| 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 |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{5} \) |
$15.47256$ |
$(1/3a^3+1/3a^2-3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$312.4324334$ |
2.301282211 |
\( -\frac{1940359378}{50421} a^{3} - \frac{6297971513}{50421} a^{2} + \frac{994429675}{16807} a + \frac{3499312361}{16807} \) |
\( \bigl[\frac{1}{3} a^{2} - 1\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 2 a - 1\) , \( \frac{1}{3} a^{2} + a - 2\) , \( \frac{2}{3} a^{3} + \frac{8}{3} a^{2} - 12 a - 18\) , \( -\frac{8}{3} a^{3} - \frac{5}{3} a^{2} + 23 a + 25\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-1\right){x}{y}+\left(\frac{1}{3}a^{2}+a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+2a-1\right){x}^{2}+\left(\frac{2}{3}a^{3}+\frac{8}{3}a^{2}-12a-18\right){x}-\frac{8}{3}a^{3}-\frac{5}{3}a^{2}+23a+25$ |
| 7.1-b1 |
7.1-b |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{5} \) |
$15.47256$ |
$(1/3a^3+1/3a^2-3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$186.2904708$ |
1.372158908 |
\( -\frac{1940359378}{50421} a^{3} - \frac{6297971513}{50421} a^{2} + \frac{994429675}{16807} a + \frac{3499312361}{16807} \) |
\( \bigl[\frac{1}{3} a^{2} + a - 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + 3\) , \( a + 1\) , \( -a^{3} - \frac{14}{3} a^{2} - a + 12\) , \( -2 a^{3} + 11 a^{2} + 36 a - 64\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-4a+3\right){x}^{2}+\left(-a^{3}-\frac{14}{3}a^{2}-a+12\right){x}-2a^{3}+11a^{2}+36a-64$ |
| 7.2-a1 |
7.2-a |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7^{5} \) |
$15.47256$ |
$(1/3a^3-3a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$312.4324334$ |
2.301282211 |
\( \frac{4826648459}{50421} a^{3} + \frac{6297971513}{50421} a^{2} - \frac{16420304755}{16807} a - \frac{21692573691}{16807} \) |
\( \bigl[\frac{1}{3} a^{2} - 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a - 1\) , \( \frac{1}{3} a^{3} - 3 a\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - a + 9\) , \( a^{2} - 2 a - 4\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-1\right){x}{y}+\left(\frac{1}{3}a^{3}-3a\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-4a-1\right){x}^{2}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-a+9\right){x}+a^{2}-2a-4$ |
| 7.2-b1 |
7.2-b |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7^{5} \) |
$15.47256$ |
$(1/3a^3-3a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$186.2904708$ |
1.372158908 |
\( \frac{4826648459}{50421} a^{3} + \frac{6297971513}{50421} a^{2} - \frac{16420304755}{16807} a - \frac{21692573691}{16807} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( a + 1\) , \( \frac{1}{3} a^{3} - 3 a + 1\) , \( \frac{8}{3} a^{3} + \frac{13}{3} a^{2} - 27 a - 42\) , \( -\frac{19}{3} a^{3} - 11 a^{2} + 51 a + 68\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){x}{y}+\left(\frac{1}{3}a^{3}-3a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(\frac{8}{3}a^{3}+\frac{13}{3}a^{2}-27a-42\right){x}-\frac{19}{3}a^{3}-11a^{2}+51a+68$ |
| 7.3-a1 |
7.3-a |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
7.3 |
\( 7 \) |
\( 7^{5} \) |
$15.47256$ |
$(1/3a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$312.4324334$ |
2.301282211 |
\( -\frac{4826648459}{50421} a^{3} + \frac{6297971513}{50421} a^{2} + \frac{16420304755}{16807} a - \frac{21692573691}{16807} \) |
\( \bigl[\frac{1}{3} a^{2} - 1\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 4 a - 1\) , \( \frac{1}{3} a^{3} - 3 a\) , \( -\frac{1}{3} a^{3} - \frac{5}{3} a^{2} + 9\) , \( a^{2} + 2 a - 4\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-1\right){x}{y}+\left(\frac{1}{3}a^{3}-3a\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+4a-1\right){x}^{2}+\left(-\frac{1}{3}a^{3}-\frac{5}{3}a^{2}+9\right){x}+a^{2}+2a-4$ |
| 7.3-b1 |
7.3-b |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
7.3 |
\( 7 \) |
\( 7^{5} \) |
$15.47256$ |
$(1/3a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$186.2904708$ |
1.372158908 |
\( -\frac{4826648459}{50421} a^{3} + \frac{6297971513}{50421} a^{2} + \frac{16420304755}{16807} a - \frac{21692573691}{16807} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( a + 1\) , \( \frac{1}{3} a^{2} - 1\) , \( -3 a^{3} + \frac{11}{3} a^{2} + 35 a - 36\) , \( \frac{29}{3} a^{3} - \frac{44}{3} a^{2} - 86 a + 124\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){x}{y}+\left(\frac{1}{3}a^{2}-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a^{3}+\frac{11}{3}a^{2}+35a-36\right){x}+\frac{29}{3}a^{3}-\frac{44}{3}a^{2}-86a+124$ |
| 7.4-a1 |
7.4-a |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
7.4 |
\( 7 \) |
\( 7^{5} \) |
$15.47256$ |
$(-1/3a^3+1/3a^2+3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$312.4324334$ |
2.301282211 |
\( \frac{1940359378}{50421} a^{3} - \frac{6297971513}{50421} a^{2} - \frac{994429675}{16807} a + \frac{3499312361}{16807} \) |
\( \bigl[\frac{1}{3} a^{2} - 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( \frac{1}{3} a^{2} + a - 2\) , \( -a^{3} + \frac{8}{3} a^{2} + 13 a - 18\) , \( \frac{7}{3} a^{3} - \frac{5}{3} a^{2} - 21 a + 25\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-1\right){x}{y}+\left(\frac{1}{3}a^{2}+a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){x}^{2}+\left(-a^{3}+\frac{8}{3}a^{2}+13a-18\right){x}+\frac{7}{3}a^{3}-\frac{5}{3}a^{2}-21a+25$ |
| 7.4-b1 |
7.4-b |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
7.4 |
\( 7 \) |
\( 7^{5} \) |
$15.47256$ |
$(-1/3a^3+1/3a^2+3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$186.2904708$ |
1.372158908 |
\( \frac{1940359378}{50421} a^{3} - \frac{6297971513}{50421} a^{2} - \frac{994429675}{16807} a + \frac{3499312361}{16807} \) |
\( \bigl[\frac{1}{3} a^{2} + a - 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + 3\) , \( \frac{1}{3} a^{2} - 1\) , \( \frac{8}{3} a^{3} - \frac{13}{3} a^{2} - 16 a + 12\) , \( \frac{1}{3} a^{3} + \frac{43}{3} a^{2} - 32 a - 50\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+a-1\right){x}{y}+\left(\frac{1}{3}a^{2}-1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-4a+3\right){x}^{2}+\left(\frac{8}{3}a^{3}-\frac{13}{3}a^{2}-16a+12\right){x}+\frac{1}{3}a^{3}+\frac{43}{3}a^{2}-32a-50$ |
| 9.1-a1 |
9.1-a |
$4$ |
$10$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$15.96633$ |
$(-1/3a^3-a^2+a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \cdot 5 \) |
$0.112241099$ |
$571.6658535$ |
4.726154708 |
\( \frac{58591911104}{243} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{1}{3} a^{2} - 1\) , \( \frac{1}{3} a^{2} + a - 1\) , \( \frac{10358}{3} a^{3} + 4533 a^{2} - 35279 a - 46690\) , \( -\frac{1098665}{3} a^{3} - \frac{1455457}{3} a^{2} + 3750460 a + 4971231\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){x}{y}+\left(\frac{1}{3}a^{2}+a-1\right){y}={x}^{3}+\left(\frac{1}{3}a^{2}-1\right){x}^{2}+\left(\frac{10358}{3}a^{3}+4533a^{2}-35279a-46690\right){x}-\frac{1098665}{3}a^{3}-\frac{1455457}{3}a^{2}+3750460a+4971231$ |
| 9.1-a2 |
9.1-a |
$4$ |
$10$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$15.96633$ |
$(-1/3a^3-a^2+a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$0.561205498$ |
$571.6658535$ |
4.726154708 |
\( \frac{85184}{3} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{1}{3} a^{2} - 1\) , \( \frac{1}{3} a^{2} + a - 1\) , \( \frac{118}{3} a^{3} + 53 a^{2} - 399 a - 530\) , \( \frac{1385}{3} a^{3} + \frac{1838}{3} a^{2} - 4720 a - 6259\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){x}{y}+\left(\frac{1}{3}a^{2}+a-1\right){y}={x}^{3}+\left(\frac{1}{3}a^{2}-1\right){x}^{2}+\left(\frac{118}{3}a^{3}+53a^{2}-399a-530\right){x}+\frac{1385}{3}a^{3}+\frac{1838}{3}a^{2}-4720a-6259$ |
| 9.1-a3 |
9.1-a |
$4$ |
$10$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{40} \) |
$15.96633$ |
$(-1/3a^3-a^2+a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.224482199$ |
$142.9164633$ |
4.726154708 |
\( -\frac{873722816}{59049} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( -\frac{1}{3} a^{2} + a + 3\) , \( a + 1\) , \( \frac{2549}{3} a^{3} + 1116 a^{2} - 8677 a - 11484\) , \( -45782 a^{3} - \frac{181900}{3} a^{2} + 468830 a + 621405\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{2}+a+3\right){x}^{2}+\left(\frac{2549}{3}a^{3}+1116a^{2}-8677a-11484\right){x}-45782a^{3}-\frac{181900}{3}a^{2}+468830a+621405$ |
| 9.1-a4 |
9.1-a |
$4$ |
$10$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$15.96633$ |
$(-1/3a^3-a^2+a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1.122410996$ |
$142.9164633$ |
4.726154708 |
\( \frac{64}{9} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( -\frac{1}{3} a^{2} + a + 3\) , \( a + 1\) , \( -\frac{11}{3} a^{3} - 4 a^{2} + 43 a + 56\) , \( \frac{548}{3} a^{3} + \frac{731}{3} a^{2} - 1862 a - 2471\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{2}+a+3\right){x}^{2}+\left(-\frac{11}{3}a^{3}-4a^{2}+43a+56\right){x}+\frac{548}{3}a^{3}+\frac{731}{3}a^{2}-1862a-2471$ |
| 9.1-b1 |
9.1-b |
$4$ |
$10$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{40} \) |
$15.96633$ |
$(-1/3a^3-a^2+a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2 \) |
$21.47764528$ |
$1.605094755$ |
2.031379650 |
\( -\frac{873722816}{59049} \) |
\( \bigl[\frac{1}{3} a^{2} - 2\) , \( \frac{1}{3} a^{2} - 3\) , \( \frac{1}{3} a^{2} - 1\) , \( 13 a^{2} - 138\) , \( \frac{152}{3} a^{2} - 524\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-2\right){x}{y}+\left(\frac{1}{3}a^{2}-1\right){y}={x}^{3}+\left(\frac{1}{3}a^{2}-3\right){x}^{2}+\left(13a^{2}-138\right){x}+\frac{152}{3}a^{2}-524$ |
| 9.1-b2 |
9.1-b |
$4$ |
$10$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$15.96633$ |
$(-1/3a^3-a^2+a+3)$ |
$2$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$0.859105811$ |
$1003.184222$ |
2.031379650 |
\( \frac{64}{9} \) |
\( \bigl[\frac{1}{3} a^{2} - 2\) , \( \frac{1}{3} a^{2} - 3\) , \( \frac{1}{3} a^{2} - 1\) , \( -\frac{1}{3} a^{2} + 2\) , \( -\frac{1}{3} a^{2} + 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-2\right){x}{y}+\left(\frac{1}{3}a^{2}-1\right){y}={x}^{3}+\left(\frac{1}{3}a^{2}-3\right){x}^{2}+\left(-\frac{1}{3}a^{2}+2\right){x}-\frac{1}{3}a^{2}+2$ |
| 9.1-b3 |
9.1-b |
$4$ |
$10$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$15.96633$ |
$(-1/3a^3-a^2+a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2 \) |
$5.369411322$ |
$6.420379023$ |
2.031379650 |
\( \frac{58591911104}{243} \) |
\( \bigl[\frac{1}{3} a^{2} - 2\) , \( -\frac{1}{3} a^{2} + 2\) , \( \frac{1}{3} a^{2} - 1\) , \( \frac{161}{3} a^{2} - 565\) , \( 498 a^{2} - 5118\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-2\right){x}{y}+\left(\frac{1}{3}a^{2}-1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{2}+2\right){x}^{2}+\left(\frac{161}{3}a^{2}-565\right){x}+498a^{2}-5118$ |
| 9.1-b4 |
9.1-b |
$4$ |
$10$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$15.96633$ |
$(-1/3a^3-a^2+a+3)$ |
$2$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$0.214776452$ |
$4012.736889$ |
2.031379650 |
\( \frac{85184}{3} \) |
\( \bigl[\frac{1}{3} a^{2} - 2\) , \( -\frac{1}{3} a^{2} + 2\) , \( \frac{1}{3} a^{2} - 1\) , \( \frac{1}{3} a^{2} - 5\) , \( -\frac{1}{3} a^{2} + 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-2\right){x}{y}+\left(\frac{1}{3}a^{2}-1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{2}+2\right){x}^{2}+\left(\frac{1}{3}a^{2}-5\right){x}-\frac{1}{3}a^{2}+2$ |
| 14.1-a1 |
14.1-a |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{10} \cdot 7 \) |
$16.87294$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3-3a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.025195860$ |
$735.2416484$ |
5.457994060 |
\( \frac{8873189}{168} a^{3} + \frac{11782807}{168} a^{2} - \frac{7571461}{14} a - \frac{5020622}{7} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + 1\) , \( \frac{1}{3} a^{3} - 2 a + 1\) , \( -\frac{29}{3} a^{3} + \frac{38}{3} a^{2} + 98 a - 131\) , \( 251 a^{3} - \frac{1001}{3} a^{2} - 2572 a + 3411\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){x}{y}+\left(\frac{1}{3}a^{3}-2a+1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-4a+1\right){x}^{2}+\left(-\frac{29}{3}a^{3}+\frac{38}{3}a^{2}+98a-131\right){x}+251a^{3}-\frac{1001}{3}a^{2}-2572a+3411$ |
| 14.1-b1 |
14.1-b |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{10} \cdot 7 \) |
$16.87294$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3-3a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$112.7279071$ |
1.660638908 |
\( \frac{8873189}{168} a^{3} + \frac{11782807}{168} a^{2} - \frac{7571461}{14} a - \frac{5020622}{7} \) |
\( \bigl[\frac{1}{3} a^{3} - 2 a + 1\) , \( \frac{1}{3} a^{3} - 3 a\) , \( 1\) , \( \frac{2}{3} a^{3} + \frac{4}{3} a^{2} - 3 a + 3\) , \( a^{3} + \frac{7}{3} a^{2} - 4 a - 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-2a+1\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{3}a^{3}-3a\right){x}^{2}+\left(\frac{2}{3}a^{3}+\frac{4}{3}a^{2}-3a+3\right){x}+a^{3}+\frac{7}{3}a^{2}-4a-2$ |
| 14.2-a1 |
14.2-a |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( 2^{10} \cdot 7 \) |
$16.87294$ |
$(-1/3a^3+1/3a^2+3a-2), (-1/3a^3+1/3a^2+3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.025195860$ |
$735.2416484$ |
5.457994060 |
\( \frac{3666277}{168} a^{3} - \frac{11782807}{168} a^{2} - \frac{1062821}{28} a + \frac{1741563}{14} \) |
\( \bigl[\frac{1}{3} a^{2} + a - 1\) , \( -1\) , \( \frac{1}{3} a^{3} - 2 a + 1\) , \( -\frac{13}{3} a^{3} - 14 a^{2} + 9 a + 29\) , \( 104 a^{3} + \frac{998}{3} a^{2} - 183 a - 587\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+a-1\right){x}{y}+\left(\frac{1}{3}a^{3}-2a+1\right){y}={x}^{3}-{x}^{2}+\left(-\frac{13}{3}a^{3}-14a^{2}+9a+29\right){x}+104a^{3}+\frac{998}{3}a^{2}-183a-587$ |
| 14.2-b1 |
14.2-b |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( 2^{10} \cdot 7 \) |
$16.87294$ |
$(-1/3a^3+1/3a^2+3a-2), (-1/3a^3+1/3a^2+3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$112.7279071$ |
1.660638908 |
\( \frac{3666277}{168} a^{3} - \frac{11782807}{168} a^{2} - \frac{1062821}{28} a + \frac{1741563}{14} \) |
\( \bigl[\frac{1}{3} a^{3} - 2 a + 1\) , \( -\frac{1}{3} a^{3} + 4 a\) , \( \frac{1}{3} a^{2} - 1\) , \( \frac{2}{3} a^{2} + 3 a + 7\) , \( a^{2} + 5 a + 4\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-2a+1\right){x}{y}+\left(\frac{1}{3}a^{2}-1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+4a\right){x}^{2}+\left(\frac{2}{3}a^{2}+3a+7\right){x}+a^{2}+5a+4$ |
| 14.3-a1 |
14.3-a |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( 2^{10} \cdot 7 \) |
$16.87294$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3+1/3a^2-3a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.025195860$ |
$735.2416484$ |
5.457994060 |
\( -\frac{3666277}{168} a^{3} - \frac{11782807}{168} a^{2} + \frac{1062821}{28} a + \frac{1741563}{14} \) |
\( \bigl[\frac{1}{3} a^{2} + a - 1\) , \( -\frac{1}{3} a^{3} + 4 a - 1\) , \( \frac{1}{3} a^{2} + a - 1\) , \( \frac{14}{3} a^{3} - \frac{41}{3} a^{2} - 11 a + 32\) , \( -\frac{353}{3} a^{3} + 377 a^{2} + 213 a - 669\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+a-1\right){x}{y}+\left(\frac{1}{3}a^{2}+a-1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+4a-1\right){x}^{2}+\left(\frac{14}{3}a^{3}-\frac{41}{3}a^{2}-11a+32\right){x}-\frac{353}{3}a^{3}+377a^{2}+213a-669$ |
| 14.3-b1 |
14.3-b |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
14.3 |
\( 2 \cdot 7 \) |
\( 2^{10} \cdot 7 \) |
$16.87294$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3+1/3a^2-3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$112.7279071$ |
1.660638908 |
\( -\frac{3666277}{168} a^{3} - \frac{11782807}{168} a^{2} + \frac{1062821}{28} a + \frac{1741563}{14} \) |
\( \bigl[\frac{1}{3} a^{3} - 2 a + 1\) , \( a\) , \( \frac{1}{3} a^{2} + a - 1\) , \( \frac{2}{3} a^{3} + \frac{2}{3} a^{2} - 3 a + 4\) , \( \frac{2}{3} a^{3} + 2 a^{2} - a - 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-2a+1\right){x}{y}+\left(\frac{1}{3}a^{2}+a-1\right){y}={x}^{3}+a{x}^{2}+\left(\frac{2}{3}a^{3}+\frac{2}{3}a^{2}-3a+4\right){x}+\frac{2}{3}a^{3}+2a^{2}-a-2$ |
| 14.4-a1 |
14.4-a |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
14.4 |
\( 2 \cdot 7 \) |
\( 2^{10} \cdot 7 \) |
$16.87294$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^2+a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.025195860$ |
$735.2416484$ |
5.457994060 |
\( -\frac{8873189}{168} a^{3} + \frac{11782807}{168} a^{2} + \frac{7571461}{14} a - \frac{5020622}{7} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 3 a + 1\) , \( \frac{1}{3} a^{3} - 2 a + 1\) , \( 9 a^{3} + \frac{38}{3} a^{2} - 95 a - 131\) , \( -\frac{754}{3} a^{3} - \frac{1001}{3} a^{2} + 2574 a + 3411\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){x}{y}+\left(\frac{1}{3}a^{3}-2a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+3a+1\right){x}^{2}+\left(9a^{3}+\frac{38}{3}a^{2}-95a-131\right){x}-\frac{754}{3}a^{3}-\frac{1001}{3}a^{2}+2574a+3411$ |
| 14.4-b1 |
14.4-b |
$1$ |
$1$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
14.4 |
\( 2 \cdot 7 \) |
\( 2^{10} \cdot 7 \) |
$16.87294$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$112.7279071$ |
1.660638908 |
\( -\frac{8873189}{168} a^{3} + \frac{11782807}{168} a^{2} + \frac{7571461}{14} a - \frac{5020622}{7} \) |
\( \bigl[\frac{1}{3} a^{3} - 2 a + 1\) , \( \frac{1}{3} a^{3} - 4 a\) , \( \frac{1}{3} a^{3} - 3 a + 1\) , \( \frac{1}{3} a^{2} - a + 6\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - 4 a - 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-2a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-3a+1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-4a\right){x}^{2}+\left(\frac{1}{3}a^{2}-a+6\right){x}+\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-4a-2$ |
| 28.1-a1 |
28.1-a |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{4} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3+1/3a^2-3a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.350549734$ |
$815.2175433$ |
4.209852938 |
\( -\frac{6745644800}{7203} a^{3} - \frac{2982650816}{2401} a^{2} + \frac{23032563520}{2401} a + \frac{30545979680}{2401} \) |
\( \bigl[\frac{1}{3} a^{2} - 2\) , \( \frac{1}{3} a^{2} - 3\) , \( \frac{1}{3} a^{2} + a - 2\) , \( 6 a^{3} - 20 a^{2} - 9 a + 34\) , \( -52 a^{3} + \frac{497}{3} a^{2} + 92 a - 292\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-2\right){x}{y}+\left(\frac{1}{3}a^{2}+a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{2}-3\right){x}^{2}+\left(6a^{3}-20a^{2}-9a+34\right){x}-52a^{3}+\frac{497}{3}a^{2}+92a-292$ |
| 28.1-a2 |
28.1-a |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3+1/3a^2-3a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.175274867$ |
$1630.435086$ |
4.209852938 |
\( -\frac{53617664}{147} a^{3} + \frac{171812608}{147} a^{2} + \frac{31160064}{49} a - \frac{100052608}{49} \) |
\( \bigl[\frac{1}{3} a^{3} - 2 a\) , \( -\frac{1}{3} a^{2} + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{79}{3} a^{3} - \frac{256}{3} a^{2} - 46 a + 147\) , \( -\frac{1088}{3} a^{3} + \frac{3481}{3} a^{2} + 636 a - 2040\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-2a\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{2}+1\right){x}^{2}+\left(\frac{79}{3}a^{3}-\frac{256}{3}a^{2}-46a+147\right){x}-\frac{1088}{3}a^{3}+\frac{3481}{3}a^{2}+636a-2040$ |
| 28.1-b1 |
28.1-b |
$2$ |
$3$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3+1/3a^2-3a-3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$220.1947252$ |
1.621887327 |
\( \frac{83050941619971548738}{1029} a^{3} + \frac{110096837557310529292}{1029} a^{2} - \frac{283553651246763011838}{343} a - \frac{375894115962556592650}{343} \) |
\( \bigl[\frac{1}{3} a^{2} + a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{55}{3} a^{3} + \frac{76}{3} a^{2} - 191 a - 250\) , \( -\frac{566}{3} a^{3} - \frac{746}{3} a^{2} + 1930 a + 2557\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+a-2\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-4a-2\right){x}^{2}+\left(\frac{55}{3}a^{3}+\frac{76}{3}a^{2}-191a-250\right){x}-\frac{566}{3}a^{3}-\frac{746}{3}a^{2}+1930a+2557$ |
| 28.1-b2 |
28.1-b |
$2$ |
$3$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3+1/3a^2-3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$220.1947252$ |
1.621887327 |
\( \frac{378488}{7} a^{3} + \frac{1450574}{21} a^{2} - \frac{3884502}{7} a - \frac{5116602}{7} \) |
\( \bigl[\frac{1}{3} a^{2} + a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( -\frac{4}{3} a^{2} - a + 10\) , \( -\frac{4}{3} a^{2} + 7\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+a-2\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-4a-2\right){x}^{2}+\left(-\frac{4}{3}a^{2}-a+10\right){x}-\frac{4}{3}a^{2}+7$ |
| 28.1-c1 |
28.1-c |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{4} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3+1/3a^2-3a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.410060932$ |
$206.6291436$ |
3.744596185 |
\( -\frac{6745644800}{7203} a^{3} - \frac{2982650816}{2401} a^{2} + \frac{23032563520}{2401} a + \frac{30545979680}{2401} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{1}{3} a^{3} - 2 a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( \frac{5}{3} a^{3} + \frac{13}{3} a^{2} - 9 a - 17\) , \( \frac{8}{3} a^{3} + 7 a^{2} - 12 a - 23\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-2a\right){x}^{2}+\left(\frac{5}{3}a^{3}+\frac{13}{3}a^{2}-9a-17\right){x}+\frac{8}{3}a^{3}+7a^{2}-12a-23$ |
| 28.1-c2 |
28.1-c |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3+1/3a^2-3a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.205030466$ |
$413.2582873$ |
3.744596185 |
\( -\frac{53617664}{147} a^{3} + \frac{171812608}{147} a^{2} + \frac{31160064}{49} a - \frac{100052608}{49} \) |
\( \bigl[\frac{1}{3} a^{3} - 2 a\) , \( -\frac{1}{3} a^{3} + 4 a + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 4 a + 4\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-2a\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+4a+1\right){x}^{2}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+4a+4\right){x}$ |
| 28.1-d1 |
28.1-d |
$2$ |
$3$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3+1/3a^2-3a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$4.268109803$ |
0.848815139 |
\( \frac{83050941619971548738}{1029} a^{3} + \frac{110096837557310529292}{1029} a^{2} - \frac{283553651246763011838}{343} a - \frac{375894115962556592650}{343} \) |
\( \bigl[\frac{1}{3} a^{3} - 3 a\) , \( -\frac{1}{3} a^{3} + 3 a + 1\) , \( \frac{1}{3} a^{3} - 3 a\) , \( -26 a^{3} + 50 a^{2} + 294 a - 407\) , \( -\frac{832}{3} a^{3} + \frac{1187}{3} a^{2} + 2891 a - 3873\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-3a\right){x}{y}+\left(\frac{1}{3}a^{3}-3a\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+3a+1\right){x}^{2}+\left(-26a^{3}+50a^{2}+294a-407\right){x}-\frac{832}{3}a^{3}+\frac{1187}{3}a^{2}+2891a-3873$ |
| 28.1-d2 |
28.1-d |
$2$ |
$3$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3+1/3a^2-3a-3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$345.7168940$ |
0.848815139 |
\( \frac{378488}{7} a^{3} + \frac{1450574}{21} a^{2} - \frac{3884502}{7} a - \frac{5116602}{7} \) |
\( \bigl[a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{40}{3} a^{3} - \frac{59}{3} a^{2} - 139 a + 200\) , \( -322 a^{3} + \frac{1282}{3} a^{2} + 3296 a - 4379\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-4a-2\right){x}^{2}+\left(\frac{40}{3}a^{3}-\frac{59}{3}a^{2}-139a+200\right){x}-322a^{3}+\frac{1282}{3}a^{2}+3296a-4379$ |
| 28.2-a1 |
28.2-a |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{4} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.350549734$ |
$815.2175433$ |
4.209852938 |
\( -\frac{2795629120}{7203} a^{3} + \frac{2982650816}{2401} a^{2} + \frac{1641242560}{2401} a - \frac{5245830112}{2401} \) |
\( \bigl[\frac{1}{3} a^{2} - 2\) , \( -\frac{1}{3} a^{2} + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( -15 a^{3} + 20 a^{2} + 153 a - 206\) , \( \frac{376}{3} a^{3} - \frac{497}{3} a^{2} - 1284 a + 1696\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-2\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{2}+1\right){x}^{2}+\left(-15a^{3}+20a^{2}+153a-206\right){x}+\frac{376}{3}a^{3}-\frac{497}{3}a^{2}-1284a+1696$ |
| 28.2-a2 |
28.2-a |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.175274867$ |
$1630.435086$ |
4.209852938 |
\( \frac{43230976}{49} a^{3} - \frac{171812608}{147} a^{2} - \frac{442696448}{49} a + \frac{587197824}{49} \) |
\( \bigl[\frac{1}{3} a^{3} - 2 a\) , \( \frac{1}{3} a^{2} - 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( -64 a^{3} + \frac{254}{3} a^{2} + 654 a - 869\) , \( 966 a^{3} - \frac{3842}{3} a^{2} - 9896 a + 13116\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-2a\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{2}-3\right){x}^{2}+\left(-64a^{3}+\frac{254}{3}a^{2}+654a-869\right){x}+966a^{3}-\frac{3842}{3}a^{2}-9896a+13116$ |
| 28.2-b1 |
28.2-b |
$2$ |
$3$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3-3a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$220.1947252$ |
1.621887327 |
\( \frac{159370}{7} a^{3} - \frac{1450574}{21} a^{2} - \frac{298866}{7} a + \frac{685694}{7} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{1}{3} a^{2} - a\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 2 a - 3\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+2\right){x}^{2}+\left(\frac{1}{3}a^{2}-a\right){x}-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+2a-3$ |
| 28.2-b2 |
28.2-b |
$2$ |
$3$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3-3a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$220.1947252$ |
1.621887327 |
\( \frac{11466942128949455208}{343} a^{3} - \frac{110096837557310529292}{1029} a^{2} - \frac{20151537540573548134}{343} a + \frac{64493234266685524518}{343} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{25}{3} a^{3} - \frac{79}{3} a^{2} - 21 a + 60\) , \( -\frac{233}{3} a^{3} + \frac{743}{3} a^{2} + 132 a - 421\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+2\right){x}^{2}+\left(\frac{25}{3}a^{3}-\frac{79}{3}a^{2}-21a+60\right){x}-\frac{233}{3}a^{3}+\frac{743}{3}a^{2}+132a-421$ |
| 28.2-c1 |
28.2-c |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{4} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.410060932$ |
$206.6291436$ |
3.744596185 |
\( -\frac{2795629120}{7203} a^{3} + \frac{2982650816}{2401} a^{2} + \frac{1641242560}{2401} a - \frac{5245830112}{2401} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{1}{3} a^{3} - 3 a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} + a^{2} - 3 a - 3\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-3a\right){x}^{2}+\left(a^{3}+a^{2}-5a-3\right){x}+a^{3}+a^{2}-3a-3$ |
| 28.2-c2 |
28.2-c |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.205030466$ |
$413.2582873$ |
3.744596185 |
\( \frac{43230976}{49} a^{3} - \frac{171812608}{147} a^{2} - \frac{442696448}{49} a + \frac{587197824}{49} \) |
\( \bigl[\frac{1}{3} a^{3} - 2 a\) , \( -\frac{1}{3} a^{3} + 2 a + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( -\frac{2}{3} a^{3} + a^{2} - 4\) , \( -\frac{2}{3} a^{3} + \frac{4}{3} a^{2} - 4\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-2a\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+2a+1\right){x}^{2}+\left(-\frac{2}{3}a^{3}+a^{2}-4\right){x}-\frac{2}{3}a^{3}+\frac{4}{3}a^{2}-4$ |
| 28.2-d1 |
28.2-d |
$2$ |
$3$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3-3a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$345.7168940$ |
0.848815139 |
\( \frac{159370}{7} a^{3} - \frac{1450574}{21} a^{2} - \frac{298866}{7} a + \frac{685694}{7} \) |
\( \bigl[\frac{1}{3} a^{3} - 3 a\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{19}{3} a^{3} + \frac{56}{3} a^{2} - 17 a - 30\) , \( -133 a^{3} - \frac{1285}{3} a^{2} + 230 a + 755\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-3a\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+2\right){x}^{2}+\left(\frac{19}{3}a^{3}+\frac{56}{3}a^{2}-17a-30\right){x}-133a^{3}-\frac{1285}{3}a^{2}+230a+755$ |
| 28.2-d2 |
28.2-d |
$2$ |
$3$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^3-3a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$4.268109803$ |
0.848815139 |
\( \frac{11466942128949455208}{343} a^{3} - \frac{110096837557310529292}{1029} a^{2} - \frac{20151537540573548134}{343} a + \frac{64493234266685524518}{343} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -20 a^{3} - 50 a^{2} + 102 a + 193\) , \( -\frac{395}{3} a^{3} - \frac{1187}{3} a^{2} + 353 a + 875\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-20a^{3}-50a^{2}+102a+193\right){x}-\frac{395}{3}a^{3}-\frac{1187}{3}a^{2}+353a+875$ |
| 28.3-a1 |
28.3-a |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.3 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{4} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.350549734$ |
$815.2175433$ |
4.209852938 |
\( \frac{2795629120}{7203} a^{3} + \frac{2982650816}{2401} a^{2} - \frac{1641242560}{2401} a - \frac{5245830112}{2401} \) |
\( \bigl[\frac{1}{3} a^{2} - 2\) , \( -\frac{1}{3} a^{2} + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( \frac{46}{3} a^{3} + 20 a^{2} - 157 a - 206\) , \( -125 a^{3} - \frac{497}{3} a^{2} + 1280 a + 1696\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-2\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{2}+1\right){x}^{2}+\left(\frac{46}{3}a^{3}+20a^{2}-157a-206\right){x}-125a^{3}-\frac{497}{3}a^{2}+1280a+1696$ |
| 28.3-a2 |
28.3-a |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.3 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.175274867$ |
$1630.435086$ |
4.209852938 |
\( -\frac{43230976}{49} a^{3} - \frac{171812608}{147} a^{2} + \frac{442696448}{49} a + \frac{587197824}{49} \) |
\( \bigl[\frac{1}{3} a^{3} - 2 a\) , \( \frac{1}{3} a^{2} - 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( 64 a^{3} + \frac{254}{3} a^{2} - 656 a - 869\) , \( -966 a^{3} - \frac{3842}{3} a^{2} + 9894 a + 13116\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-2a\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{2}-3\right){x}^{2}+\left(64a^{3}+\frac{254}{3}a^{2}-656a-869\right){x}-966a^{3}-\frac{3842}{3}a^{2}+9894a+13116$ |
| 28.3-b1 |
28.3-b |
$2$ |
$3$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.3 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$220.1947252$ |
1.621887327 |
\( -\frac{159370}{7} a^{3} - \frac{1450574}{21} a^{2} + \frac{298866}{7} a + \frac{685694}{7} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( -\frac{1}{3} a^{2} + a + 2\) , \( 0\) , \( -a^{3} - \frac{2}{3} a^{2} + 9 a + 10\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + 4 a + 5\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{2}+a+2\right){x}^{2}+\left(-a^{3}-\frac{2}{3}a^{2}+9a+10\right){x}-\frac{1}{3}a^{3}-\frac{2}{3}a^{2}+4a+5$ |
| 28.3-b2 |
28.3-b |
$2$ |
$3$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.3 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^2+a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$220.1947252$ |
1.621887327 |
\( -\frac{11466942128949455208}{343} a^{3} - \frac{110096837557310529292}{1029} a^{2} + \frac{20151537540573548134}{343} a + \frac{64493234266685524518}{343} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( -\frac{1}{3} a^{2} + a + 2\) , \( 0\) , \( -\frac{28}{3} a^{3} - \frac{82}{3} a^{2} + 29 a + 70\) , \( \frac{151}{3} a^{3} + \frac{500}{3} a^{2} - 66 a - 263\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{2}+a+2\right){x}^{2}+\left(-\frac{28}{3}a^{3}-\frac{82}{3}a^{2}+29a+70\right){x}+\frac{151}{3}a^{3}+\frac{500}{3}a^{2}-66a-263$ |
| 28.3-c1 |
28.3-c |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.3 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{4} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.410060932$ |
$206.6291436$ |
3.744596185 |
\( \frac{2795629120}{7203} a^{3} + \frac{2982650816}{2401} a^{2} - \frac{1641242560}{2401} a - \frac{5245830112}{2401} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( -\frac{1}{3} a^{3} + 4 a\) , \( \frac{1}{3} a^{2} + a - 2\) , \( -a^{2} + 3 a + 15\) , \( -a^{3} - a^{2} + 9 a + 6\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){x}{y}+\left(\frac{1}{3}a^{2}+a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+4a\right){x}^{2}+\left(-a^{2}+3a+15\right){x}-a^{3}-a^{2}+9a+6$ |
| 28.3-c2 |
28.3-c |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.3 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^2+a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.205030466$ |
$413.2582873$ |
3.744596185 |
\( -\frac{43230976}{49} a^{3} - \frac{171812608}{147} a^{2} + \frac{442696448}{49} a + \frac{587197824}{49} \) |
\( \bigl[\frac{1}{3} a^{3} - 2 a\) , \( \frac{1}{3} a^{3} - 2 a + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{2}{3} a^{3} + a^{2} - 2 a - 4\) , \( \frac{2}{3} a^{3} + \frac{4}{3} a^{2} - 2 a - 4\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-2a\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-2a+1\right){x}^{2}+\left(\frac{2}{3}a^{3}+a^{2}-2a-4\right){x}+\frac{2}{3}a^{3}+\frac{4}{3}a^{2}-2a-4$ |
| 28.3-d1 |
28.3-d |
$2$ |
$3$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.3 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^2+a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$345.7168940$ |
0.848815139 |
\( -\frac{159370}{7} a^{3} - \frac{1450574}{21} a^{2} + \frac{298866}{7} a + \frac{685694}{7} \) |
\( \bigl[\frac{1}{3} a^{3} - 3 a\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 2 a + 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( -6 a^{3} + \frac{56}{3} a^{2} + 13 a - 30\) , \( 133 a^{3} - \frac{1285}{3} a^{2} - 232 a + 755\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-3a\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+2a+2\right){x}^{2}+\left(-6a^{3}+\frac{56}{3}a^{2}+13a-30\right){x}+133a^{3}-\frac{1285}{3}a^{2}-232a+755$ |
| 28.3-d2 |
28.3-d |
$2$ |
$3$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.3 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (1/3a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$4.268109803$ |
0.848815139 |
\( -\frac{11466942128949455208}{343} a^{3} - \frac{110096837557310529292}{1029} a^{2} + \frac{20151537540573548134}{343} a + \frac{64493234266685524518}{343} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 20 a^{3} - 50 a^{2} - 102 a + 193\) , \( \frac{395}{3} a^{3} - \frac{1187}{3} a^{2} - 353 a + 875\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(20a^{3}-50a^{2}-102a+193\right){x}+\frac{395}{3}a^{3}-\frac{1187}{3}a^{2}-353a+875$ |
| 28.4-a1 |
28.4-a |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.4 |
\( 2^{2} \cdot 7 \) |
\( 2^{4} \cdot 7^{4} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (-1/3a^3+1/3a^2+3a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.350549734$ |
$815.2175433$ |
4.209852938 |
\( \frac{6745644800}{7203} a^{3} - \frac{2982650816}{2401} a^{2} - \frac{23032563520}{2401} a + \frac{30545979680}{2401} \) |
\( \bigl[\frac{1}{3} a^{2} - 2\) , \( \frac{1}{3} a^{2} - 3\) , \( \frac{1}{3} a^{2} + a - 2\) , \( -\frac{19}{3} a^{3} - 20 a^{2} + 11 a + 34\) , \( \frac{155}{3} a^{3} + \frac{497}{3} a^{2} - 90 a - 292\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-2\right){x}{y}+\left(\frac{1}{3}a^{2}+a-2\right){y}={x}^{3}+\left(\frac{1}{3}a^{2}-3\right){x}^{2}+\left(-\frac{19}{3}a^{3}-20a^{2}+11a+34\right){x}+\frac{155}{3}a^{3}+\frac{497}{3}a^{2}-90a-292$ |
| 28.4-a2 |
28.4-a |
$2$ |
$2$ |
4.4.18432.1 |
$4$ |
$[4, 0]$ |
28.4 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$18.40007$ |
$(-1/3a^3+1/3a^2+3a-2), (-1/3a^3+1/3a^2+3a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.175274867$ |
$1630.435086$ |
4.209852938 |
\( \frac{53617664}{147} a^{3} + \frac{171812608}{147} a^{2} - \frac{31160064}{49} a - \frac{100052608}{49} \) |
\( \bigl[\frac{1}{3} a^{3} - 2 a\) , \( -\frac{1}{3} a^{2} + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( -\frac{79}{3} a^{3} - \frac{256}{3} a^{2} + 44 a + 147\) , \( \frac{1088}{3} a^{3} + \frac{3481}{3} a^{2} - 638 a - 2040\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-2a\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{2}+1\right){x}^{2}+\left(-\frac{79}{3}a^{3}-\frac{256}{3}a^{2}+44a+147\right){x}+\frac{1088}{3}a^{3}+\frac{3481}{3}a^{2}-638a-2040$ |
*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.
