| 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 |
| 8.1-a1 |
8.1-a |
$2$ |
$3$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{27} \) |
$117.82220$ |
$(1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$16.91687096$ |
1.23587 |
\( \frac{534330837929}{128} a^{5} - \frac{534330837929}{16} a^{3} + \frac{1602992513787}{32} a - \frac{377828931641}{16} \) |
\( \bigl[\frac{1}{4} a^{4} + \frac{1}{2} a^{3} - a^{2} - 2 a - 1\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - 4 a\) , \( 0\) , \( \frac{69}{4} a^{5} - 19 a^{4} - \frac{233}{2} a^{3} + \frac{305}{2} a^{2} + 73 a - 75\) , \( 35 a^{5} - \frac{103}{4} a^{4} - 232 a^{3} + \frac{493}{2} a^{2} + 174 a - 149\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-a^{2}-2a-1\right){x}{y}={x}^{3}+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-4a\right){x}^{2}+\left(\frac{69}{4}a^{5}-19a^{4}-\frac{233}{2}a^{3}+\frac{305}{2}a^{2}+73a-75\right){x}+35a^{5}-\frac{103}{4}a^{4}-232a^{3}+\frac{493}{2}a^{2}+174a-149$ |
| 8.1-a2 |
8.1-a |
$2$ |
$3$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$117.82220$ |
$(1/4a^5-2a^3+3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$12332.39893$ |
1.23587 |
\( -\frac{18529}{16} a^{5} + \frac{18529}{2} a^{3} - \frac{55587}{4} a - \frac{18949}{2} \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - a^{2} + 4 a - 1\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - \frac{3}{2} a^{3} + a^{2}\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - 3 a + 2\) , \( \frac{3}{4} a^{5} + \frac{1}{4} a^{4} - \frac{11}{2} a^{3} + \frac{3}{2} a^{2} + 6 a - 3\) , \( \frac{11}{4} a^{5} - \frac{3}{4} a^{4} - \frac{47}{2} a^{3} + 11 a^{2} + 45 a - 27\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-a^{2}+4a-1\right){x}{y}+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-\frac{3}{2}a^{3}+a^{2}\right){x}^{2}+\left(\frac{3}{4}a^{5}+\frac{1}{4}a^{4}-\frac{11}{2}a^{3}+\frac{3}{2}a^{2}+6a-3\right){x}+\frac{11}{4}a^{5}-\frac{3}{4}a^{4}-\frac{47}{2}a^{3}+11a^{2}+45a-27$ |
| 8.1-b1 |
8.1-b |
$4$ |
$21$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$117.82220$ |
$(1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.6.1[3] |
$81$ |
\( 1 \) |
$1$ |
$13.26871297$ |
0.969355 |
\( \frac{106762307747263}{16} a^{5} - \frac{106762307747263}{2} a^{3} + \frac{320286923241789}{4} a - \frac{75492351782981}{2} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + \frac{1}{2} a^{2} + 3 a - 1\) , \( -\frac{1}{4} a^{4} - \frac{1}{2} a^{3} + 2 a^{2} + 3 a - 2\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} - 1\) , \( \frac{47}{4} a^{5} - 3 a^{4} - 89 a^{3} - 23 a^{2} + 156 a + 87\) , \( \frac{659}{4} a^{5} + \frac{71}{4} a^{4} - \frac{2799}{2} a^{3} - 592 a^{2} + 2725 a + 1614\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+\frac{1}{2}a^{2}+3a-1\right){x}{y}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}-1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{4}-\frac{1}{2}a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(\frac{47}{4}a^{5}-3a^{4}-89a^{3}-23a^{2}+156a+87\right){x}+\frac{659}{4}a^{5}+\frac{71}{4}a^{4}-\frac{2799}{2}a^{3}-592a^{2}+2725a+1614$ |
| 8.1-b2 |
8.1-b |
$4$ |
$21$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{63} \) |
$117.82220$ |
$(1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.6.1[3] |
$81$ |
\( 1 \) |
$1$ |
$13.26871297$ |
0.969355 |
\( -\frac{2124901247}{8192} a^{5} + \frac{2124901247}{1024} a^{3} - \frac{6374703741}{2048} a - \frac{1502373901}{1024} \) |
\( \bigl[\frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} + a - 1\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + a + 1\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - 3 a + 1\) , \( -\frac{35}{4} a^{5} - \frac{7}{4} a^{4} + \frac{169}{2} a^{3} + \frac{81}{2} a^{2} - 178 a - 106\) , \( -39 a^{5} - \frac{93}{2} a^{4} + 436 a^{3} + \frac{695}{2} a^{2} - 984 a - 646\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}+a-1\right){x}{y}+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-3a+1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+a+1\right){x}^{2}+\left(-\frac{35}{4}a^{5}-\frac{7}{4}a^{4}+\frac{169}{2}a^{3}+\frac{81}{2}a^{2}-178a-106\right){x}-39a^{5}-\frac{93}{2}a^{4}+436a^{3}+\frac{695}{2}a^{2}-984a-646$ |
| 8.1-b3 |
8.1-b |
$4$ |
$21$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{3} \) |
$117.82220$ |
$(1/4a^5-2a^3+3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$9672.891755$ |
0.969355 |
\( -\frac{753047}{8} a^{5} + 753047 a^{3} - \frac{2259141}{2} a - 574009 \) |
\( \bigl[\frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} + a - 1\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - \frac{3}{2} a^{3} + 2 a^{2} - a - 4\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - a^{2} + 3 a - 1\) , \( \frac{5}{2} a^{5} - 4 a^{4} - 12 a^{3} + 16 a^{2} + 6 a - 5\) , \( \frac{35}{4} a^{5} - 19 a^{4} - 35 a^{3} + 68 a^{2} + 19 a - 22\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}+a-1\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-a^{2}+3a-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-\frac{3}{2}a^{3}+2a^{2}-a-4\right){x}^{2}+\left(\frac{5}{2}a^{5}-4a^{4}-12a^{3}+16a^{2}+6a-5\right){x}+\frac{35}{4}a^{5}-19a^{4}-35a^{3}+68a^{2}+19a-22$ |
| 8.1-b4 |
8.1-b |
$4$ |
$21$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{21} \) |
$117.82220$ |
$(1/4a^5-2a^3+3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$9672.891755$ |
0.969355 |
\( \frac{1063}{64} a^{5} - \frac{1063}{8} a^{3} + \frac{3189}{16} a - \frac{569}{8} \) |
\( \bigl[\frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} + a - 1\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + a + 1\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - 3 a + 1\) , \( \frac{5}{4} a^{5} + 2 a^{4} - \frac{11}{2} a^{3} - 7 a^{2} + 2 a + 4\) , \( \frac{3}{2} a^{5} + \frac{21}{4} a^{4} - 5 a^{3} - 17 a^{2} - a + 3\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}+a-1\right){x}{y}+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-3a+1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+a+1\right){x}^{2}+\left(\frac{5}{4}a^{5}+2a^{4}-\frac{11}{2}a^{3}-7a^{2}+2a+4\right){x}+\frac{3}{2}a^{5}+\frac{21}{4}a^{4}-5a^{3}-17a^{2}-a+3$ |
| 8.1-c1 |
8.1-c |
$4$ |
$21$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$117.82220$ |
$(1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.6.1[3] |
$81$ |
\( 1 \) |
$1$ |
$13.26871297$ |
0.969355 |
\( -\frac{106762307747263}{16} a^{5} + \frac{106762307747263}{2} a^{3} - \frac{320286923241789}{4} a - \frac{75492351782981}{2} \) |
\( \bigl[\frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} - 2\) , \( \frac{1}{4} a^{5} - \frac{5}{2} a^{3} + \frac{1}{2} a^{2} + 6 a - 1\) , \( \frac{1}{4} a^{5} - 2 a^{3} + \frac{1}{2} a^{2} + 3 a - 1\) , \( -190 a^{5} + 118 a^{4} + \frac{3641}{2} a^{3} - \frac{2275}{2} a^{2} - 3816 a + 2396\) , \( -16677 a^{5} + \frac{41963}{4} a^{4} + \frac{320303}{2} a^{3} - \frac{201543}{2} a^{2} - 336752 a + 211922\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}-2\right){x}{y}+\left(\frac{1}{4}a^{5}-2a^{3}+\frac{1}{2}a^{2}+3a-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{5}{2}a^{3}+\frac{1}{2}a^{2}+6a-1\right){x}^{2}+\left(-190a^{5}+118a^{4}+\frac{3641}{2}a^{3}-\frac{2275}{2}a^{2}-3816a+2396\right){x}-16677a^{5}+\frac{41963}{4}a^{4}+\frac{320303}{2}a^{3}-\frac{201543}{2}a^{2}-336752a+211922$ |
| 8.1-c2 |
8.1-c |
$4$ |
$21$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{63} \) |
$117.82220$ |
$(1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.6.1[3] |
$81$ |
\( 1 \) |
$1$ |
$13.26871297$ |
0.969355 |
\( \frac{2124901247}{8192} a^{5} - \frac{2124901247}{1024} a^{3} + \frac{6374703741}{2048} a - \frac{1502373901}{1024} \) |
\( \bigl[\frac{1}{2} a^{2} + a - 2\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + \frac{3}{2} a^{3} - a^{2} - a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( 223 a^{5} - 140 a^{4} - \frac{4285}{2} a^{3} + \frac{2697}{2} a^{2} + 4505 a - 2836\) , \( \frac{23839}{4} a^{5} - \frac{15003}{4} a^{4} - \frac{114479}{2} a^{3} + 36025 a^{2} + 120371 a - 75765\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{1}{4}a^{4}+\frac{3}{2}a^{3}-a^{2}-a\right){x}^{2}+\left(223a^{5}-140a^{4}-\frac{4285}{2}a^{3}+\frac{2697}{2}a^{2}+4505a-2836\right){x}+\frac{23839}{4}a^{5}-\frac{15003}{4}a^{4}-\frac{114479}{2}a^{3}+36025a^{2}+120371a-75765$ |
| 8.1-c3 |
8.1-c |
$4$ |
$21$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{3} \) |
$117.82220$ |
$(1/4a^5-2a^3+3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$9672.891755$ |
0.969355 |
\( \frac{753047}{8} a^{5} - 753047 a^{3} + \frac{2259141}{2} a - 574009 \) |
\( \bigl[\frac{1}{2} a^{2} + a - 2\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - 2 a^{3} + 2 a^{2} + 2 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( \frac{19}{4} a^{5} - \frac{17}{4} a^{4} - 46 a^{3} + 37 a^{2} + 95 a - 68\) , \( -21 a^{5} + \frac{49}{4} a^{4} + 199 a^{3} - \frac{243}{2} a^{2} - 414 a + 254\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-2a^{3}+2a^{2}+2a-2\right){x}^{2}+\left(\frac{19}{4}a^{5}-\frac{17}{4}a^{4}-46a^{3}+37a^{2}+95a-68\right){x}-21a^{5}+\frac{49}{4}a^{4}+199a^{3}-\frac{243}{2}a^{2}-414a+254$ |
| 8.1-c4 |
8.1-c |
$4$ |
$21$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{21} \) |
$117.82220$ |
$(1/4a^5-2a^3+3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.6.1[3] |
$1$ |
\( 1 \) |
$1$ |
$9672.891755$ |
0.969355 |
\( -\frac{1063}{64} a^{5} + \frac{1063}{8} a^{3} - \frac{3189}{16} a - \frac{569}{8} \) |
\( \bigl[\frac{1}{2} a^{2} + a - 2\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + \frac{3}{2} a^{3} - a^{2} - a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( -2 a^{5} + \frac{5}{4} a^{4} + \frac{35}{2} a^{3} - 9 a^{2} - 35 a + 19\) , \( 29 a^{5} - \frac{71}{4} a^{4} - 280 a^{3} + 175 a^{2} + 590 a - 374\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{1}{4}a^{4}+\frac{3}{2}a^{3}-a^{2}-a\right){x}^{2}+\left(-2a^{5}+\frac{5}{4}a^{4}+\frac{35}{2}a^{3}-9a^{2}-35a+19\right){x}+29a^{5}-\frac{71}{4}a^{4}-280a^{3}+175a^{2}+590a-374$ |
| 8.1-d1 |
8.1-d |
$2$ |
$3$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{27} \) |
$117.82220$ |
$(1/4a^5-2a^3+3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$16.91687096$ |
1.23587 |
\( -\frac{534330837929}{128} a^{5} + \frac{534330837929}{16} a^{3} - \frac{1602992513787}{32} a - \frac{377828931641}{16} \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - \frac{3}{2} a^{2} + 4 a + 1\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - a^{2} + 3 a\) , \( \frac{1}{2} a^{3} - 3 a\) , \( -\frac{47}{2} a^{5} + \frac{3}{4} a^{4} + \frac{399}{2} a^{3} + \frac{143}{2} a^{2} - 389 a - 220\) , \( -170 a^{5} - \frac{285}{4} a^{4} + 1574 a^{3} + \frac{1729}{2} a^{2} - 3253 a - 2005\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-\frac{3}{2}a^{2}+4a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-3a\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-a^{2}+3a\right){x}^{2}+\left(-\frac{47}{2}a^{5}+\frac{3}{4}a^{4}+\frac{399}{2}a^{3}+\frac{143}{2}a^{2}-389a-220\right){x}-170a^{5}-\frac{285}{4}a^{4}+1574a^{3}+\frac{1729}{2}a^{2}-3253a-2005$ |
| 8.1-d2 |
8.1-d |
$2$ |
$3$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$117.82220$ |
$(1/4a^5-2a^3+3a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$12332.39893$ |
1.23587 |
\( \frac{18529}{16} a^{5} - \frac{18529}{2} a^{3} + \frac{55587}{4} a - \frac{18949}{2} \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - \frac{3}{2} a^{2} + 3 a + 1\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - \frac{5}{2} a^{3} + 2 a^{2} + 7 a - 2\) , \( \frac{1}{4} a^{4} - a^{2} - 1\) , \( -\frac{31}{4} a^{5} - \frac{19}{4} a^{4} + 74 a^{3} + 45 a^{2} - 152 a - 88\) , \( -53 a^{5} - \frac{135}{4} a^{4} + \frac{1017}{2} a^{3} + 324 a^{2} - 1066 a - 677\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-\frac{3}{2}a^{2}+3a+1\right){x}{y}+\left(\frac{1}{4}a^{4}-a^{2}-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-\frac{5}{2}a^{3}+2a^{2}+7a-2\right){x}^{2}+\left(-\frac{31}{4}a^{5}-\frac{19}{4}a^{4}+74a^{3}+45a^{2}-152a-88\right){x}-53a^{5}-\frac{135}{4}a^{4}+\frac{1017}{2}a^{3}+324a^{2}-1066a-677$ |
| 41.1-a1 |
41.1-a |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$135.01072$ |
$(1/4a^4+1/2a^3-3/2a^2-3a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.002191902$ |
$124836.9195$ |
4.44228 |
\( -\frac{3015328}{1681} a^{5} - \frac{1250800}{1681} a^{4} + \frac{14853824}{1681} a^{3} + \frac{21322496}{1681} a^{2} + \frac{3865600}{1681} a - \frac{14089216}{1681} \) |
\( \bigl[\frac{1}{4} a^{5} - \frac{3}{2} a^{3}\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - \frac{3}{2} a^{3} + a^{2}\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} + a - 1\) , \( \frac{1}{2} a^{5} - a^{4} - \frac{7}{2} a^{3} + \frac{13}{2} a^{2} - 3\) , \( \frac{9}{4} a^{5} - 21 a^{3} - \frac{7}{2} a^{2} + 38 a + 20\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}\right){x}{y}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-\frac{3}{2}a^{3}+a^{2}\right){x}^{2}+\left(\frac{1}{2}a^{5}-a^{4}-\frac{7}{2}a^{3}+\frac{13}{2}a^{2}-3\right){x}+\frac{9}{4}a^{5}-21a^{3}-\frac{7}{2}a^{2}+38a+20$ |
| 41.1-a2 |
41.1-a |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$135.01072$ |
$(1/4a^4+1/2a^3-3/2a^2-3a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.008767609$ |
$62418.45977$ |
4.44228 |
\( -\frac{115519456}{41} a^{5} + \frac{72873632}{41} a^{4} + \frac{1109430144}{41} a^{3} - \frac{699871904}{41} a^{2} - \frac{2332968448}{41} a + \frac{1471821760}{41} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 4 a\) , \( -\frac{1}{4} a^{5} + \frac{3}{2} a^{3} + \frac{1}{2} a^{2} - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -2 a^{5} - \frac{7}{4} a^{4} + \frac{37}{2} a^{3} + 16 a^{2} - 39 a - 27\) , \( \frac{21}{4} a^{5} + \frac{15}{4} a^{4} - \frac{103}{2} a^{3} - 35 a^{2} + 111 a + 71\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+4a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{3}{2}a^{3}+\frac{1}{2}a^{2}-2\right){x}^{2}+\left(-2a^{5}-\frac{7}{4}a^{4}+\frac{37}{2}a^{3}+16a^{2}-39a-27\right){x}+\frac{21}{4}a^{5}+\frac{15}{4}a^{4}-\frac{103}{2}a^{3}-35a^{2}+111a+71$ |
| 41.1-b1 |
41.1-b |
$1$ |
$1$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( -41 \) |
$135.01072$ |
$(1/4a^4+1/2a^3-3/2a^2-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.007616084$ |
$63579.86188$ |
2.62042 |
\( \frac{9151}{82} a^{5} - \frac{103753}{82} a^{4} + \frac{13839}{82} a^{3} + \frac{373586}{41} a^{2} - \frac{265085}{41} a - \frac{308611}{41} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + \frac{1}{2} a^{2} + 4 a - 2\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + 2 a^{3} - 2 a^{2} - 3 a + 3\) , \( \frac{1}{4} a^{5} - 2 a^{3} + 4 a\) , \( -\frac{1}{2} a^{5} + \frac{1}{4} a^{4} + 5 a^{3} - \frac{5}{2} a^{2} - 11 a + 6\) , \( -\frac{3}{4} a^{5} + \frac{1}{2} a^{4} + \frac{15}{2} a^{3} - \frac{9}{2} a^{2} - 16 a + 9\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+\frac{1}{2}a^{2}+4a-2\right){x}{y}+\left(\frac{1}{4}a^{5}-2a^{3}+4a\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{1}{4}a^{4}+2a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-\frac{1}{2}a^{5}+\frac{1}{4}a^{4}+5a^{3}-\frac{5}{2}a^{2}-11a+6\right){x}-\frac{3}{4}a^{5}+\frac{1}{2}a^{4}+\frac{15}{2}a^{3}-\frac{9}{2}a^{2}-16a+9$ |
| 41.2-a1 |
41.2-a |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.2 |
\( 41 \) |
\( 41 \) |
$135.01072$ |
$(1/2a^2+a-2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.008767609$ |
$62418.45977$ |
4.44228 |
\( \frac{74291456}{41} a^{5} - \frac{131315056}{41} a^{4} - \frac{511875648}{41} a^{3} + \frac{904773184}{41} a^{2} + \frac{191124480}{41} a - \frac{337724608}{41} \) |
\( \bigl[\frac{1}{4} a^{5} - \frac{3}{2} a^{3}\) , \( -\frac{1}{4} a^{5} - \frac{1}{4} a^{4} + 2 a^{3} + \frac{3}{2} a^{2} - 3 a - 1\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - a^{2} - 3 a - 1\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + a^{3} - a\) , \( -\frac{1}{2} a^{4} + \frac{1}{2} a^{3} + \frac{5}{2} a^{2} - 2 a - 2\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}\right){x}{y}+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-a^{2}-3a-1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}-\frac{1}{4}a^{4}+2a^{3}+\frac{3}{2}a^{2}-3a-1\right){x}^{2}+\left(-\frac{1}{4}a^{5}+\frac{1}{4}a^{4}+a^{3}-a\right){x}-\frac{1}{2}a^{4}+\frac{1}{2}a^{3}+\frac{5}{2}a^{2}-2a-2$ |
| 41.2-a2 |
41.2-a |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.2 |
\( 41 \) |
\( 41^{2} \) |
$135.01072$ |
$(1/2a^2+a-2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.002191902$ |
$124836.9195$ |
4.44228 |
\( \frac{6906144}{1681} a^{5} + \frac{6908848}{1681} a^{4} - \frac{63030784}{1681} a^{3} - \frac{52769184}{1681} a^{2} + \frac{132537856}{1681} a + \frac{91449152}{1681} \) |
\( \bigl[\frac{1}{4} a^{5} - \frac{3}{2} a^{3}\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + \frac{5}{2} a^{3} - \frac{3}{2} a^{2} - 7 a + 1\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} + a - 2\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - 3 a^{2} - 2 a + 6\) , \( -\frac{17}{4} a^{5} - \frac{17}{2} a^{4} + 30 a^{3} + \frac{113}{2} a^{2} - 14 a - 21\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}\right){x}{y}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}+a-2\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{1}{4}a^{4}+\frac{5}{2}a^{3}-\frac{3}{2}a^{2}-7a+1\right){x}^{2}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-3a^{2}-2a+6\right){x}-\frac{17}{4}a^{5}-\frac{17}{2}a^{4}+30a^{3}+\frac{113}{2}a^{2}-14a-21$ |
| 41.2-b1 |
41.2-b |
$1$ |
$1$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.2 |
\( 41 \) |
\( -41 \) |
$135.01072$ |
$(1/2a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.007616084$ |
$63579.86188$ |
2.62042 |
\( \frac{10137}{41} a^{5} + \frac{62327}{82} a^{4} - \frac{110521}{41} a^{3} - \frac{145555}{41} a^{2} + \frac{152297}{41} a - \frac{17501}{41} \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - a^{2} + 4 a - 1\) , \( -\frac{1}{4} a^{5} - \frac{1}{4} a^{4} + 2 a^{3} + 2 a^{2} - 4 a - 4\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - \frac{3}{2} a^{2} + 4 a + 2\) , \( \frac{1}{4} a^{5} - 3 a^{3} - a^{2} + 7 a + 3\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-a^{2}+4a-1\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-\frac{3}{2}a^{2}+4a+2\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}-\frac{1}{4}a^{4}+2a^{3}+2a^{2}-4a-4\right){x}^{2}+\left(\frac{1}{4}a^{5}-3a^{3}-a^{2}+7a+3\right){x}$ |
| 41.3-a1 |
41.3-a |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( 41^{2} \) |
$135.01072$ |
$(1/4a^5+1/4a^4-5/2a^3-2a^2+5a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.002191902$ |
$124836.9195$ |
4.44228 |
\( \frac{7649728}{1681} a^{5} - \frac{5658048}{1681} a^{4} - \frac{62684992}{1681} a^{3} + \frac{31446688}{1681} a^{2} + \frac{82182144}{1681} a + \frac{28555776}{1681} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - \frac{3}{2} a^{3} + \frac{3}{2} a^{2} + a\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - \frac{3}{2} a^{2} + 4 a + 2\) , \( \frac{1}{4} a^{5} - 2 a^{3} + 3 a + 1\) , \( -\frac{1}{2} a^{5} + \frac{3}{4} a^{4} + \frac{5}{2} a^{3} - 2 a^{2} - 3 a - 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-\frac{3}{2}a^{2}+4a+2\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-\frac{3}{2}a^{3}+\frac{3}{2}a^{2}+a\right){x}^{2}+\left(\frac{1}{4}a^{5}-2a^{3}+3a+1\right){x}-\frac{1}{2}a^{5}+\frac{3}{4}a^{4}+\frac{5}{2}a^{3}-2a^{2}-3a-1$ |
| 41.3-a2 |
41.3-a |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( 41 \) |
$135.01072$ |
$(1/4a^5+1/4a^4-5/2a^3-2a^2+5a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.008767609$ |
$62418.45977$ |
4.44228 |
\( \frac{22882208}{41} a^{5} + \frac{58441424}{41} a^{4} - \frac{80239168}{41} a^{3} - \frac{204901280}{41} a^{2} + \frac{28224512}{41} a + \frac{72077952}{41} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 4 a\) , \( -\frac{1}{4} a^{5} + 2 a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( \frac{1}{4} a^{4} - \frac{3}{2} a^{2} + a + 2\) , \( -\frac{5}{4} a^{5} + \frac{3}{4} a^{4} + 11 a^{3} - \frac{13}{2} a^{2} - 22 a + 13\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - 3 a^{3} + \frac{5}{2} a^{2} + 7 a - 6\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+4a\right){x}{y}+\left(\frac{1}{4}a^{4}-\frac{3}{2}a^{2}+a+2\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+2a^{3}+\frac{1}{2}a^{2}-3a-2\right){x}^{2}+\left(-\frac{5}{4}a^{5}+\frac{3}{4}a^{4}+11a^{3}-\frac{13}{2}a^{2}-22a+13\right){x}+\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-3a^{3}+\frac{5}{2}a^{2}+7a-6$ |
| 41.3-b1 |
41.3-b |
$1$ |
$1$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.3 |
\( 41 \) |
\( -41 \) |
$135.01072$ |
$(1/4a^5+1/4a^4-5/2a^3-2a^2+5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.007616084$ |
$63579.86188$ |
2.62042 |
\( -\frac{105349}{164} a^{5} + \frac{20713}{41} a^{4} + \frac{567293}{82} a^{3} - \frac{228031}{41} a^{2} - \frac{666691}{41} a + \frac{438561}{41} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 4 a + 1\) , \( -\frac{1}{4} a^{5} + \frac{5}{2} a^{3} - \frac{1}{2} a^{2} - 7 a + 2\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - a^{2} + a - 1\) , \( -\frac{1}{2} a^{5} - \frac{1}{2} a^{4} + \frac{7}{2} a^{3} + \frac{3}{2} a^{2} - 6 a + 4\) , \( -\frac{1}{4} a^{4} - \frac{1}{2} a^{3} + a^{2} - 2\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+4a+1\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-a^{2}+a-1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{5}{2}a^{3}-\frac{1}{2}a^{2}-7a+2\right){x}^{2}+\left(-\frac{1}{2}a^{5}-\frac{1}{2}a^{4}+\frac{7}{2}a^{3}+\frac{3}{2}a^{2}-6a+4\right){x}-\frac{1}{4}a^{4}-\frac{1}{2}a^{3}+a^{2}-2$ |
| 41.4-a1 |
41.4-a |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( 41^{2} \) |
$135.01072$ |
$(-1/4a^5+1/4a^4+5/2a^3-2a^2-5a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.002191902$ |
$124836.9195$ |
4.44228 |
\( -\frac{7649728}{1681} a^{5} - \frac{5658048}{1681} a^{4} + \frac{62684992}{1681} a^{3} + \frac{31446688}{1681} a^{2} - \frac{82182144}{1681} a + \frac{28555776}{1681} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{4} a^{5} - \frac{1}{4} a^{4} + \frac{3}{2} a^{3} + \frac{3}{2} a^{2} - a\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - \frac{3}{2} a^{2} + 4 a + 2\) , \( -\frac{1}{4} a^{5} + a^{3} + 1\) , \( \frac{3}{4} a^{4} + a^{3} - 2 a^{2} - 3 a - 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-\frac{3}{2}a^{2}+4a+2\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}-\frac{1}{4}a^{4}+\frac{3}{2}a^{3}+\frac{3}{2}a^{2}-a\right){x}^{2}+\left(-\frac{1}{4}a^{5}+a^{3}+1\right){x}+\frac{3}{4}a^{4}+a^{3}-2a^{2}-3a-1$ |
| 41.4-a2 |
41.4-a |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( 41 \) |
$135.01072$ |
$(-1/4a^5+1/4a^4+5/2a^3-2a^2-5a+2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.008767609$ |
$62418.45977$ |
4.44228 |
\( -\frac{22882208}{41} a^{5} + \frac{58441424}{41} a^{4} + \frac{80239168}{41} a^{3} - \frac{204901280}{41} a^{2} - \frac{28224512}{41} a + \frac{72077952}{41} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 4 a\) , \( \frac{1}{4} a^{5} - 2 a^{3} + \frac{1}{2} a^{2} + 3 a - 2\) , \( \frac{1}{4} a^{4} - \frac{3}{2} a^{2} + a + 2\) , \( \frac{3}{4} a^{5} + \frac{3}{4} a^{4} - \frac{15}{2} a^{3} - \frac{13}{2} a^{2} + 16 a + 13\) , \( -\frac{1}{2} a^{5} - \frac{1}{4} a^{4} + \frac{9}{2} a^{3} + \frac{5}{2} a^{2} - 9 a - 6\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+4a\right){x}{y}+\left(\frac{1}{4}a^{4}-\frac{3}{2}a^{2}+a+2\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-2a^{3}+\frac{1}{2}a^{2}+3a-2\right){x}^{2}+\left(\frac{3}{4}a^{5}+\frac{3}{4}a^{4}-\frac{15}{2}a^{3}-\frac{13}{2}a^{2}+16a+13\right){x}-\frac{1}{2}a^{5}-\frac{1}{4}a^{4}+\frac{9}{2}a^{3}+\frac{5}{2}a^{2}-9a-6$ |
| 41.4-b1 |
41.4-b |
$1$ |
$1$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.4 |
\( 41 \) |
\( -41 \) |
$135.01072$ |
$(-1/4a^5+1/4a^4+5/2a^3-2a^2-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.007616084$ |
$63579.86188$ |
2.62042 |
\( \frac{105349}{164} a^{5} + \frac{20713}{41} a^{4} - \frac{567293}{82} a^{3} - \frac{228031}{41} a^{2} + \frac{666691}{41} a + \frac{438561}{41} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 4 a + 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 3 a + 2\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - a^{2} + a - 1\) , \( \frac{1}{4} a^{5} - \frac{1}{2} a^{4} - \frac{7}{2} a^{3} + \frac{3}{2} a^{2} + 10 a + 4\) , \( -\frac{1}{4} a^{4} - \frac{1}{2} a^{3} + a^{2} + a - 2\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+4a+1\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-a^{2}+a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+3a+2\right){x}^{2}+\left(\frac{1}{4}a^{5}-\frac{1}{2}a^{4}-\frac{7}{2}a^{3}+\frac{3}{2}a^{2}+10a+4\right){x}-\frac{1}{4}a^{4}-\frac{1}{2}a^{3}+a^{2}+a-2$ |
| 41.5-a1 |
41.5-a |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.5 |
\( 41 \) |
\( 41 \) |
$135.01072$ |
$(1/2a^2-a-2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.008767609$ |
$62418.45977$ |
4.44228 |
\( -\frac{74291456}{41} a^{5} - \frac{131315056}{41} a^{4} + \frac{511875648}{41} a^{3} + \frac{904773184}{41} a^{2} - \frac{191124480}{41} a - \frac{337724608}{41} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 4 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 4 a - 2\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} + a - 1\) , \( \frac{5}{4} a^{5} - a^{4} - \frac{27}{2} a^{3} + \frac{17}{2} a^{2} + 31 a - 11\) , \( a^{5} - \frac{3}{4} a^{4} - \frac{21}{2} a^{3} + \frac{17}{2} a^{2} + 22 a - 22\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+4a\right){x}{y}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-4a-2\right){x}^{2}+\left(\frac{5}{4}a^{5}-a^{4}-\frac{27}{2}a^{3}+\frac{17}{2}a^{2}+31a-11\right){x}+a^{5}-\frac{3}{4}a^{4}-\frac{21}{2}a^{3}+\frac{17}{2}a^{2}+22a-22$ |
| 41.5-a2 |
41.5-a |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.5 |
\( 41 \) |
\( 41^{2} \) |
$135.01072$ |
$(1/2a^2-a-2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.002191902$ |
$124836.9195$ |
4.44228 |
\( -\frac{6906144}{1681} a^{5} + \frac{6908848}{1681} a^{4} + \frac{63030784}{1681} a^{3} - \frac{52769184}{1681} a^{2} - \frac{132537856}{1681} a + \frac{91449152}{1681} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 4 a\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - 2 a^{3} + a^{2} + 4 a + 1\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - a^{2} - 1\) , \( \frac{1}{2} a^{5} - \frac{11}{2} a^{3} + 13 a + 1\) , \( \frac{5}{4} a^{5} - \frac{3}{2} a^{4} - \frac{17}{2} a^{3} + \frac{19}{2} a^{2} + 2 a - 1\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+4a\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-a^{2}-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-2a^{3}+a^{2}+4a+1\right){x}^{2}+\left(\frac{1}{2}a^{5}-\frac{11}{2}a^{3}+13a+1\right){x}+\frac{5}{4}a^{5}-\frac{3}{2}a^{4}-\frac{17}{2}a^{3}+\frac{19}{2}a^{2}+2a-1$ |
| 41.5-b1 |
41.5-b |
$1$ |
$1$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.5 |
\( 41 \) |
\( -41 \) |
$135.01072$ |
$(1/2a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.007616084$ |
$63579.86188$ |
2.62042 |
\( -\frac{10137}{41} a^{5} + \frac{62327}{82} a^{4} + \frac{110521}{41} a^{3} - \frac{145555}{41} a^{2} - \frac{152297}{41} a - \frac{17501}{41} \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - a^{2} + 4 a - 1\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - 2 a^{3} + 2 a^{2} + 3 a - 4\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - 3 a + 2\) , \( \frac{1}{4} a^{5} + a^{4} - 4 a^{2} - 4 a + 4\) , \( \frac{1}{2} a^{5} + \frac{7}{4} a^{4} - a^{3} - \frac{15}{2} a^{2} - 2 a + 5\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-a^{2}+4a-1\right){x}{y}+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-2a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(\frac{1}{4}a^{5}+a^{4}-4a^{2}-4a+4\right){x}+\frac{1}{2}a^{5}+\frac{7}{4}a^{4}-a^{3}-\frac{15}{2}a^{2}-2a+5$ |
| 41.6-a1 |
41.6-a |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.6 |
\( 41 \) |
\( 41^{2} \) |
$135.01072$ |
$(1/4a^4-1/2a^3-3/2a^2+3a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.002191902$ |
$124836.9195$ |
4.44228 |
\( \frac{3015328}{1681} a^{5} - \frac{1250800}{1681} a^{4} - \frac{14853824}{1681} a^{3} + \frac{21322496}{1681} a^{2} - \frac{3865600}{1681} a - \frac{14089216}{1681} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{4} a^{5} - \frac{1}{4} a^{4} - 2 a^{3} + 2 a^{2} + 3 a - 4\) , \( \frac{1}{4} a^{4} - a^{2}\) , \( \frac{1}{2} a^{5} + \frac{5}{4} a^{4} - 3 a^{3} - 9 a^{2} - 3 a + 6\) , \( \frac{1}{2} a^{5} + \frac{1}{2} a^{4} - \frac{7}{2} a^{3} - 4 a^{2} + 2 a + 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{4}a^{4}-a^{2}\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{1}{4}a^{4}-2a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(\frac{1}{2}a^{5}+\frac{5}{4}a^{4}-3a^{3}-9a^{2}-3a+6\right){x}+\frac{1}{2}a^{5}+\frac{1}{2}a^{4}-\frac{7}{2}a^{3}-4a^{2}+2a+1$ |
| 41.6-a2 |
41.6-a |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.6 |
\( 41 \) |
\( 41 \) |
$135.01072$ |
$(1/4a^4-1/2a^3-3/2a^2+3a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.008767609$ |
$62418.45977$ |
4.44228 |
\( \frac{115519456}{41} a^{5} + \frac{72873632}{41} a^{4} - \frac{1109430144}{41} a^{3} - \frac{699871904}{41} a^{2} + \frac{2332968448}{41} a + \frac{1471821760}{41} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + 2 a^{3} - \frac{3}{2} a^{2} - 3 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 1\) , \( -\frac{1}{2} a^{5} - \frac{5}{4} a^{4} + \frac{5}{2} a^{3} + \frac{19}{2} a^{2} + 2 a - 6\) , \( \frac{1}{4} a^{5} + \frac{5}{4} a^{4} - \frac{3}{2} a^{3} - \frac{17}{2} a^{2} - 2 a + 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{1}{4}a^{4}+2a^{3}-\frac{3}{2}a^{2}-3a\right){x}^{2}+\left(-\frac{1}{2}a^{5}-\frac{5}{4}a^{4}+\frac{5}{2}a^{3}+\frac{19}{2}a^{2}+2a-6\right){x}+\frac{1}{4}a^{5}+\frac{5}{4}a^{4}-\frac{3}{2}a^{3}-\frac{17}{2}a^{2}-2a+3$ |
| 41.6-b1 |
41.6-b |
$1$ |
$1$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
41.6 |
\( 41 \) |
\( -41 \) |
$135.01072$ |
$(1/4a^4-1/2a^3-3/2a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.007616084$ |
$63579.86188$ |
2.62042 |
\( -\frac{9151}{82} a^{5} - \frac{103753}{82} a^{4} - \frac{13839}{82} a^{3} + \frac{373586}{41} a^{2} + \frac{265085}{41} a - \frac{308611}{41} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + \frac{1}{2} a^{2} + 4 a - 2\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + \frac{5}{2} a^{3} - 2 a^{2} - 5 a + 3\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + a\) , \( -a^{5} + \frac{3}{4} a^{4} + 11 a^{3} - 6 a^{2} - 25 a + 12\) , \( -\frac{1}{4} a^{5} + \frac{3}{2} a^{4} + 4 a^{3} - \frac{23}{2} a^{2} - 10 a + 20\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+\frac{1}{2}a^{2}+4a-2\right){x}{y}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+a\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{1}{4}a^{4}+\frac{5}{2}a^{3}-2a^{2}-5a+3\right){x}^{2}+\left(-a^{5}+\frac{3}{4}a^{4}+11a^{3}-6a^{2}-25a+12\right){x}-\frac{1}{4}a^{5}+\frac{3}{2}a^{4}+4a^{3}-\frac{23}{2}a^{2}-10a+20$ |
| 49.1-a1 |
49.1-a |
$6$ |
$18$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{9} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$39368.65074$ |
1.97264 |
\( -\frac{52672}{49} a^{5} + \frac{421376}{49} a^{3} - \frac{632064}{49} a + \frac{302912}{49} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 3 a\) , \( -\frac{1}{4} a^{5} + 2 a^{3} - 3 a + 1\) , \( 1\) , \( -\frac{1}{4} a^{5} + 2 a^{3} - 3 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+3a\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{4}a^{5}+2a^{3}-3a+1\right){x}^{2}+\left(-\frac{1}{4}a^{5}+2a^{3}-3a+1\right){x}$ |
| 49.1-a2 |
49.1-a |
$6$ |
$18$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{9} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$39368.65074$ |
1.97264 |
\( \frac{52672}{49} a^{5} - \frac{421376}{49} a^{3} + \frac{632064}{49} a + \frac{302912}{49} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 3 a\) , \( \frac{1}{4} a^{5} - 2 a^{3} + 3 a + 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+3a\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{4}a^{5}-2a^{3}+3a+1\right){x}^{2}+{x}$ |
| 49.1-a3 |
49.1-a |
$6$ |
$18$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{27} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$9$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$54.00363613$ |
1.97264 |
\( -\frac{3304980800}{117649} a^{5} + \frac{26439846400}{117649} a^{3} - \frac{39659769600}{117649} a + \frac{18683377472}{117649} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 3 a\) , \( -\frac{1}{4} a^{5} + 2 a^{3} - 3 a + 1\) , \( 1\) , \( a^{5} - 8 a^{3} + 12 a - 9\) , \( \frac{7}{2} a^{5} - 28 a^{3} + 42 a - 27\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+3a\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{4}a^{5}+2a^{3}-3a+1\right){x}^{2}+\left(a^{5}-8a^{3}+12a-9\right){x}+\frac{7}{2}a^{5}-28a^{3}+42a-27$ |
| 49.1-a4 |
49.1-a |
$6$ |
$18$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{27} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$9$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$54.00363613$ |
1.97264 |
\( \frac{3304980800}{117649} a^{5} - \frac{26439846400}{117649} a^{3} + \frac{39659769600}{117649} a + \frac{18683377472}{117649} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 3 a\) , \( \frac{1}{4} a^{5} - 2 a^{3} + 3 a + 1\) , \( 1\) , \( -\frac{5}{4} a^{5} + 10 a^{3} - 15 a - 9\) , \( -\frac{7}{2} a^{5} + 28 a^{3} - 42 a - 27\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+3a\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{4}a^{5}-2a^{3}+3a+1\right){x}^{2}+\left(-\frac{5}{4}a^{5}+10a^{3}-15a-9\right){x}-\frac{7}{2}a^{5}+28a^{3}-42a-27$ |
| 49.1-a5 |
49.1-a |
$6$ |
$18$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{9} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$6561$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.074079061$ |
1.97264 |
\( -\frac{137929867150322368}{49} a^{5} + \frac{1103438937202578944}{49} a^{3} - \frac{1655158405803868416}{49} a + \frac{780249146376863552}{49} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 3 a\) , \( -\frac{1}{4} a^{5} + 2 a^{3} - 3 a + 1\) , \( 1\) , \( \frac{389}{4} a^{5} - 778 a^{3} + 1167 a - 919\) , \( \frac{7231}{4} a^{5} - 14462 a^{3} + 21693 a - 12956\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+3a\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{4}a^{5}+2a^{3}-3a+1\right){x}^{2}+\left(\frac{389}{4}a^{5}-778a^{3}+1167a-919\right){x}+\frac{7231}{4}a^{5}-14462a^{3}+21693a-12956$ |
| 49.1-a6 |
49.1-a |
$6$ |
$18$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{9} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$6561$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.074079061$ |
1.97264 |
\( \frac{137929867150322368}{49} a^{5} - \frac{1103438937202578944}{49} a^{3} + \frac{1655158405803868416}{49} a + \frac{780249146376863552}{49} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 3 a\) , \( \frac{1}{4} a^{5} - 2 a^{3} + 3 a + 1\) , \( 1\) , \( -\frac{195}{2} a^{5} + 780 a^{3} - 1170 a - 919\) , \( -\frac{7231}{4} a^{5} + 14462 a^{3} - 21693 a - 12956\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+3a\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{4}a^{5}-2a^{3}+3a+1\right){x}^{2}+\left(-\frac{195}{2}a^{5}+780a^{3}-1170a-919\right){x}-\frac{7231}{4}a^{5}+14462a^{3}-21693a-12956$ |
| 49.1-b1 |
49.1-b |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3398.768570$ |
1.53271 |
\( -1131575958208 a^{5} - \frac{13968698444800}{7} a^{4} + \frac{54576571387904}{7} a^{3} + \frac{96245502865408}{7} a^{2} - \frac{20376192773376}{7} a - 5133330156736 \) |
\( \bigl[a\) , \( -\frac{1}{4} a^{5} + \frac{5}{2} a^{3} + \frac{1}{2} a^{2} - 7 a - 3\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} - 1\) , \( \frac{3}{2} a^{5} - \frac{1}{4} a^{4} - 15 a^{3} + a^{2} + 32 a + 4\) , \( -\frac{5}{4} a^{5} + \frac{1}{4} a^{4} + \frac{23}{2} a^{3} - \frac{3}{2} a^{2} - 23 a - 2\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}-1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{5}{2}a^{3}+\frac{1}{2}a^{2}-7a-3\right){x}^{2}+\left(\frac{3}{2}a^{5}-\frac{1}{4}a^{4}-15a^{3}+a^{2}+32a+4\right){x}-\frac{5}{4}a^{5}+\frac{1}{4}a^{4}+\frac{23}{2}a^{3}-\frac{3}{2}a^{2}-23a-2$ |
| 49.1-b2 |
49.1-b |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3398.768570$ |
1.53271 |
\( 1131575958208 a^{5} - \frac{13968698444800}{7} a^{4} - \frac{54576571387904}{7} a^{3} + \frac{96245502865408}{7} a^{2} + \frac{20376192773376}{7} a - 5133330156736 \) |
\( \bigl[a\) , \( \frac{1}{4} a^{5} - \frac{5}{2} a^{3} + \frac{1}{2} a^{2} + 7 a - 3\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} - 1\) , \( -\frac{3}{2} a^{5} - \frac{1}{4} a^{4} + \frac{29}{2} a^{3} + a^{2} - 31 a + 4\) , \( a^{5} + \frac{1}{4} a^{4} - 10 a^{3} - \frac{3}{2} a^{2} + 22 a - 2\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}-\frac{5}{2}a^{3}+\frac{1}{2}a^{2}+7a-3\right){x}^{2}+\left(-\frac{3}{2}a^{5}-\frac{1}{4}a^{4}+\frac{29}{2}a^{3}+a^{2}-31a+4\right){x}+a^{5}+\frac{1}{4}a^{4}-10a^{3}-\frac{3}{2}a^{2}+22a-2$ |
| 49.1-c1 |
49.1-c |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3398.768570$ |
1.53271 |
\( -\frac{2439508186048}{7} a^{5} + \frac{6216656098304}{7} a^{4} + \frac{8553018445568}{7} a^{3} - \frac{21795851896832}{7} a^{2} - \frac{3005274604800}{7} a + \frac{7658392696512}{7} \) |
\( \bigl[\frac{1}{4} a^{5} - \frac{3}{2} a^{3} + a\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - \frac{3}{2} a^{2} - a\) , \( \frac{1}{4} a^{4} - a^{2} - 1\) , \( \frac{1}{2} a^{5} - \frac{1}{2} a^{4} - \frac{9}{2} a^{3} + \frac{11}{2} a^{2} + 5 a - 4\) , \( -\frac{1}{4} a^{5} - \frac{11}{4} a^{4} + 2 a^{3} + 19 a^{2} - 2 a - 6\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+a\right){x}{y}+\left(\frac{1}{4}a^{4}-a^{2}-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-\frac{3}{2}a^{2}-a\right){x}^{2}+\left(\frac{1}{2}a^{5}-\frac{1}{2}a^{4}-\frac{9}{2}a^{3}+\frac{11}{2}a^{2}+5a-4\right){x}-\frac{1}{4}a^{5}-\frac{11}{4}a^{4}+2a^{3}+19a^{2}-2a-6$ |
| 49.1-c2 |
49.1-c |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3398.768570$ |
1.53271 |
\( \frac{2439508186048}{7} a^{5} + \frac{6216656098304}{7} a^{4} - \frac{8553018445568}{7} a^{3} - \frac{21795851896832}{7} a^{2} + \frac{3005274604800}{7} a + \frac{7658392696512}{7} \) |
\( \bigl[\frac{1}{4} a^{5} - \frac{3}{2} a^{3} + a\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + \frac{3}{2} a^{3} - \frac{3}{2} a^{2} + a\) , \( \frac{1}{4} a^{4} - a^{2} - 1\) , \( -\frac{1}{2} a^{5} - \frac{1}{2} a^{4} + \frac{7}{2} a^{3} + \frac{11}{2} a^{2} - 4 a - 4\) , \( \frac{1}{4} a^{5} - \frac{11}{4} a^{4} - 2 a^{3} + 19 a^{2} + 2 a - 6\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+a\right){x}{y}+\left(\frac{1}{4}a^{4}-a^{2}-1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{1}{4}a^{4}+\frac{3}{2}a^{3}-\frac{3}{2}a^{2}+a\right){x}^{2}+\left(-\frac{1}{2}a^{5}-\frac{1}{2}a^{4}+\frac{7}{2}a^{3}+\frac{11}{2}a^{2}-4a-4\right){x}+\frac{1}{4}a^{5}-\frac{11}{4}a^{4}-2a^{3}+19a^{2}+2a-6$ |
| 49.1-d1 |
49.1-d |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3398.768570$ |
1.53271 |
\( -\frac{12316872843328}{7} a^{5} + 1107434620928 a^{4} + \frac{118289712061184}{7} a^{3} - \frac{74449650968576}{7} a^{2} - \frac{248747485463808}{7} a + \frac{156557694633664}{7} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{4} a^{4} + \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - 4 a - 2\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - 2 a + 2\) , \( a^{5} - \frac{1}{2} a^{4} - 7 a^{3} + \frac{7}{2} a^{2} + 8 a - 2\) , \( -\frac{3}{4} a^{4} - \frac{3}{2} a^{3} + 6 a^{2} + 4 a - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(-\frac{1}{4}a^{4}+\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-4a-2\right){x}^{2}+\left(a^{5}-\frac{1}{2}a^{4}-7a^{3}+\frac{7}{2}a^{2}+8a-2\right){x}-\frac{3}{4}a^{4}-\frac{3}{2}a^{3}+6a^{2}+4a-5$ |
| 49.1-d2 |
49.1-d |
$2$ |
$2$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3398.768570$ |
1.53271 |
\( \frac{12316872843328}{7} a^{5} + 1107434620928 a^{4} - \frac{118289712061184}{7} a^{3} - \frac{74449650968576}{7} a^{2} + \frac{248747485463808}{7} a + \frac{156557694633664}{7} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{4} a^{4} - \frac{1}{2} a^{3} + \frac{3}{2} a^{2} + 4 a - 2\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - 2 a + 2\) , \( -\frac{3}{4} a^{5} - \frac{1}{2} a^{4} + \frac{9}{2} a^{3} + \frac{7}{2} a^{2} - 3 a - 2\) , \( -\frac{3}{4} a^{4} + \frac{1}{2} a^{3} + 6 a^{2} - a - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(-\frac{1}{4}a^{4}-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+4a-2\right){x}^{2}+\left(-\frac{3}{4}a^{5}-\frac{1}{2}a^{4}+\frac{9}{2}a^{3}+\frac{7}{2}a^{2}-3a-2\right){x}-\frac{3}{4}a^{4}+\frac{1}{2}a^{3}+6a^{2}-a-5$ |
| 49.2-a1 |
49.2-a |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{3} \) |
$137.03115$ |
$(-1/2a^3+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$7$ |
7B.6.1[3] |
$1$ |
\( 2 \) |
$0.258702844$ |
$1566.213001$ |
4.38533 |
\( -\frac{3543899323}{4} a^{5} + 7087798646 a^{3} - 10631697969 a - 5012646531 \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - a^{2} + 4 a - 1\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{5}{2} a^{3} - \frac{3}{2} a^{2} + 7 a\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - a^{2} - 2 a - 1\) , \( 5 a^{5} + \frac{17}{4} a^{4} - 54 a^{3} - \frac{33}{2} a^{2} + 142 a - 66\) , \( \frac{215}{4} a^{5} - 50 a^{4} - \frac{903}{2} a^{3} + \frac{793}{2} a^{2} + 667 a - 462\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-a^{2}+4a-1\right){x}{y}+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-a^{2}-2a-1\right){y}={x}^{3}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{5}{2}a^{3}-\frac{3}{2}a^{2}+7a\right){x}^{2}+\left(5a^{5}+\frac{17}{4}a^{4}-54a^{3}-\frac{33}{2}a^{2}+142a-66\right){x}+\frac{215}{4}a^{5}-50a^{4}-\frac{903}{2}a^{3}+\frac{793}{2}a^{2}+667a-462$ |
| 49.2-a2 |
49.2-a |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{9} \) |
$137.03115$ |
$(-1/2a^3+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$7$ |
7B.6.1[3] |
$1$ |
\( 2 \) |
$0.036957549$ |
$10963.49100$ |
4.38533 |
\( \frac{589}{4} a^{5} - 1178 a^{3} + 1767 a + 843 \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - \frac{3}{2} a^{2} + a + 2\) , \( -\frac{1}{4} a^{4} + \frac{1}{2} a^{3} + a^{2} - 3 a + 1\) , \( 0\) , \( \frac{3}{4} a^{5} + \frac{3}{4} a^{4} - 4 a^{3} - 2 a^{2} + 2 a + 5\) , \( \frac{3}{4} a^{5} + a^{4} - \frac{7}{2} a^{3} - 2 a^{2} + a + 2\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-\frac{3}{2}a^{2}+a+2\right){x}{y}={x}^{3}+\left(-\frac{1}{4}a^{4}+\frac{1}{2}a^{3}+a^{2}-3a+1\right){x}^{2}+\left(\frac{3}{4}a^{5}+\frac{3}{4}a^{4}-4a^{3}-2a^{2}+2a+5\right){x}+\frac{3}{4}a^{5}+a^{4}-\frac{7}{2}a^{3}-2a^{2}+a+2$ |
| 49.2-b1 |
49.2-b |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{9} \) |
$137.03115$ |
$(-1/2a^3+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$7$ |
7B.1.6[3] |
$49$ |
\( 2 \) |
$3.948140896$ |
$1.503024395$ |
3.14706 |
\( -\frac{3543899323}{4} a^{5} + 7087798646 a^{3} - 10631697969 a - 5012646531 \) |
\( \bigl[\frac{1}{4} a^{4} + \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - 3 a + 2\) , \( -\frac{1}{4} a^{5} + 2 a^{3} - 3 a - 1\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + a + 1\) , \( -\frac{9}{2} a^{5} - 5 a^{4} + \frac{119}{2} a^{3} + \frac{29}{2} a^{2} - 137 a - 75\) , \( -a^{5} - 54 a^{4} + 163 a^{3} + 190 a^{2} - 503 a - 342\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-3a+2\right){x}{y}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+a+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+2a^{3}-3a-1\right){x}^{2}+\left(-\frac{9}{2}a^{5}-5a^{4}+\frac{119}{2}a^{3}+\frac{29}{2}a^{2}-137a-75\right){x}-a^{5}-54a^{4}+163a^{3}+190a^{2}-503a-342$ |
| 49.2-b2 |
49.2-b |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{3} \) |
$137.03115$ |
$(-1/2a^3+3a+1)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$7$ |
7B.1.1[3] |
$1$ |
\( 2 \) |
$0.564020128$ |
$25261.33100$ |
3.14706 |
\( \frac{589}{4} a^{5} - 1178 a^{3} + 1767 a + 843 \) |
\( \bigl[\frac{1}{4} a^{4} + \frac{1}{2} a^{3} - a^{2} - 2 a - 1\) , \( -\frac{1}{4} a^{4} + a^{2} + a\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - \frac{3}{2} a^{2} + 1\) , \( \frac{1}{4} a^{5} + \frac{1}{2} a^{4} - 2 a^{3} - \frac{3}{2} a^{2} + 2 a + 2\) , \( \frac{1}{4} a^{5} + \frac{3}{4} a^{4} - \frac{1}{2} a^{3} - \frac{9}{2} a^{2} - a + 3\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-a^{2}-2a-1\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-\frac{3}{2}a^{3}-\frac{3}{2}a^{2}+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{4}+a^{2}+a\right){x}^{2}+\left(\frac{1}{4}a^{5}+\frac{1}{2}a^{4}-2a^{3}-\frac{3}{2}a^{2}+2a+2\right){x}+\frac{1}{4}a^{5}+\frac{3}{4}a^{4}-\frac{1}{2}a^{3}-\frac{9}{2}a^{2}-a+3$ |
| 49.3-a1 |
49.3-a |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{3} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$7$ |
7B.6.1[3] |
$1$ |
\( 2 \) |
$0.258702844$ |
$1566.213001$ |
4.38533 |
\( \frac{3543899323}{4} a^{5} - 7087798646 a^{3} + 10631697969 a - 5012646531 \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - \frac{3}{2} a^{2} + 3 a + 1\) , \( -\frac{1}{4} a^{5} + 2 a^{3} + \frac{1}{2} a^{2} - 4 a - 2\) , \( \frac{1}{4} a^{5} - 2 a^{3} + \frac{1}{2} a^{2} + 3 a - 1\) , \( -\frac{295}{4} a^{5} - \frac{201}{4} a^{4} + \frac{1431}{2} a^{3} + \frac{927}{2} a^{2} - 1513 a - 959\) , \( -\frac{4305}{4} a^{5} - 666 a^{4} + \frac{20627}{2} a^{3} + \frac{12903}{2} a^{2} - 21664 a - 13622\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-\frac{3}{2}a^{2}+3a+1\right){x}{y}+\left(\frac{1}{4}a^{5}-2a^{3}+\frac{1}{2}a^{2}+3a-1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+2a^{3}+\frac{1}{2}a^{2}-4a-2\right){x}^{2}+\left(-\frac{295}{4}a^{5}-\frac{201}{4}a^{4}+\frac{1431}{2}a^{3}+\frac{927}{2}a^{2}-1513a-959\right){x}-\frac{4305}{4}a^{5}-666a^{4}+\frac{20627}{2}a^{3}+\frac{12903}{2}a^{2}-21664a-13622$ |
| 49.3-a2 |
49.3-a |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{9} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$7$ |
7B.6.1[3] |
$1$ |
\( 2 \) |
$0.036957549$ |
$10963.49100$ |
4.38533 |
\( -\frac{589}{4} a^{5} + 1178 a^{3} - 1767 a + 843 \) |
\( \bigl[\frac{1}{4} a^{4} - a^{2} + a\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + \frac{3}{2} a^{3} - a^{2} - 1\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3}\) , \( -\frac{21}{4} a^{5} + 4 a^{4} + \frac{105}{2} a^{3} - 33 a^{2} - 114 a + 72\) , \( -a^{5} + 3 a^{4} + \frac{25}{2} a^{3} - \frac{35}{2} a^{2} - 28 a + 21\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{4}-a^{2}+a\right){x}{y}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}+\frac{1}{4}a^{4}+\frac{3}{2}a^{3}-a^{2}-1\right){x}^{2}+\left(-\frac{21}{4}a^{5}+4a^{4}+\frac{105}{2}a^{3}-33a^{2}-114a+72\right){x}-a^{5}+3a^{4}+\frac{25}{2}a^{3}-\frac{35}{2}a^{2}-28a+21$ |
| 49.3-b1 |
49.3-b |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{9} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$7$ |
7B.1.6[3] |
$49$ |
\( 2 \) |
$3.948140896$ |
$1.503024395$ |
3.14706 |
\( \frac{3543899323}{4} a^{5} - 7087798646 a^{3} + 10631697969 a - 5012646531 \) |
\( \bigl[\frac{1}{4} a^{4} + \frac{1}{2} a^{3} - a^{2} - 2 a\) , \( -\frac{1}{4} a^{5} - \frac{1}{4} a^{4} + \frac{5}{2} a^{3} + 2 a^{2} - 7 a - 2\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - a^{2} + 4 a - 1\) , \( \frac{353}{2} a^{5} - 108 a^{4} - \frac{3391}{2} a^{3} + \frac{2085}{2} a^{2} + 3562 a - 2226\) , \( \frac{8531}{2} a^{5} - \frac{10723}{4} a^{4} - 40977 a^{3} + \frac{51495}{2} a^{2} + 86190 a - 54233\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{4}+\frac{1}{2}a^{3}-a^{2}-2a\right){x}{y}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-a^{2}+4a-1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{5}-\frac{1}{4}a^{4}+\frac{5}{2}a^{3}+2a^{2}-7a-2\right){x}^{2}+\left(\frac{353}{2}a^{5}-108a^{4}-\frac{3391}{2}a^{3}+\frac{2085}{2}a^{2}+3562a-2226\right){x}+\frac{8531}{2}a^{5}-\frac{10723}{4}a^{4}-40977a^{3}+\frac{51495}{2}a^{2}+86190a-54233$ |
| 49.3-b2 |
49.3-b |
$2$ |
$7$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{3} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
✓ |
$7$ |
7B.1.1[3] |
$1$ |
\( 2 \) |
$0.564020128$ |
$25261.33100$ |
3.14706 |
\( -\frac{589}{4} a^{5} + 1178 a^{3} - 1767 a + 843 \) |
\( \bigl[\frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - \frac{3}{2} a^{2} + 4 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 3\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} + a - 2\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 3 a^{3} - \frac{5}{2} a^{2} + 6 a + 6\) , \( \frac{15}{4} a^{5} + \frac{5}{2} a^{4} - \frac{73}{2} a^{3} - 23 a^{2} + 77 a + 46\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-2a^{3}-\frac{3}{2}a^{2}+4a+1\right){x}{y}+\left(\frac{1}{4}a^{5}-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}+a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-3\right){x}^{2}+\left(\frac{1}{4}a^{5}+\frac{1}{4}a^{4}-3a^{3}-\frac{5}{2}a^{2}+6a+6\right){x}+\frac{15}{4}a^{5}+\frac{5}{2}a^{4}-\frac{73}{2}a^{3}-23a^{2}+77a+46$ |
*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.
