5} a^{3} - \frac{31}{5} a^{2} - \frac{164}{5} a + \frac{158}{5}\) , \( -\frac{4}{5} a^{3} + \frac{16}{5} a^{2} + \frac{49}{5} a - \frac{63}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{4}{5}\right){y}={x}^{3}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{9}{5}\right){x}^{2}+\left(\frac{19}{5}a^{3}-\frac{31}{5}a^{2}-\frac{164}{5}a+\frac{158}{5}\right){x}-\frac{4}{5}a^{3}+\frac{16}{5}a^{2}+\frac{49}{5}a-\frac{63}{5}$ |
| 17.3-b2 |
17.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( -17 \) |
$13.24274$ |
$(-4/5a^3+6/5a^2+39/5a-28/5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$177.3048262$ |
1.704854098 |
\( -\frac{709857174}{85} a^{3} + \frac{3265233116}{85} a^{2} - \frac{2516789381}{85} a + \frac{156299687}{85} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{12}{5}\) , \( \frac{4}{5} a^{3} - \frac{6}{5} a^{2} - \frac{39}{5} a + \frac{18}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{17}{5} a - \frac{9}{5}\) , \( -\frac{3}{5} a^{3} + \frac{2}{5} a^{2} + \frac{28}{5} a + \frac{4}{5}\) , \( \frac{1}{5} a^{3} - \frac{4}{5} a^{2} - \frac{11}{5} a + \frac{2}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{6}{5}a-\frac{12}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{17}{5}a-\frac{9}{5}\right){y}={x}^{3}+\left(\frac{4}{5}a^{3}-\frac{6}{5}a^{2}-\frac{39}{5}a+\frac{18}{5}\right){x}^{2}+\left(-\frac{3}{5}a^{3}+\frac{2}{5}a^{2}+\frac{28}{5}a+\frac{4}{5}\right){x}+\frac{1}{5}a^{3}-\frac{4}{5}a^{2}-\frac{11}{5}a+\frac{2}{5}$ |
| 17.3-c1 |
17.3-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( - 17^{6} \) |
$13.24274$ |
$(-4/5a^3+6/5a^2+39/5a-28/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$7.173584364$ |
0.310395477 |
\( -\frac{749587644870392160801298542}{120687845} a^{3} + \frac{3535796825385846868156796008}{120687845} a^{2} - \frac{2860432984505674685940207573}{120687845} a + \frac{275889077822388495587120336}{120687845} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{17}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{14}{5}\) , \( -\frac{4}{5} a^{3} + \frac{6}{5} a^{2} + \frac{39}{5} a - \frac{13}{5}\) , \( \frac{283}{5} a^{3} - \frac{1357}{5} a^{2} + \frac{1222}{5} a - \frac{249}{5}\) , \( 1357 a^{3} - 6406 a^{2} + 5214 a - 550\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{17}{5}\right){x}{y}+\left(-\frac{4}{5}a^{3}+\frac{6}{5}a^{2}+\frac{39}{5}a-\frac{13}{5}\right){y}={x}^{3}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{14}{5}\right){x}^{2}+\left(\frac{283}{5}a^{3}-\frac{1357}{5}a^{2}+\frac{1222}{5}a-\frac{249}{5}\right){x}+1357a^{3}-6406a^{2}+5214a-550$ |
| 17.3-c2 |
17.3-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( 17^{3} \) |
$13.24274$ |
$(-4/5a^3+6/5a^2+39/5a-28/5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$14.34716872$ |
0.310395477 |
\( \frac{7193420678544}{24565} a^{3} - \frac{36468467907271}{24565} a^{2} + \frac{33703765801976}{24565} a + \frac{9161545003008}{24565} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{17}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{14}{5}\) , \( -\frac{4}{5} a^{3} + \frac{6}{5} a^{2} + \frac{39}{5} a - \frac{13}{5}\) , \( \frac{8}{5} a^{3} - \frac{57}{5} a^{2} + \frac{172}{5} a - \frac{149}{5}\) , \( \frac{84}{5} a^{3} - \frac{411}{5} a^{2} + \frac{481}{5} a - \frac{277}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{17}{5}\right){x}{y}+\left(-\frac{4}{5}a^{3}+\frac{6}{5}a^{2}+\frac{39}{5}a-\frac{13}{5}\right){y}={x}^{3}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{14}{5}\right){x}^{2}+\left(\frac{8}{5}a^{3}-\frac{57}{5}a^{2}+\frac{172}{5}a-\frac{149}{5}\right){x}+\frac{84}{5}a^{3}-\frac{411}{5}a^{2}+\frac{481}{5}a-\frac{277}{5}$ |
| 17.3-c3 |
17.3-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( 17 \) |
$13.24274$ |
$(-4/5a^3+6/5a^2+39/5a-28/5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1162.120667$ |
0.310395477 |
\( -\frac{381182}{85} a^{3} - \frac{685667}{85} a^{2} + \frac{1033052}{85} a + \frac{48971}{85} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{17}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{14}{5}\) , \( -\frac{4}{5} a^{3} + \frac{6}{5} a^{2} + \frac{39}{5} a - \frac{13}{5}\) , \( -\frac{2}{5} a^{3} + \frac{8}{5} a^{2} + \frac{32}{5} a - \frac{19}{5}\) , \( a^{3} - 7 a\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{17}{5}\right){x}{y}+\left(-\frac{4}{5}a^{3}+\frac{6}{5}a^{2}+\frac{39}{5}a-\frac{13}{5}\right){y}={x}^{3}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{14}{5}\right){x}^{2}+\left(-\frac{2}{5}a^{3}+\frac{8}{5}a^{2}+\frac{32}{5}a-\frac{19}{5}\right){x}+a^{3}-7a$ |
| 17.3-c4 |
17.3-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( - 17^{2} \) |
$13.24274$ |
$(-4/5a^3+6/5a^2+39/5a-28/5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$581.0603335$ |
0.310395477 |
\( \frac{1938997758127}{1445} a^{3} + \frac{3330350014742}{1445} a^{2} - \frac{5077127723477}{1445} a + \frac{521745941574}{1445} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{17}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{22}{5} a - \frac{14}{5}\) , \( -\frac{4}{5} a^{3} + \frac{6}{5} a^{2} + \frac{39}{5} a - \frac{13}{5}\) , \( \frac{3}{5} a^{3} - \frac{12}{5} a^{2} + \frac{27}{5} a - \frac{9}{5}\) , \( \frac{11}{5} a^{3} - \frac{34}{5} a^{2} - \frac{6}{5} a - \frac{3}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{17}{5}\right){x}{y}+\left(-\frac{4}{5}a^{3}+\frac{6}{5}a^{2}+\frac{39}{5}a-\frac{13}{5}\right){y}={x}^{3}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{22}{5}a-\frac{14}{5}\right){x}^{2}+\left(\frac{3}{5}a^{3}-\frac{12}{5}a^{2}+\frac{27}{5}a-\frac{9}{5}\right){x}+\frac{11}{5}a^{3}-\frac{34}{5}a^{2}-\frac{6}{5}a-\frac{3}{5}$ |
| 17.4-a1 |
17.4-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.4 |
\( 17 \) |
\( - 17^{2} \) |
$13.24274$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$242.4088719$ |
1.165427268 |
\( -\frac{17250812019971382}{1445} a^{3} + \frac{4786585239232244}{85} a^{2} - \frac{65829502952109023}{1445} a + \frac{6349421329772531}{1445} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{26}{5}\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{16}{5} a - \frac{8}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{17}{5} a - \frac{4}{5}\) , \( \frac{164}{5} a^{3} - \frac{141}{5} a^{2} - \frac{1684}{5} a - \frac{212}{5}\) , \( \frac{1026}{5} a^{3} - \frac{954}{5} a^{2} - \frac{10436}{5} a - \frac{718}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{26}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{17}{5}a-\frac{4}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{16}{5}a-\frac{8}{5}\right){x}^{2}+\left(\frac{164}{5}a^{3}-\frac{141}{5}a^{2}-\frac{1684}{5}a-\frac{212}{5}\right){x}+\frac{1026}{5}a^{3}-\frac{954}{5}a^{2}-\frac{10436}{5}a-\frac{718}{5}$ |
| 17.4-a2 |
17.4-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.4 |
\( 17 \) |
\( 17 \) |
$13.24274$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$484.8177438$ |
1.165427268 |
\( \frac{3927595156}{85} a^{3} + \frac{410428673}{5} a^{2} - \frac{10514944186}{85} a + \frac{1078861677}{85} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{26}{5}\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{16}{5} a - \frac{8}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{17}{5} a - \frac{4}{5}\) , \( \frac{4}{5} a^{3} - \frac{1}{5} a^{2} - \frac{49}{5} a - \frac{7}{5}\) , \( \frac{24}{5} a^{3} - \frac{21}{5} a^{2} - \frac{249}{5} a - \frac{17}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{26}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{17}{5}a-\frac{4}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{16}{5}a-\frac{8}{5}\right){x}^{2}+\left(\frac{4}{5}a^{3}-\frac{1}{5}a^{2}-\frac{49}{5}a-\frac{7}{5}\right){x}+\frac{24}{5}a^{3}-\frac{21}{5}a^{2}-\frac{249}{5}a-\frac{17}{5}$ |
| 17.4-a3 |
17.4-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.4 |
\( 17 \) |
\( - 17^{10} \) |
$13.24274$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$242.4088719$ |
1.165427268 |
\( -\frac{3801370127425654473}{10079969502245} a^{3} + \frac{246040346420433341}{592939382485} a^{2} + \frac{38006059742033125978}{10079969502245} a - \frac{3838915778569238236}{10079969502245} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{26}{5}\) , \( \frac{3}{5} a^{3} - \frac{7}{5} a^{2} - \frac{28}{5} a + \frac{26}{5}\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{8}{5}\) , \( \frac{27}{5} a^{3} - \frac{28}{5} a^{2} - \frac{207}{5} a + \frac{159}{5}\) , \( -\frac{49}{5} a^{3} - \frac{149}{5} a^{2} + \frac{14}{5} a + \frac{162}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{26}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{8}{5}\right){y}={x}^{3}+\left(\frac{3}{5}a^{3}-\frac{7}{5}a^{2}-\frac{28}{5}a+\frac{26}{5}\right){x}^{2}+\left(\frac{27}{5}a^{3}-\frac{28}{5}a^{2}-\frac{207}{5}a+\frac{159}{5}\right){x}-\frac{49}{5}a^{3}-\frac{149}{5}a^{2}+\frac{14}{5}a+\frac{162}{5}$ |
| 17.4-a4 |
17.4-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.4 |
\( 17 \) |
\( 17^{5} \) |
$13.24274$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$484.8177438$ |
1.165427268 |
\( -\frac{8904033506}{7099285} a^{3} + \frac{3056162927}{417605} a^{2} - \frac{54013725364}{7099285} a + \frac{5387842038}{7099285} \) |
\( \bigl[-\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{17}{5} a - \frac{4}{5}\) , \( a^{3} - a^{2} - 10 a + 3\) , \( \frac{1}{5} a^{3} + \frac{1}{5} a^{2} - \frac{11}{5} a - \frac{3}{5}\) , \( \frac{6}{5} a^{3} - \frac{14}{5} a^{2} - \frac{51}{5} a + \frac{97}{5}\) , \( \frac{1553}{5} a^{3} - \frac{2932}{5} a^{2} - \frac{14308}{5} a + \frac{13921}{5}\bigr] \) |
${y}^2+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{17}{5}a-\frac{4}{5}\right){x}{y}+\left(\frac{1}{5}a^{3}+\frac{1}{5}a^{2}-\frac{11}{5}a-\frac{3}{5}\right){y}={x}^{3}+\left(a^{3}-a^{2}-10a+3\right){x}^{2}+\left(\frac{6}{5}a^{3}-\frac{14}{5}a^{2}-\frac{51}{5}a+\frac{97}{5}\right){x}+\frac{1553}{5}a^{3}-\frac{2932}{5}a^{2}-\frac{14308}{5}a+\frac{13921}{5}$ |
| 17.4-b1 |
17.4-b |
$2$ |
$5$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.4 |
\( 17 \) |
\( - 17^{5} \) |
$13.24274$ |
$(-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$177.3048262$ |
1.704854098 |
\( \frac{10821661047}{7099285} a^{3} - \frac{2243564339}{417605} a^{2} - \frac{131311707002}{7099285} a + \frac{151466428214}{7099285} \) |
\( \bigl[-\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{1}{5} a^{3} - \frac{1}{5} a^{2} + \frac{16}{5} a + \frac{8}{5}\) , \( -\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -\frac{6}{5} a^{3} + \frac{14}{5} a^{2} + \frac{36}{5} a - \frac{2}{5}\) , \( \frac{1}{5} a^{3} - \frac{14}{5} a^{2} + \frac{49}{5} a - \frac{8}{5}\bigr] \) |
${y}^2+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){x}{y}+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){y}={x}^{3}+\left(-\frac{1}{5}a^{3}-\frac{1}{5}a^{2}+\frac{16}{5}a+\frac{8}{5}\right){x}^{2}+\left(-\frac{6}{5}a^{3}+\frac{14}{5}a^{2}+\frac{36}{5}a-\frac{2}{5}\right){x}+\frac{1}{5}a^{3}-\frac{14}{5}a^{2}+\frac{49}{5}a-\frac{8}{5}$ |
| 17.4-b2 |
17.4-b |
$2$ |
$5$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.4 |
\( 17 \) |
\( -17 \) |
$13.24274$ |
$(-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$177.3048262$ |
1.704854098 |
\( \frac{5789959578}{85} a^{3} - \frac{640316866}{5} a^{2} - \frac{53364337063}{85} a + \frac{51409948621}{85} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{6}{5} a - \frac{12}{5}\) , \( \frac{1}{5} a^{3} - \frac{4}{5} a^{2} - \frac{11}{5} a + \frac{17}{5}\) , \( -\frac{2}{5} a^{3} + \frac{3}{5} a^{2} + \frac{17}{5} a - \frac{9}{5}\) , \( a^{3} - a^{2} - 9 a + 3\) , \( \frac{3}{5} a^{3} - \frac{2}{5} a^{2} - \frac{33}{5} a - \frac{14}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{6}{5}a-\frac{12}{5}\right){x}{y}+\left(-\frac{2}{5}a^{3}+\frac{3}{5}a^{2}+\frac{17}{5}a-\frac{9}{5}\right){y}={x}^{3}+\left(\frac{1}{5}a^{3}-\frac{4}{5}a^{2}-\frac{11}{5}a+\frac{17}{5}\right){x}^{2}+\left(a^{3}-a^{2}-9a+3\right){x}+\frac{3}{5}a^{3}-\frac{2}{5}a^{2}-\frac{33}{5}a-\frac{14}{5}$ |
| 17.4-c1 |
17.4-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.4 |
\( 17 \) |
\( 17^{3} \) |
$13.24274$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$14.34716872$ |
0.310395477 |
\( -\frac{12505804884532}{4913} a^{3} + \frac{1405551453217}{289} a^{2} + \frac{114997575076660}{4913} a - \frac{112274565369392}{4913} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{17}{5}\) , \( -\frac{3}{5} a^{3} + \frac{2}{5} a^{2} + \frac{33}{5} a - \frac{6}{5}\) , \( -\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -32 a^{3} + 58 a^{2} + 298 a - 279\) , \( -\frac{1016}{5} a^{3} + \frac{1904}{5} a^{2} + \frac{9361}{5} a - \frac{9082}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{17}{5}\right){x}{y}+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){y}={x}^{3}+\left(-\frac{3}{5}a^{3}+\frac{2}{5}a^{2}+\frac{33}{5}a-\frac{6}{5}\right){x}^{2}+\left(-32a^{3}+58a^{2}+298a-279\right){x}-\frac{1016}{5}a^{3}+\frac{1904}{5}a^{2}+\frac{9361}{5}a-\frac{9082}{5}$ |
| 17.4-c2 |
17.4-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{13})\) |
$4$ |
$[4, 0]$ |
17.4 |
\( 17 \) |
\( - 17^{2} \) |
$13.24274$ |
$(-a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$581.0603335$ |
0.310395477 |
\( -\frac{3210711531231}{289} a^{3} + \frac{209899880380}{17} a^{2} + \frac{32067457320357}{289} a - \frac{3611257380674}{289} \) |
\( \bigl[-\frac{1}{5} a^{3} + \frac{4}{5} a^{2} + \frac{11}{5} a - \frac{17}{5}\) , \( -\frac{3}{5} a^{3} + \frac{2}{5} a^{2} + \frac{33}{5} a - \frac{6}{5}\) , \( -\frac{3}{5} a^{3} + \frac{7}{5} a^{2} + \frac{28}{5} a - \frac{21}{5}\) , \( -7 a^{3} + 13 a^{2} + 63 a - 59\) , \( -\frac{101}{5} a^{3} + \frac{189}{5} a^{2} + \frac{936}{5} a - \frac{912}{5}\bigr] \) |
${y}^2+\left(-\frac{1}{5}a^{3}+\frac{4}{5}a^{2}+\frac{11}{5}a-\frac{17}{5}\right){x}{y}+\left(-\frac{3}{5}a^{3}+\frac{7}{5}a^{2}+\frac{28}{5}a-\frac{21}{5}\right){y}={x}^{3}+\left(-\frac{3}{5}a^{3}+\frac{2}{5}a^{2}+\frac{33}{5}a-\frac{6}{5}\right){x}^{2}+\left(-7a^{3}+13a^{2}+63a-59\right){x}-\frac{101}{5}a^{3}+\frac{189}{5}a^{2}+\frac{936}{5}a-\frac{912}{5}$ |
*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.
