| 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 |
| 7.1-a1 |
7.1-a |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$13.43061$ |
$(1/3a^3-2/3a^2-7/3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$223.0004007$ |
1.892281700 |
\( \frac{37729567370}{21} a^{3} + \frac{49648197854}{21} a^{2} - \frac{99317907635}{21} a - \frac{34163722112}{7} \) |
\( \bigl[a\) , \( -a^{2} + 5\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{5}{3} a^{3} + \frac{7}{3} a^{2} + \frac{20}{3} a - 4\) , \( -\frac{14}{3} a^{3} + \frac{37}{3} a^{2} + \frac{50}{3} a - 39\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{4}{3}a-3\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-\frac{5}{3}a^{3}+\frac{7}{3}a^{2}+\frac{20}{3}a-4\right){x}-\frac{14}{3}a^{3}+\frac{37}{3}a^{2}+\frac{50}{3}a-39$ |
| 7.1-a2 |
7.1-a |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$13.43061$ |
$(1/3a^3-2/3a^2-7/3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$223.0004007$ |
1.892281700 |
\( -\frac{1081509563885}{1029} a^{3} + \frac{3140764344406}{1029} a^{2} + \frac{4731169352873}{1029} a - \frac{3588809847660}{343} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{4}{3} a + 5\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -12 a^{3} + 35 a^{2} + 49 a - 124\) , \( -\frac{266}{3} a^{3} + \frac{688}{3} a^{2} + \frac{1274}{3} a - 704\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{1}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-\frac{4}{3}a+5\right){x}^{2}+\left(-12a^{3}+35a^{2}+49a-124\right){x}-\frac{266}{3}a^{3}+\frac{688}{3}a^{2}+\frac{1274}{3}a-704$ |
| 7.1-b1 |
7.1-b |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$13.43061$ |
$(1/3a^3-2/3a^2-7/3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.012743831$ |
$2178.566117$ |
2.827041244 |
\( -\frac{1081509563885}{1029} a^{3} + \frac{3140764344406}{1029} a^{2} + \frac{4731169352873}{1029} a - \frac{3588809847660}{343} \) |
\( \bigl[a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{4}{3} a - 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 3\) , \( \frac{5}{3} a^{3} - \frac{7}{3} a^{2} - \frac{5}{3} a + 2\) , \( -\frac{16}{3} a^{3} + \frac{29}{3} a^{2} + \frac{100}{3} a + 18\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{4}{3}a-3\right){x}^{2}+\left(\frac{5}{3}a^{3}-\frac{7}{3}a^{2}-\frac{5}{3}a+2\right){x}-\frac{16}{3}a^{3}+\frac{29}{3}a^{2}+\frac{100}{3}a+18$ |
| 7.1-b2 |
7.1-b |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$13.43061$ |
$(1/3a^3-2/3a^2-7/3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.038231493$ |
$2178.566117$ |
2.827041244 |
\( \frac{37729567370}{21} a^{3} + \frac{49648197854}{21} a^{2} - \frac{99317907635}{21} a - \frac{34163722112}{7} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 2\) , \( a^{2} - 2 a - 5\) , \( a\) , \( -\frac{4}{3} a^{3} - \frac{1}{3} a^{2} + \frac{13}{3} a + 2\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} + \frac{10}{3} a + 5\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-\frac{4}{3}a^{3}-\frac{1}{3}a^{2}+\frac{13}{3}a+2\right){x}+\frac{2}{3}a^{3}+\frac{5}{3}a^{2}+\frac{10}{3}a+5$ |
| 7.2-a1 |
7.2-a |
$2$ |
$2$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7^{6} \) |
$13.43061$ |
$(1/3a^3+1/3a^2-1/3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$325.2702318$ |
1.380048882 |
\( \frac{16788736}{1029} a^{3} - \frac{39209984}{1029} a^{2} - \frac{85822720}{1029} a + \frac{5105472}{49} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( 0\) , \( a^{2} - a - 4\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{4}{3} a - 6\) , \( a^{3} - 4 a - 1\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-2\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{4}{3}a-6\right){x}+a^{3}-4a-1$ |
| 7.2-a2 |
7.2-a |
$2$ |
$2$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{3} \) |
$13.43061$ |
$(1/3a^3+1/3a^2-1/3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$650.5404636$ |
1.380048882 |
\( -\frac{29891855104}{147} a^{3} + \frac{1975961600}{21} a^{2} + \frac{32929422592}{21} a + \frac{58333784896}{49} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -a^{2} + a + 5\) , \( 1\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{16}{3} a + 8\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - \frac{11}{3} a - 1\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-2\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{16}{3}a+8\right){x}+\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-\frac{11}{3}a-1$ |
| 7.2-b1 |
7.2-b |
$2$ |
$2$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7^{6} \) |
$13.43061$ |
$(1/3a^3+1/3a^2-1/3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.239408029$ |
$222.0408881$ |
2.706469043 |
\( \frac{6811136}{1029} a^{3} - \frac{7989760}{1029} a^{2} - \frac{8576768}{1029} a + \frac{2640576}{343} \) |
\( \bigl[a^{2} - a - 3\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{1}{3} a + 5\) , \( a^{2} - a - 4\) , \( -285 a^{3} + 827 a^{2} + 1247 a - 2836\) , \( 4203 a^{3} - 12206 a^{2} - 18386 a + 41840\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-\frac{1}{3}a+5\right){x}^{2}+\left(-285a^{3}+827a^{2}+1247a-2836\right){x}+4203a^{3}-12206a^{2}-18386a+41840$ |
| 7.2-b2 |
7.2-b |
$2$ |
$2$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{3} \) |
$13.43061$ |
$(1/3a^3+1/3a^2-1/3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$0.478816058$ |
$222.0408881$ |
2.706469043 |
\( -\frac{7848998400}{49} a^{3} + \frac{4430760448}{7} a^{2} - \frac{797645568}{7} a - \frac{36197779648}{49} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{1}{3} a - 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 2\) , \( \frac{7}{3} a^{3} + \frac{1}{3} a^{2} - \frac{61}{3} a - 19\) , \( -\frac{16}{3} a^{3} + \frac{8}{3} a^{2} + \frac{115}{3} a + 27\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{1}{3}a-1\right){x}^{2}+\left(\frac{7}{3}a^{3}+\frac{1}{3}a^{2}-\frac{61}{3}a-19\right){x}-\frac{16}{3}a^{3}+\frac{8}{3}a^{2}+\frac{115}{3}a+27$ |
| 7.2-c1 |
7.2-c |
$2$ |
$2$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{3} \) |
$13.43061$ |
$(1/3a^3+1/3a^2-1/3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$650.5404636$ |
1.380048882 |
\( -\frac{7848998400}{49} a^{3} + \frac{4430760448}{7} a^{2} - \frac{797645568}{7} a - \frac{36197779648}{49} \) |
\( \bigl[a^{2} - a - 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 2\) , \( a^{3} - 2 a - 1\) , \( a^{3} + a^{2} - 2 a - 3\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{1}{3}a+1\right){x}^{2}+\left(a^{3}-2a-1\right){x}+a^{3}+a^{2}-2a-3$ |
| 7.2-c2 |
7.2-c |
$2$ |
$2$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7^{6} \) |
$13.43061$ |
$(1/3a^3+1/3a^2-1/3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$325.2702318$ |
1.380048882 |
\( \frac{6811136}{1029} a^{3} - \frac{7989760}{1029} a^{2} - \frac{8576768}{1029} a + \frac{2640576}{343} \) |
\( \bigl[a^{2} - a - 3\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{10}{3} a + 2\) , \( a^{2} - a - 4\) , \( -a^{3} + 7 a + 3\) , \( -\frac{2}{3} a^{3} + \frac{1}{3} a^{2} + \frac{14}{3} a + 2\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{10}{3}a+2\right){x}^{2}+\left(-a^{3}+7a+3\right){x}-\frac{2}{3}a^{3}+\frac{1}{3}a^{2}+\frac{14}{3}a+2$ |
| 7.2-d1 |
7.2-d |
$2$ |
$2$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7^{6} \) |
$13.43061$ |
$(1/3a^3+1/3a^2-1/3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.239408029$ |
$222.0408881$ |
2.706469043 |
\( \frac{16788736}{1029} a^{3} - \frac{39209984}{1029} a^{2} - \frac{85822720}{1029} a + \frac{5105472}{49} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{10}{3} a + 2\) , \( a^{2} - a - 4\) , \( -\frac{13}{3} a^{3} + \frac{5}{3} a^{2} + \frac{40}{3} a + 8\) , \( -a^{3} + 8 a^{2} + 4 a - 5\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-2\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{10}{3}a+2\right){x}^{2}+\left(-\frac{13}{3}a^{3}+\frac{5}{3}a^{2}+\frac{40}{3}a+8\right){x}-a^{3}+8a^{2}+4a-5$ |
| 7.2-d2 |
7.2-d |
$2$ |
$2$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{3} \) |
$13.43061$ |
$(1/3a^3+1/3a^2-1/3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$0.478816058$ |
$222.0408881$ |
2.706469043 |
\( -\frac{29891855104}{147} a^{3} + \frac{1975961600}{21} a^{2} + \frac{32929422592}{21} a + \frac{58333784896}{49} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 2\) , \( \frac{5}{3} a^{3} - \frac{19}{3} a^{2} + \frac{7}{3} a + 5\) , \( -\frac{23}{3} a^{3} + \frac{88}{3} a^{2} - \frac{1}{3} a - 41\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{1}{3}a\right){x}^{2}+\left(\frac{5}{3}a^{3}-\frac{19}{3}a^{2}+\frac{7}{3}a+5\right){x}-\frac{23}{3}a^{3}+\frac{88}{3}a^{2}-\frac{1}{3}a-41$ |
| 7.3-a1 |
7.3-a |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{3} \) |
$13.43061$ |
$(-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$223.0004007$ |
1.892281700 |
\( -\frac{294635720350}{1029} a^{3} - \frac{388473775936}{1029} a^{2} + \frac{773411784067}{1029} a + \frac{266343344894}{343} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{2} - a - 3\) , \( -\frac{10}{3} a^{3} - \frac{19}{3} a^{2} + \frac{34}{3} a + 13\) , \( -30 a^{3} + 7 a^{2} + 49 a + 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-\frac{10}{3}a^{3}-\frac{19}{3}a^{2}+\frac{34}{3}a+13\right){x}-30a^{3}+7a^{2}+49a+16$ |
| 7.3-a2 |
7.3-a |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.3 |
\( 7 \) |
\( -7 \) |
$13.43061$ |
$(-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$223.0004007$ |
1.892281700 |
\( \frac{138334576381}{21} a^{3} - \frac{401776485356}{21} a^{2} - \frac{604938667369}{21} a + \frac{458963405296}{7} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 2\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a\) , \( a\) , \( -\frac{2}{3} a^{3} + \frac{4}{3} a^{2} + \frac{14}{3} a - 3\) , \( -2 a^{3} + a^{2} + 8 a - 4\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{1}{3}a+2\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a\right){x}^{2}+\left(-\frac{2}{3}a^{3}+\frac{4}{3}a^{2}+\frac{14}{3}a-3\right){x}-2a^{3}+a^{2}+8a-4$ |
| 7.3-b1 |
7.3-b |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{3} \) |
$13.43061$ |
$(-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.012743831$ |
$2178.566117$ |
2.827041244 |
\( -\frac{294635720350}{1029} a^{3} - \frac{388473775936}{1029} a^{2} + \frac{773411784067}{1029} a + \frac{266343344894}{343} \) |
\( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{4}{3} a + 5\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{11}{3} a^{3} + \frac{28}{3} a^{2} + \frac{44}{3} a - 34\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{7}{3} a + 4\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{4}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-\frac{4}{3}a+5\right){x}^{2}+\left(-\frac{11}{3}a^{3}+\frac{28}{3}a^{2}+\frac{44}{3}a-34\right){x}+\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-\frac{7}{3}a+4$ |
| 7.3-b2 |
7.3-b |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
7.3 |
\( 7 \) |
\( -7 \) |
$13.43061$ |
$(-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.038231493$ |
$2178.566117$ |
2.827041244 |
\( \frac{138334576381}{21} a^{3} - \frac{401776485356}{21} a^{2} - \frac{604938667369}{21} a + \frac{458963405296}{7} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 2\) , \( -a^{2} + 2 a + 5\) , \( a\) , \( -3 a^{3} + 6 a^{2} + 17 a - 18\) , \( \frac{5}{3} a^{3} - \frac{16}{3} a^{2} - \frac{29}{3} a + 28\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-3a^{3}+6a^{2}+17a-18\right){x}+\frac{5}{3}a^{3}-\frac{16}{3}a^{2}-\frac{29}{3}a+28$ |
| 16.1-a1 |
16.1-a |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1045.294536$ |
2.217475525 |
\( -\frac{857152}{3} a^{3} + \frac{2490416}{3} a^{2} + \frac{3735520}{3} a - 2833008 \) |
\( \bigl[a^{2} - a - 3\) , \( a - 1\) , \( 0\) , \( \frac{2}{3} a^{3} + \frac{2}{3} a^{2} - \frac{5}{3} a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(\frac{2}{3}a^{3}+\frac{2}{3}a^{2}-\frac{5}{3}a-1\right){x}$ |
| 16.1-a2 |
16.1-a |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$261.3236341$ |
2.217475525 |
\( 872813324976 a^{3} - 2534719133048 a^{2} - 3818106104460 a + 8688750756668 \) |
\( \bigl[a^{2} - a - 3\) , \( a - 1\) , \( 0\) , \( -\frac{8}{3} a^{3} - \frac{8}{3} a^{2} + \frac{20}{3} a + 4\) , \( -\frac{58}{3} a^{3} - \frac{82}{3} a^{2} + \frac{148}{3} a + 56\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{8}{3}a^{3}-\frac{8}{3}a^{2}+\frac{20}{3}a+4\right){x}-\frac{58}{3}a^{3}-\frac{82}{3}a^{2}+\frac{148}{3}a+56$ |
| 16.1-a3 |
16.1-a |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$261.3236341$ |
2.217475525 |
\( -141475015320 a^{3} + 65462998280 a^{2} + 1090960239300 a + 828263760716 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{4}{3} a - 6\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{79}{3} a^{3} + \frac{230}{3} a^{2} + \frac{346}{3} a - 264\) , \( 218 a^{3} - 633 a^{2} - 954 a + 2170\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{4}{3}a-6\right){x}^{2}+\left(-\frac{79}{3}a^{3}+\frac{230}{3}a^{2}+\frac{346}{3}a-264\right){x}+218a^{3}-633a^{2}-954a+2170$ |
| 16.1-a4 |
16.1-a |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1045.294536$ |
2.217475525 |
\( -\frac{312704}{3} a^{3} + \frac{224368}{3} a^{2} + \frac{2218976}{3} a + 530576 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{4}{3} a - 6\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( 2 a^{3} - 5 a^{2} - 8 a + 16\) , \( \frac{25}{3} a^{3} - \frac{71}{3} a^{2} - \frac{109}{3} a + 81\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{4}{3}a-6\right){x}^{2}+\left(2a^{3}-5a^{2}-8a+16\right){x}+\frac{25}{3}a^{3}-\frac{71}{3}a^{2}-\frac{109}{3}a+81$ |
| 16.1-b1 |
16.1-b |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$86.09321820$ |
0.730548558 |
\( \frac{713402204180}{3} a^{3} + \frac{940473040928}{3} a^{2} - \frac{1873050403052}{3} a - 644972166500 \) |
\( \bigl[a^{2} - a - 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{10}{3} a - 4\) , \( a^{2} - a - 3\) , \( -\frac{14}{3} a^{3} + \frac{22}{3} a^{2} + \frac{80}{3} a - 11\) , \( 29 a^{3} - 27 a^{2} - 214 a - 100\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{10}{3}a-4\right){x}^{2}+\left(-\frac{14}{3}a^{3}+\frac{22}{3}a^{2}+\frac{80}{3}a-11\right){x}+29a^{3}-27a^{2}-214a-100$ |
| 16.1-b2 |
16.1-b |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$344.3728728$ |
0.730548558 |
\( -\frac{257344}{3} a^{3} + \frac{915728}{3} a^{2} + \frac{61216}{3} a - 294464 \) |
\( \bigl[a^{2} - a - 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{7}{3} a\) , \( a^{2} - a - 3\) , \( -a^{2} + a + 1\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{4}{3} a - 2\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{7}{3}a\right){x}^{2}+\left(-a^{2}+a+1\right){x}-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{4}{3}a-2$ |
| 16.1-b3 |
16.1-b |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$86.09321820$ |
0.730548558 |
\( -\frac{334338932660}{3} a^{3} + \frac{1321138962400}{3} a^{2} - \frac{237824803420}{3} a - 513973239204 \) |
\( \bigl[a^{2} - a - 3\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{4}{3} a + 4\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( \frac{137}{3} a^{3} - \frac{547}{3} a^{2} + \frac{106}{3} a + 218\) , \( 603 a^{3} - 2384 a^{2} + 432 a + 2784\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{4}{3}a+4\right){x}^{2}+\left(\frac{137}{3}a^{3}-\frac{547}{3}a^{2}+\frac{106}{3}a+218\right){x}+603a^{3}-2384a^{2}+432a+2784$ |
| 16.1-b4 |
16.1-b |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$344.3728728$ |
0.730548558 |
\( -\frac{237440}{3} a^{3} - \frac{301232}{3} a^{2} + \frac{642848}{3} a + 217344 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{10}{3} a + 4\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{1}{3} a^{3} - \frac{16}{3} a^{2} + \frac{52}{3} a + 20\) , \( -7 a^{3} + 14 a^{2} + 20 a + 1\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{10}{3}a+4\right){x}^{2}+\left(-\frac{1}{3}a^{3}-\frac{16}{3}a^{2}+\frac{52}{3}a+20\right){x}-7a^{3}+14a^{2}+20a+1$ |
| 16.1-c1 |
16.1-c |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$261.3236341$ |
2.217475525 |
\( \frac{713402204180}{3} a^{3} + \frac{940473040928}{3} a^{2} - \frac{1873050403052}{3} a - 644972166500 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{7}{3} a + 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{37}{3} a^{3} + \frac{98}{3} a^{2} + \frac{175}{3} a - 104\) , \( -\frac{149}{3} a^{3} + \frac{424}{3} a^{2} + \frac{665}{3} a - 477\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{7}{3}a+3\right){x}^{2}+\left(-\frac{37}{3}a^{3}+\frac{98}{3}a^{2}+\frac{175}{3}a-104\right){x}-\frac{149}{3}a^{3}+\frac{424}{3}a^{2}+\frac{665}{3}a-477$ |
| 16.1-c2 |
16.1-c |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1045.294536$ |
2.217475525 |
\( -\frac{237440}{3} a^{3} - \frac{301232}{3} a^{2} + \frac{642848}{3} a + 217344 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{7}{3} a + 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{2}{3} a^{3} - \frac{2}{3} a^{2} + \frac{20}{3} a + 11\) , \( -\frac{11}{3} a^{3} + \frac{25}{3} a^{2} + \frac{59}{3} a - 21\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{7}{3}a+3\right){x}^{2}+\left(-\frac{2}{3}a^{3}-\frac{2}{3}a^{2}+\frac{20}{3}a+11\right){x}-\frac{11}{3}a^{3}+\frac{25}{3}a^{2}+\frac{59}{3}a-21$ |
| 16.1-c3 |
16.1-c |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$261.3236341$ |
2.217475525 |
\( -\frac{334338932660}{3} a^{3} + \frac{1321138962400}{3} a^{2} - \frac{237824803420}{3} a - 513973239204 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -a^{2} + 2 a + 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( a^{3} - 2 a^{2} - 6 a - 4\) , \( -\frac{53}{3} a^{3} + \frac{25}{3} a^{2} + \frac{416}{3} a + 105\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(a^{3}-2a^{2}-6a-4\right){x}-\frac{53}{3}a^{3}+\frac{25}{3}a^{2}+\frac{416}{3}a+105$ |
| 16.1-c4 |
16.1-c |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1045.294536$ |
2.217475525 |
\( -\frac{257344}{3} a^{3} + \frac{915728}{3} a^{2} + \frac{61216}{3} a - 294464 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{4}{3} a + 5\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( \frac{4}{3} a^{3} - \frac{5}{3} a^{2} - \frac{16}{3} a + 5\) , \( \frac{8}{3} a^{3} + \frac{5}{3} a^{2} - \frac{23}{3} a - 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-\frac{4}{3}a+5\right){x}^{2}+\left(\frac{4}{3}a^{3}-\frac{5}{3}a^{2}-\frac{16}{3}a+5\right){x}+\frac{8}{3}a^{3}+\frac{5}{3}a^{2}-\frac{23}{3}a-2$ |
| 16.1-d1 |
16.1-d |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$344.3728728$ |
0.730548558 |
\( -\frac{857152}{3} a^{3} + \frac{2490416}{3} a^{2} + \frac{3735520}{3} a - 2833008 \) |
\( \bigl[a^{2} - a - 3\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{7}{3} a + 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{128}{3} a^{3} + \frac{367}{3} a^{2} + \frac{563}{3} a - 414\) , \( -\frac{1088}{3} a^{3} + \frac{3157}{3} a^{2} + \frac{4763}{3} a - 3605\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{7}{3}a+3\right){x}^{2}+\left(-\frac{128}{3}a^{3}+\frac{367}{3}a^{2}+\frac{563}{3}a-414\right){x}-\frac{1088}{3}a^{3}+\frac{3157}{3}a^{2}+\frac{4763}{3}a-3605$ |
| 16.1-d2 |
16.1-d |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$86.09321820$ |
0.730548558 |
\( 872813324976 a^{3} - 2534719133048 a^{2} - 3818106104460 a + 8688750756668 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} - \frac{2}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -3 a^{3} + 10 a^{2} + 2 a - 22\) , \( \frac{40}{3} a^{3} - \frac{164}{3} a^{2} + \frac{44}{3} a + 55\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}-\frac{2}{3}a-4\right){x}^{2}+\left(-3a^{3}+10a^{2}+2a-22\right){x}+\frac{40}{3}a^{3}-\frac{164}{3}a^{2}+\frac{44}{3}a+55$ |
| 16.1-d3 |
16.1-d |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$86.09321820$ |
0.730548558 |
\( -141475015320 a^{3} + 65462998280 a^{2} + 1090960239300 a + 828263760716 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{4}{3} a + 6\) , \( 0\) , \( -4 a^{3} + 12 a^{2} + 12 a - 52\) , \( -\frac{70}{3} a^{3} + \frac{206}{3} a^{2} + \frac{232}{3} a - 284\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-2\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-\frac{4}{3}a+6\right){x}^{2}+\left(-4a^{3}+12a^{2}+12a-52\right){x}-\frac{70}{3}a^{3}+\frac{206}{3}a^{2}+\frac{232}{3}a-284$ |
| 16.1-d4 |
16.1-d |
$4$ |
$6$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$14.89270$ |
$(1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$344.3728728$ |
0.730548558 |
\( -\frac{312704}{3} a^{3} + \frac{224368}{3} a^{2} + \frac{2218976}{3} a + 530576 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{4}{3} a + 6\) , \( 0\) , \( a^{3} - 3 a^{2} - 3 a + 13\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-2\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-\frac{4}{3}a+6\right){x}^{2}+\left(a^{3}-3a^{2}-3a+13\right){x}$ |
| 28.1-a1 |
28.1-a |
$2$ |
$5$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{2} \cdot 7^{5} \) |
$15.97177$ |
$(1/3a^3-2/3a^2-7/3a+1), (1/3a^3-2/3a^2-4/3a+1)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$0.790186093$ |
$602.0712177$ |
3.229589922 |
\( -\frac{5814380907}{33614} a^{3} + \frac{16966182151}{33614} a^{2} + \frac{25433678299}{33614} a - \frac{29096936969}{16807} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{7}{3} a + 4\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 2\) , \( -\frac{10}{3} a^{3} + \frac{26}{3} a^{2} + \frac{49}{3} a - 26\) , \( 4 a^{3} - 11 a^{2} - 16 a + 39\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{1}{3}a+2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{7}{3}a+4\right){x}^{2}+\left(-\frac{10}{3}a^{3}+\frac{26}{3}a^{2}+\frac{49}{3}a-26\right){x}+4a^{3}-11a^{2}-16a+39$ |
| 28.1-a2 |
28.1-a |
$2$ |
$5$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{10} \cdot 7 \) |
$15.97177$ |
$(1/3a^3-2/3a^2-7/3a+1), (1/3a^3-2/3a^2-4/3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$3.950930465$ |
$0.963313948$ |
3.229589922 |
\( \frac{202187801615606581240}{7} a^{3} + \frac{2132341421075931165969}{56} a^{2} - \frac{4246781510624005040425}{56} a - \frac{4387050770704462768903}{56} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{7}{3} a + 4\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 2\) , \( \frac{65}{3} a^{3} - \frac{259}{3} a^{2} - \frac{311}{3} a + 269\) , \( -\frac{46}{3} a^{3} - \frac{166}{3} a^{2} - \frac{524}{3} a - 280\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{1}{3}a+2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{7}{3}a+4\right){x}^{2}+\left(\frac{65}{3}a^{3}-\frac{259}{3}a^{2}-\frac{311}{3}a+269\right){x}-\frac{46}{3}a^{3}-\frac{166}{3}a^{2}-\frac{524}{3}a-280$ |
| 28.1-b1 |
28.1-b |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{6} \cdot 7^{3} \) |
$15.97177$ |
$(1/3a^3-2/3a^2-7/3a+1), (1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$166.4454675$ |
1.412381822 |
\( \frac{8642508041}{4116} a^{3} - \frac{3993611659}{4116} a^{2} - \frac{66629144975}{4116} a - \frac{4215560890}{343} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} - \frac{2}{3} a - 6\) , \( a^{2} - 4\) , \( a^{3} + 4 a^{2} - 8 a - 2\) , \( -14 a^{3} + 69 a^{2} - 4 a - 107\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{4}{3}a-3\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}-\frac{2}{3}a-6\right){x}^{2}+\left(a^{3}+4a^{2}-8a-2\right){x}-14a^{3}+69a^{2}-4a-107$ |
| 28.1-b2 |
28.1-b |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{18} \cdot 7 \) |
$15.97177$ |
$(1/3a^3-2/3a^2-7/3a+1), (1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$166.4454675$ |
1.412381822 |
\( \frac{1699955}{672} a^{3} + \frac{1140949}{336} a^{2} - \frac{277817}{42} a - \frac{1579615}{224} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{4}{3} a - 5\) , \( 0\) , \( \frac{2}{3} a^{3} - \frac{10}{3} a^{2} - \frac{5}{3} a + 8\) , \( \frac{8}{3} a^{3} - \frac{61}{3} a^{2} + \frac{28}{3} a + 24\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{4}{3}a-5\right){x}^{2}+\left(\frac{2}{3}a^{3}-\frac{10}{3}a^{2}-\frac{5}{3}a+8\right){x}+\frac{8}{3}a^{3}-\frac{61}{3}a^{2}+\frac{28}{3}a+24$ |
| 28.1-c1 |
28.1-c |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{18} \cdot 7 \) |
$15.97177$ |
$(1/3a^3-2/3a^2-7/3a+1), (1/3a^3-2/3a^2-4/3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.613766593$ |
$147.7113886$ |
3.077211628 |
\( \frac{1699955}{672} a^{3} + \frac{1140949}{336} a^{2} - \frac{277817}{42} a - \frac{1579615}{224} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 3\) , \( 1\) , \( a^{2} - 4\) , \( -\frac{8}{3} a^{3} + \frac{19}{3} a^{2} + \frac{41}{3} a - 17\) , \( -\frac{40}{3} a^{3} + \frac{113}{3} a^{2} + \frac{181}{3} a - 125\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-3\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+{x}^{2}+\left(-\frac{8}{3}a^{3}+\frac{19}{3}a^{2}+\frac{41}{3}a-17\right){x}-\frac{40}{3}a^{3}+\frac{113}{3}a^{2}+\frac{181}{3}a-125$ |
| 28.1-c2 |
28.1-c |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{6} \cdot 7^{3} \) |
$15.97177$ |
$(1/3a^3-2/3a^2-7/3a+1), (1/3a^3-2/3a^2-4/3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.204588864$ |
$147.7113886$ |
3.077211628 |
\( \frac{8642508041}{4116} a^{3} - \frac{3993611659}{4116} a^{2} - \frac{66629144975}{4116} a - \frac{4215560890}{343} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{10}{3} a - 2\) , \( 1\) , \( -\frac{2}{3} a^{3} + \frac{10}{3} a^{2} + \frac{5}{3} a\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{13}{3} a - 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{1}{3}a+1\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{10}{3}a-2\right){x}^{2}+\left(-\frac{2}{3}a^{3}+\frac{10}{3}a^{2}+\frac{5}{3}a\right){x}+\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{13}{3}a-2$ |
| 28.1-d1 |
28.1-d |
$2$ |
$5$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{10} \cdot 7 \) |
$15.97177$ |
$(1/3a^3-2/3a^2-7/3a+1), (1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$8.084491074$ |
1.715034420 |
\( \frac{202187801615606581240}{7} a^{3} + \frac{2132341421075931165969}{56} a^{2} - \frac{4246781510624005040425}{56} a - \frac{4387050770704462768903}{56} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{1}{3} a - 4\) , \( a\) , \( \frac{566}{3} a^{3} - \frac{1876}{3} a^{2} - \frac{1424}{3} a + 1521\) , \( \frac{4609}{3} a^{3} - \frac{16778}{3} a^{2} - \frac{3562}{3} a + 9459\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{1}{3}a-4\right){x}^{2}+\left(\frac{566}{3}a^{3}-\frac{1876}{3}a^{2}-\frac{1424}{3}a+1521\right){x}+\frac{4609}{3}a^{3}-\frac{16778}{3}a^{2}-\frac{3562}{3}a+9459$ |
| 28.1-d2 |
28.1-d |
$2$ |
$5$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{2} \cdot 7^{5} \) |
$15.97177$ |
$(1/3a^3-2/3a^2-7/3a+1), (1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$202.1122768$ |
1.715034420 |
\( -\frac{5814380907}{33614} a^{3} + \frac{16966182151}{33614} a^{2} + \frac{25433678299}{33614} a - \frac{29096936969}{16807} \) |
\( \bigl[a + 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{4}{3} a - 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 1\) , \( -\frac{2}{3} a^{3} - \frac{5}{3} a^{2} + \frac{5}{3} a + 3\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - \frac{2}{3} a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{1}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{4}{3}a-1\right){x}^{2}+\left(-\frac{2}{3}a^{3}-\frac{5}{3}a^{2}+\frac{5}{3}a+3\right){x}+\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-\frac{2}{3}a$ |
| 28.2-a1 |
28.2-a |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{2} \) |
$15.97177$ |
$(1/3a^3+1/3a^2-1/3a-1), (1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$100.3396673$ |
1.702875114 |
\( -\frac{9073387}{84} a^{3} - \frac{3135904}{21} a^{2} + \frac{10933271}{42} a + \frac{7712361}{28} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{4}{3} a\) , \( a\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{2}{3} a - 1\) , \( -2 a - 2\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{4}{3}a\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{2}{3}a-1\right){x}-2a-2$ |
| 28.2-a2 |
28.2-a |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{6} \) |
$15.97177$ |
$(1/3a^3+1/3a^2-1/3a-1), (1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$100.3396673$ |
1.702875114 |
\( \frac{547727}{2058} a^{3} - \frac{1237028}{1029} a^{2} + \frac{297209}{1029} a + \frac{251089}{98} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 2\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{1}{3} a - 5\) , \( 1\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{8}{3} a\) , \( a^{3} + 2 a^{2} - 3 a - 6\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{1}{3}a+2\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{1}{3}a-5\right){x}^{2}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{8}{3}a\right){x}+a^{3}+2a^{2}-3a-6$ |
| 28.2-b1 |
28.2-b |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{2} \) |
$15.97177$ |
$(1/3a^3+1/3a^2-1/3a-1), (1/3a^3-2/3a^2-4/3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.234951027$ |
$193.3774891$ |
3.084277167 |
\( -\frac{34342649}{84} a^{3} + \frac{24843922}{21} a^{2} + \frac{75898801}{42} a - \frac{114437073}{28} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 3\) , \( -a^{2} + 3\) , \( a^{2} - a - 3\) , \( \frac{28}{3} a^{3} - \frac{122}{3} a^{2} + \frac{35}{3} a + 52\) , \( \frac{155}{3} a^{3} - \frac{622}{3} a^{2} + \frac{127}{3} a + 246\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(\frac{28}{3}a^{3}-\frac{122}{3}a^{2}+\frac{35}{3}a+52\right){x}+\frac{155}{3}a^{3}-\frac{622}{3}a^{2}+\frac{127}{3}a+246$ |
| 28.2-b2 |
28.2-b |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{6} \) |
$15.97177$ |
$(1/3a^3+1/3a^2-1/3a-1), (1/3a^3-2/3a^2-4/3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.078317009$ |
$193.3774891$ |
3.084277167 |
\( \frac{557101}{2058} a^{3} + \frac{132200}{1029} a^{2} - \frac{2506865}{1029} a - \frac{1440367}{686} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{1}{3} a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{4}{3} a - 2\) , \( \frac{10}{3} a^{3} - \frac{32}{3} a^{2} - \frac{61}{3} a + 42\) , \( \frac{541}{3} a^{3} - \frac{1574}{3} a^{2} - \frac{2383}{3} a + 1802\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{1}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{4}{3}a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{1}{3}a\right){x}^{2}+\left(\frac{10}{3}a^{3}-\frac{32}{3}a^{2}-\frac{61}{3}a+42\right){x}+\frac{541}{3}a^{3}-\frac{1574}{3}a^{2}-\frac{2383}{3}a+1802$ |
| 28.2-c1 |
28.2-c |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{6} \) |
$15.97177$ |
$(1/3a^3+1/3a^2-1/3a-1), (1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$100.3396673$ |
1.702875114 |
\( \frac{557101}{2058} a^{3} + \frac{132200}{1029} a^{2} - \frac{2506865}{1029} a - \frac{1440367}{686} \) |
\( \bigl[a\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} - \frac{2}{3} a - 6\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 2\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{2}{3} a + 4\) , \( -\frac{2}{3} a^{3} + \frac{7}{3} a^{2} + \frac{2}{3} a - 5\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}-\frac{2}{3}a-6\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{2}{3}a+4\right){x}-\frac{2}{3}a^{3}+\frac{7}{3}a^{2}+\frac{2}{3}a-5$ |
| 28.2-c2 |
28.2-c |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{2} \) |
$15.97177$ |
$(1/3a^3+1/3a^2-1/3a-1), (1/3a^3-2/3a^2-4/3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$100.3396673$ |
1.702875114 |
\( -\frac{34342649}{84} a^{3} + \frac{24843922}{21} a^{2} + \frac{75898801}{42} a - \frac{114437073}{28} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{4}{3} a\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 2\) , \( -a^{3} + 2 a^{2} + 5 a - 5\) , \( -\frac{2}{3} a^{3} + \frac{1}{3} a^{2} + \frac{14}{3} a - 3\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{1}{3}a+2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{4}{3}a\right){x}^{2}+\left(-a^{3}+2a^{2}+5a-5\right){x}-\frac{2}{3}a^{3}+\frac{1}{3}a^{2}+\frac{14}{3}a-3$ |
| 28.2-d1 |
28.2-d |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{6} \cdot 7^{2} \) |
$15.97177$ |
$(1/3a^3+1/3a^2-1/3a-1), (1/3a^3-2/3a^2-4/3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.234951027$ |
$193.3774891$ |
3.084277167 |
\( -\frac{9073387}{84} a^{3} - \frac{3135904}{21} a^{2} + \frac{10933271}{42} a + \frac{7712361}{28} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 3\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{10}{3} a + 4\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{53}{3} a^{3} + \frac{136}{3} a^{2} + \frac{260}{3} a - 134\) , \( -\frac{325}{3} a^{3} + \frac{926}{3} a^{2} + \frac{1450}{3} a - 1038\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{7}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{10}{3}a+4\right){x}^{2}+\left(-\frac{53}{3}a^{3}+\frac{136}{3}a^{2}+\frac{260}{3}a-134\right){x}-\frac{325}{3}a^{3}+\frac{926}{3}a^{2}+\frac{1450}{3}a-1038$ |
| 28.2-d2 |
28.2-d |
$2$ |
$3$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{6} \) |
$15.97177$ |
$(1/3a^3+1/3a^2-1/3a-1), (1/3a^3-2/3a^2-4/3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.078317009$ |
$193.3774891$ |
3.084277167 |
\( \frac{547727}{2058} a^{3} - \frac{1237028}{1029} a^{2} + \frac{297209}{1029} a + \frac{251089}{98} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{1}{3} a - 6\) , \( a\) , \( \frac{23}{3} a^{3} - \frac{49}{3} a^{2} - \frac{11}{3} a + 20\) , \( \frac{97}{3} a^{3} - \frac{275}{3} a^{2} + \frac{2}{3} a + 97\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{4}{3}a-3\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{1}{3}a-6\right){x}^{2}+\left(\frac{23}{3}a^{3}-\frac{49}{3}a^{2}-\frac{11}{3}a+20\right){x}+\frac{97}{3}a^{3}-\frac{275}{3}a^{2}+\frac{2}{3}a+97$ |
| 28.3-a1 |
28.3-a |
$2$ |
$5$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.3 |
\( 2^{2} \cdot 7 \) |
\( - 2^{10} \cdot 7 \) |
$15.97177$ |
$(-a+1), (1/3a^3-2/3a^2-4/3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$3.950930465$ |
$0.963313948$ |
3.229589922 |
\( \frac{5936809291233745480211}{56} a^{3} - \frac{17240964829393127426231}{56} a^{2} - \frac{25970465306010387480099}{56} a + \frac{29550107113814174736753}{28} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{37}{3} a^{3} + \frac{200}{3} a^{2} + \frac{208}{3} a - 237\) , \( -\frac{293}{3} a^{3} + \frac{925}{3} a^{2} + \frac{1838}{3} a - 1362\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{4}{3}a-3\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-\frac{37}{3}a^{3}+\frac{200}{3}a^{2}+\frac{208}{3}a-237\right){x}-\frac{293}{3}a^{3}+\frac{925}{3}a^{2}+\frac{1838}{3}a-1362$ |
| 28.3-a2 |
28.3-a |
$2$ |
$5$ |
4.4.13888.1 |
$4$ |
$[4, 0]$ |
28.3 |
\( 2^{2} \cdot 7 \) |
\( - 2^{2} \cdot 7^{5} \) |
$15.97177$ |
$(-a+1), (1/3a^3-2/3a^2-4/3a+1)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$0.790186093$ |
$602.0712177$ |
3.229589922 |
\( -\frac{765357896}{16807} a^{3} - \frac{2275988753}{33614} a^{2} + \frac{3946708497}{33614} a + \frac{4870059111}{33614} \) |
\( \bigl[a\) , \( a\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 1\) , \( \frac{35}{3} a^{3} - \frac{136}{3} a^{2} + \frac{25}{3} a + 54\) , \( -83 a^{3} + 329 a^{2} - 60 a - 385\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+a{x}^{2}+\left(\frac{35}{3}a^{3}-\frac{136}{3}a^{2}+\frac{25}{3}a+54\right){x}-83a^{3}+329a^{2}-60a-385$ |
*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.
