| 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 |
| 5.1-a1 |
5.1-a |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$551.9647859$ |
2.022242508 |
\( -\frac{6569669}{15} a^{3} - \frac{3208788}{5} a^{2} + \frac{68264269}{15} a + \frac{109241479}{15} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( a^{2} - 8\) , \( 1\) , \( \frac{7}{6} a^{3} + 2 a^{2} - \frac{25}{3} a - \frac{47}{6}\) , \( \frac{1}{2} a^{3} + 5 a^{2} - 6 a - \frac{47}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{41}{6}\right){x}{y}+{y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(\frac{7}{6}a^{3}+2a^{2}-\frac{25}{3}a-\frac{47}{6}\right){x}+\frac{1}{2}a^{3}+5a^{2}-6a-\frac{47}{2}$ |
| 5.1-a2 |
5.1-a |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1103.929571$ |
2.022242508 |
\( -\frac{349256939}{15} a^{3} - \frac{170938389}{5} a^{2} + \frac{3623804488}{15} a + \frac{5801350321}{15} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( -\frac{23}{3} a^{3} + 59 a^{2} - \frac{41}{3} a - \frac{629}{3}\) , \( 105 a^{3} - 358 a^{2} - 206 a + 1110\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{41}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{41}{6}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{6}\right){x}^{2}+\left(-\frac{23}{3}a^{3}+59a^{2}-\frac{41}{3}a-\frac{629}{3}\right){x}+105a^{3}-358a^{2}-206a+1110$ |
| 5.1-a3 |
5.1-a |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2207.859143$ |
2.022242508 |
\( \frac{540473}{5} a^{3} + \frac{1220538}{5} a^{2} - \frac{3552673}{5} a - \frac{6688053}{5} \) |
\( \bigl[a^{2} - 6\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{7}{3} a - \frac{47}{6}\) , \( a\) , \( -\frac{3}{2} a^{3} + 4 a^{2} + 12 a - \frac{47}{2}\) , \( -\frac{7}{6} a^{3} + 6 a^{2} + \frac{31}{3} a - \frac{301}{6}\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{7}{3}a-\frac{47}{6}\right){x}^{2}+\left(-\frac{3}{2}a^{3}+4a^{2}+12a-\frac{47}{2}\right){x}-\frac{7}{6}a^{3}+6a^{2}+\frac{31}{3}a-\frac{301}{6}$ |
| 5.1-a4 |
5.1-a |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2207.859143$ |
2.022242508 |
\( -\frac{3164}{5} a^{3} + \frac{11913}{5} a^{2} + \frac{3136}{5} a - 2900 \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( -a^{2} + a + 7\) , \( a\) , \( 9 a^{3} + 18 a^{2} - 73 a - 122\) , \( \frac{163}{6} a^{3} + 50 a^{2} - \frac{673}{3} a - \frac{2273}{6}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{35}{6}\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(9a^{3}+18a^{2}-73a-122\right){x}+\frac{163}{6}a^{3}+50a^{2}-\frac{673}{3}a-\frac{2273}{6}$ |
| 5.1-a5 |
5.1-a |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$551.9647859$ |
2.022242508 |
\( -\frac{1830682499}{75} a^{3} + \frac{503906304}{5} a^{2} + \frac{419036759}{15} a - \frac{23692257851}{75} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( -a^{2} + a + 7\) , \( a\) , \( -\frac{11}{6} a^{3} + 3 a^{2} + \frac{131}{3} a + \frac{373}{6}\) , \( \frac{119}{2} a^{3} + 105 a^{2} - 525 a - \frac{1759}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{35}{6}\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-\frac{11}{6}a^{3}+3a^{2}+\frac{131}{3}a+\frac{373}{6}\right){x}+\frac{119}{2}a^{3}+105a^{2}-525a-\frac{1759}{2}$ |
| 5.1-a6 |
5.1-a |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$275.9823929$ |
2.022242508 |
\( \frac{4425908224139}{15} a^{3} + \frac{3342835384389}{5} a^{2} - \frac{29209317541288}{15} a - \frac{55559399005201}{15} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( -\frac{1}{6} a^{3} - a^{2} + \frac{1}{3} a + \frac{35}{6}\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( -\frac{5}{6} a^{3} - a^{2} + \frac{50}{3} a - \frac{137}{6}\) , \( -\frac{17}{6} a^{3} - a^{2} + \frac{194}{3} a - \frac{653}{6}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}-a^{2}+\frac{1}{3}a+\frac{35}{6}\right){x}^{2}+\left(-\frac{5}{6}a^{3}-a^{2}+\frac{50}{3}a-\frac{137}{6}\right){x}-\frac{17}{6}a^{3}-a^{2}+\frac{194}{3}a-\frac{653}{6}$ |
| 5.1-b1 |
5.1-b |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.155372902$ |
$264.6436542$ |
2.240451368 |
\( -\frac{250992497}{30} a^{3} + \frac{170938389}{5} a^{2} + \frac{174221012}{15} a - \frac{3334232987}{30} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{7}{3} a - \frac{47}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{7}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{5}{6}\) , \( \frac{5}{6} a^{3} + 2 a^{2} - \frac{17}{3} a - \frac{85}{6}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{41}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{7}{6}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{7}{3}a-\frac{47}{6}\right){x}^{2}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{5}{6}\right){x}+\frac{5}{6}a^{3}+2a^{2}-\frac{17}{3}a-\frac{85}{6}$ |
| 5.1-b2 |
5.1-b |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.577686451$ |
$1058.574617$ |
2.240451368 |
\( -\frac{4694911}{30} a^{3} + \frac{3208788}{5} a^{2} + \frac{3072727}{15} a - \frac{12372707}{6} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( a - 1\) , \( a + 1\) , \( \frac{13}{2} a^{3} + 5 a^{2} - 35 a - \frac{85}{2}\) , \( \frac{11}{2} a^{3} + 60 a^{2} - 76 a - \frac{527}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{41}{6}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(\frac{13}{2}a^{3}+5a^{2}-35a-\frac{85}{2}\right){x}+\frac{11}{2}a^{3}+60a^{2}-76a-\frac{527}{2}$ |
| 5.1-b3 |
5.1-b |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.577686451$ |
$66.16091357$ |
2.240451368 |
\( -\frac{10364321917}{150} a^{3} - \frac{503906304}{5} a^{2} + \frac{10801512773}{15} a + \frac{172670364179}{150} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} - a + 6\) , \( a^{2} - 7\) , \( \frac{41}{3} a^{3} + 2 a^{2} - \frac{418}{3} a - \frac{148}{3}\) , \( \frac{245}{6} a^{3} + 63 a^{2} - \frac{1274}{3} a - \frac{4267}{6}\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-7\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(\frac{41}{3}a^{3}+2a^{2}-\frac{418}{3}a-\frac{148}{3}\right){x}+\frac{245}{6}a^{3}+63a^{2}-\frac{1274}{3}a-\frac{4267}{6}$ |
| 5.1-b4 |
5.1-b |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.288843225$ |
$1058.574617$ |
2.240451368 |
\( -\frac{17691}{10} a^{3} - \frac{11913}{5} a^{2} + 18588 a + \frac{317027}{10} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} - a + 6\) , \( a^{2} - 7\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 4 a - \frac{47}{2}\) , \( -4 a^{3} + 11 a^{2} + 38 a - 106\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-7\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-\frac{1}{2}a^{3}+2a^{2}+4a-\frac{47}{2}\right){x}-4a^{3}+11a^{2}+38a-106$ |
| 5.1-b5 |
5.1-b |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.155372902$ |
$264.6436542$ |
2.240451368 |
\( \frac{7574963814497}{30} a^{3} - \frac{3342835384389}{5} a^{2} - \frac{36497803509812}{15} a + \frac{188459533950827}{30} \) |
\( \bigl[1\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{1}{3} a - \frac{49}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{7}{6}\) , \( -\frac{67}{3} a^{3} + 19 a^{2} + \frac{269}{3} a + \frac{8}{3}\) , \( \frac{2762}{3} a^{3} - 3256 a^{2} - \frac{5077}{3} a + \frac{30503}{3}\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{7}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+a^{2}+\frac{1}{3}a-\frac{49}{6}\right){x}^{2}+\left(-\frac{67}{3}a^{3}+19a^{2}+\frac{269}{3}a+\frac{8}{3}\right){x}+\frac{2762}{3}a^{3}-3256a^{2}-\frac{5077}{3}a+\frac{30503}{3}$ |
| 5.1-b6 |
5.1-b |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.577686451$ |
$1058.574617$ |
2.240451368 |
\( \frac{931137}{10} a^{3} - \frac{1220538}{5} a^{2} - \frac{4495659}{5} a + \frac{4618045}{2} \) |
\( \bigl[1\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{1}{3} a - \frac{49}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{7}{6}\) , \( \frac{37}{2} a^{3} - 81 a^{2} - 22 a + \frac{547}{2}\) , \( 261 a^{3} - 1057 a^{2} - 369 a + 3424\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{7}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+a^{2}+\frac{1}{3}a-\frac{49}{6}\right){x}^{2}+\left(\frac{37}{2}a^{3}-81a^{2}-22a+\frac{547}{2}\right){x}+261a^{3}-1057a^{2}-369a+3424$ |
| 5.1-c1 |
5.1-c |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2207.859143$ |
2.022242508 |
\( \frac{931137}{10} a^{3} - \frac{1220538}{5} a^{2} - \frac{4495659}{5} a + \frac{4618045}{2} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( 0\) , \( \frac{8}{3} a^{3} + 6 a^{2} - \frac{52}{3} a - \frac{97}{3}\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{41}{6}\right){x}{y}={x}^{3}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{35}{6}\right){x}^{2}+\left(\frac{8}{3}a^{3}+6a^{2}-\frac{52}{3}a-\frac{97}{3}\right){x}$ |
| 5.1-c2 |
5.1-c |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$551.9647859$ |
2.022242508 |
\( -\frac{10364321917}{150} a^{3} - \frac{503906304}{5} a^{2} + \frac{10801512773}{15} a + \frac{172670364179}{150} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{4}{3} a - \frac{37}{6}\) , \( a^{2} - 6\) , \( \frac{5}{2} a^{3} + 24 a^{2} - 35 a - \frac{195}{2}\) , \( \frac{82}{3} a^{3} - 21 a^{2} - \frac{353}{3} a + \frac{22}{3}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{41}{6}\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+a^{2}+\frac{4}{3}a-\frac{37}{6}\right){x}^{2}+\left(\frac{5}{2}a^{3}+24a^{2}-35a-\frac{195}{2}\right){x}+\frac{82}{3}a^{3}-21a^{2}-\frac{353}{3}a+\frac{22}{3}$ |
| 5.1-c3 |
5.1-c |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2207.859143$ |
2.022242508 |
\( -\frac{17691}{10} a^{3} - \frac{11913}{5} a^{2} + 18588 a + \frac{317027}{10} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{4}{3} a - \frac{37}{6}\) , \( a^{2} - 6\) , \( \frac{35}{6} a^{3} + 9 a^{2} - \frac{95}{3} a - \frac{385}{6}\) , \( \frac{56}{3} a^{3} + 14 a^{2} - \frac{301}{3} a - \frac{355}{3}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{41}{6}\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+a^{2}+\frac{4}{3}a-\frac{37}{6}\right){x}^{2}+\left(\frac{35}{6}a^{3}+9a^{2}-\frac{95}{3}a-\frac{385}{6}\right){x}+\frac{56}{3}a^{3}+14a^{2}-\frac{301}{3}a-\frac{355}{3}$ |
| 5.1-c4 |
5.1-c |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$551.9647859$ |
2.022242508 |
\( -\frac{4694911}{30} a^{3} + \frac{3208788}{5} a^{2} + \frac{3072727}{15} a - \frac{12372707}{6} \) |
\( \bigl[a^{2} - 6\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{4}{3} a - \frac{43}{6}\) , \( a^{2} + a - 7\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 3 a - \frac{21}{2}\) , \( -\frac{5}{3} a^{3} + \frac{49}{3} a + \frac{31}{3}\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+a^{2}+\frac{4}{3}a-\frac{43}{6}\right){x}^{2}+\left(-\frac{1}{2}a^{3}+2a^{2}+3a-\frac{21}{2}\right){x}-\frac{5}{3}a^{3}+\frac{49}{3}a+\frac{31}{3}$ |
| 5.1-c5 |
5.1-c |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1103.929571$ |
2.022242508 |
\( -\frac{250992497}{30} a^{3} + \frac{170938389}{5} a^{2} + \frac{174221012}{15} a - \frac{3334232987}{30} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( a + 1\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( -\frac{79}{3} a^{3} - 31 a^{2} + \frac{911}{3} a + \frac{1379}{3}\) , \( 236 a^{3} + 370 a^{2} - 2340 a - 3809\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{35}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{41}{6}\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{79}{3}a^{3}-31a^{2}+\frac{911}{3}a+\frac{1379}{3}\right){x}+236a^{3}+370a^{2}-2340a-3809$ |
| 5.1-c6 |
5.1-c |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$275.9823929$ |
2.022242508 |
\( \frac{7574963814497}{30} a^{3} - \frac{3342835384389}{5} a^{2} - \frac{36497803509812}{15} a + \frac{188459533950827}{30} \) |
\( \bigl[a\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a - \frac{7}{6}\) , \( a\) , \( a^{3} - a^{2} - 18 a - 20\) , \( \frac{13}{3} a^{3} - \frac{230}{3} a - \frac{326}{3}\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a-\frac{7}{6}\right){x}^{2}+\left(a^{3}-a^{2}-18a-20\right){x}+\frac{13}{3}a^{3}-\frac{230}{3}a-\frac{326}{3}$ |
| 5.1-d1 |
5.1-d |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.577686451$ |
$66.16091357$ |
2.240451368 |
\( -\frac{1830682499}{75} a^{3} + \frac{503906304}{5} a^{2} + \frac{419036759}{15} a - \frac{23692257851}{75} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a - \frac{7}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{35}{6}\) , \( 8 a^{3} - 4 a^{2} - 34 a - 10\) , \( \frac{83}{6} a^{3} - 64 a^{2} - \frac{38}{3} a + \frac{1283}{6}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{41}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{35}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a-\frac{7}{6}\right){x}^{2}+\left(8a^{3}-4a^{2}-34a-10\right){x}+\frac{83}{6}a^{3}-64a^{2}-\frac{38}{3}a+\frac{1283}{6}$ |
| 5.1-d2 |
5.1-d |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.288843225$ |
$1058.574617$ |
2.240451368 |
\( -\frac{3164}{5} a^{3} + \frac{11913}{5} a^{2} + \frac{3136}{5} a - 2900 \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a - \frac{7}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{35}{6}\) , \( -\frac{7}{6} a^{3} - 4 a^{2} + \frac{28}{3} a + \frac{125}{6}\) , \( -5 a^{3} - 12 a^{2} + 34 a + 65\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{41}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{35}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a-\frac{7}{6}\right){x}^{2}+\left(-\frac{7}{6}a^{3}-4a^{2}+\frac{28}{3}a+\frac{125}{6}\right){x}-5a^{3}-12a^{2}+34a+65$ |
| 5.1-d3 |
5.1-d |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.155372902$ |
$264.6436542$ |
2.240451368 |
\( -\frac{349256939}{15} a^{3} - \frac{170938389}{5} a^{2} + \frac{3623804488}{15} a + \frac{5801350321}{15} \) |
\( \bigl[a^{2} - 6\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{7}{3} a - \frac{43}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( \frac{2}{3} a^{3} + 2 a^{2} - \frac{16}{3} a - \frac{31}{3}\) , \( \frac{2}{3} a^{3} + 3 a^{2} - \frac{13}{3} a - \frac{64}{3}\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{41}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+a^{2}+\frac{7}{3}a-\frac{43}{6}\right){x}^{2}+\left(\frac{2}{3}a^{3}+2a^{2}-\frac{16}{3}a-\frac{31}{3}\right){x}+\frac{2}{3}a^{3}+3a^{2}-\frac{13}{3}a-\frac{64}{3}$ |
| 5.1-d4 |
5.1-d |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.577686451$ |
$1058.574617$ |
2.240451368 |
\( -\frac{6569669}{15} a^{3} - \frac{3208788}{5} a^{2} + \frac{68264269}{15} a + \frac{109241479}{15} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( 0\) , \( 0\) , \( \frac{23}{2} a^{3} + 22 a^{2} - 93 a - \frac{317}{2}\) , \( \frac{7}{2} a^{3} + 19 a^{2} + 30 a + \frac{29}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{35}{6}\right){x}{y}={x}^{3}+\left(\frac{23}{2}a^{3}+22a^{2}-93a-\frac{317}{2}\right){x}+\frac{7}{2}a^{3}+19a^{2}+30a+\frac{29}{2}$ |
| 5.1-d5 |
5.1-d |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.577686451$ |
$1058.574617$ |
2.240451368 |
\( \frac{540473}{5} a^{3} + \frac{1220538}{5} a^{2} - \frac{3552673}{5} a - \frac{6688053}{5} \) |
\( \bigl[1\) , \( -a^{2} + a + 7\) , \( 1\) , \( 53 a^{3} + 81 a^{2} - 552 a - 908\) , \( 690 a^{3} + 1011 a^{2} - 7158 a - 11443\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(53a^{3}+81a^{2}-552a-908\right){x}+690a^{3}+1011a^{2}-7158a-11443$ |
| 5.1-d6 |
5.1-d |
$6$ |
$8$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$14.91276$ |
$(1/2a^3+a^2-5a-21/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.155372902$ |
$264.6436542$ |
2.240451368 |
\( \frac{4425908224139}{15} a^{3} + \frac{3342835384389}{5} a^{2} - \frac{29209317541288}{15} a - \frac{55559399005201}{15} \) |
\( \bigl[1\) , \( -a^{2} + a + 7\) , \( 1\) , \( -\frac{121}{3} a^{3} - 19 a^{2} + \frac{1229}{3} a + \frac{806}{3}\) , \( \frac{7238}{3} a^{3} + 3325 a^{2} - \frac{74980}{3} a - \frac{113659}{3}\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-\frac{121}{3}a^{3}-19a^{2}+\frac{1229}{3}a+\frac{806}{3}\right){x}+\frac{7238}{3}a^{3}+3325a^{2}-\frac{74980}{3}a-\frac{113659}{3}$ |
| 11.1-a1 |
11.1-a |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$16.45738$ |
$(1/6a^3-7/3a-11/6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.201154978$ |
$351.7147644$ |
3.095576241 |
\( -\frac{9077631989}{66} a^{3} - \frac{2221371056}{11} a^{2} + \frac{47094365738}{33} a + \frac{150783937729}{66} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( a^{2} - 7\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( \frac{59}{3} a^{3} + 85 a^{2} - \frac{544}{3} a - \frac{2368}{3}\) , \( \frac{917}{3} a^{3} + 78 a^{2} - \frac{8992}{3} a - \frac{3031}{3}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{35}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(\frac{59}{3}a^{3}+85a^{2}-\frac{544}{3}a-\frac{2368}{3}\right){x}+\frac{917}{3}a^{3}+78a^{2}-\frac{8992}{3}a-\frac{3031}{3}$ |
| 11.1-a2 |
11.1-a |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$16.45738$ |
$(1/6a^3-7/3a-11/6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.300288744$ |
$351.7147644$ |
3.095576241 |
\( -\frac{1060007393}{87846} a^{3} + \frac{746018190}{14641} a^{2} + \frac{411434192}{43923} a - \frac{13361296451}{87846} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{6}\) , \( a + 1\) , \( \frac{47}{6} a^{3} + 17 a^{2} - \frac{155}{3} a - \frac{547}{6}\) , \( \frac{611}{3} a^{3} + 320 a^{2} - \frac{6034}{3} a - \frac{9808}{3}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{35}{6}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{6}\right){x}^{2}+\left(\frac{47}{6}a^{3}+17a^{2}-\frac{155}{3}a-\frac{547}{6}\right){x}+\frac{611}{3}a^{3}+320a^{2}-\frac{6034}{3}a-\frac{9808}{3}$ |
| 11.1-a3 |
11.1-a |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$16.45738$ |
$(1/6a^3-7/3a-11/6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.300288744$ |
$1406.859057$ |
3.095576241 |
\( \frac{254322295397744397}{22} a^{3} - \frac{336710867092897954}{11} a^{2} - \frac{1225387941836094242}{11} a + \frac{6327550891105538363}{22} \) |
\( \bigl[a\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a - \frac{1}{6}\) , \( 0\) , \( -\frac{8}{3} a^{3} + 5 a^{2} + \frac{100}{3} a - \frac{200}{3}\) , \( \frac{27}{2} a^{3} - 33 a^{2} - 148 a + \frac{731}{2}\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a-\frac{1}{6}\right){x}^{2}+\left(-\frac{8}{3}a^{3}+5a^{2}+\frac{100}{3}a-\frac{200}{3}\right){x}+\frac{27}{2}a^{3}-33a^{2}-148a+\frac{731}{2}$ |
| 11.1-a4 |
11.1-a |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$16.45738$ |
$(1/6a^3-7/3a-11/6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.600577489$ |
$1406.859057$ |
3.095576241 |
\( \frac{4823165761}{242} a^{3} - \frac{6386985120}{121} a^{2} - \frac{23238969544}{121} a + \frac{120028019549}{242} \) |
\( \bigl[a\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a - \frac{1}{6}\) , \( 0\) , \( -\frac{1}{6} a^{3} + \frac{10}{3} a + \frac{5}{6}\) , \( \frac{1}{3} a^{3} - a^{2} - \frac{8}{3} a + \frac{31}{3}\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a-\frac{1}{6}\right){x}^{2}+\left(-\frac{1}{6}a^{3}+\frac{10}{3}a+\frac{5}{6}\right){x}+\frac{1}{3}a^{3}-a^{2}-\frac{8}{3}a+\frac{31}{3}$ |
| 11.1-b1 |
11.1-b |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$16.45738$ |
$(1/6a^3-7/3a-11/6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$2.610142249$ |
$47.29414455$ |
3.618123622 |
\( \frac{254322295397744397}{22} a^{3} - \frac{336710867092897954}{11} a^{2} - \frac{1225387941836094242}{11} a + \frac{6327550891105538363}{22} \) |
\( \bigl[a^{2} - 6\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{1}{3} a - \frac{37}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{35}{6}\) , \( 228 a^{3} + 349 a^{2} - 2374 a - 3918\) , \( \frac{8573}{3} a^{3} + 4234 a^{2} - \frac{88993}{3} a - \frac{143503}{3}\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{35}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+a^{2}+\frac{1}{3}a-\frac{37}{6}\right){x}^{2}+\left(228a^{3}+349a^{2}-2374a-3918\right){x}+\frac{8573}{3}a^{3}+4234a^{2}-\frac{88993}{3}a-\frac{143503}{3}$ |
| 11.1-b2 |
11.1-b |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$16.45738$ |
$(1/6a^3-7/3a-11/6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.305071124$ |
$756.7063129$ |
3.618123622 |
\( \frac{4823165761}{242} a^{3} - \frac{6386985120}{121} a^{2} - \frac{23238969544}{121} a + \frac{120028019549}{242} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( -a - 1\) , \( a^{2} + a - 6\) , \( \frac{107}{6} a^{3} + 34 a^{2} - \frac{524}{3} a - \frac{2023}{6}\) , \( -\frac{337}{3} a^{3} - 142 a^{2} + \frac{3587}{3} a + \frac{5222}{3}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{35}{6}\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(\frac{107}{6}a^{3}+34a^{2}-\frac{524}{3}a-\frac{2023}{6}\right){x}-\frac{337}{3}a^{3}-142a^{2}+\frac{3587}{3}a+\frac{5222}{3}$ |
| 11.1-b3 |
11.1-b |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$16.45738$ |
$(1/6a^3-7/3a-11/6)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.652535562$ |
$756.7063129$ |
3.618123622 |
\( -\frac{1060007393}{87846} a^{3} + \frac{746018190}{14641} a^{2} + \frac{411434192}{43923} a - \frac{13361296451}{87846} \) |
\( \bigl[a\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{4}{3} a - \frac{49}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{35}{6}\) , \( \frac{1}{2} a^{3} - 5 a + \frac{11}{2}\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{7}{3} a - \frac{55}{6}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{35}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+a^{2}+\frac{4}{3}a-\frac{49}{6}\right){x}^{2}+\left(\frac{1}{2}a^{3}-5a+\frac{11}{2}\right){x}-\frac{1}{6}a^{3}+a^{2}+\frac{7}{3}a-\frac{55}{6}$ |
| 11.1-b4 |
11.1-b |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$16.45738$ |
$(1/6a^3-7/3a-11/6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.652535562$ |
$756.7063129$ |
3.618123622 |
\( -\frac{9077631989}{66} a^{3} - \frac{2221371056}{11} a^{2} + \frac{47094365738}{33} a + \frac{150783937729}{66} \) |
\( \bigl[a\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{7}{6}\) , \( -2 a^{3} + 8 a^{2} + 19 a - 63\) , \( -\frac{22}{3} a^{3} + 22 a^{2} + \frac{218}{3} a - \frac{607}{3}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{7}{6}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){x}^{2}+\left(-2a^{3}+8a^{2}+19a-63\right){x}-\frac{22}{3}a^{3}+22a^{2}+\frac{218}{3}a-\frac{607}{3}$ |
| 11.2-a1 |
11.2-a |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$16.45738$ |
$(1/6a^3-a^2-1/3a+31/6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.300288744$ |
$351.7147644$ |
3.095576241 |
\( -\frac{3082224043}{87846} a^{3} - \frac{746018190}{14641} a^{2} + \frac{16157491552}{43923} a + \frac{51758123999}{87846} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a - \frac{5}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{6}\) , \( \frac{41}{6} a^{3} + 13 a^{2} - \frac{146}{3} a - \frac{367}{6}\) , \( \frac{242}{3} a^{3} - 226 a^{2} - \frac{610}{3} a + \frac{1997}{3}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{41}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{6}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{3}a-\frac{5}{6}\right){x}^{2}+\left(\frac{41}{6}a^{3}+13a^{2}-\frac{146}{3}a-\frac{367}{6}\right){x}+\frac{242}{3}a^{3}-226a^{2}-\frac{610}{3}a+\frac{1997}{3}$ |
| 11.2-a2 |
11.2-a |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$16.45738$ |
$(1/6a^3-a^2-1/3a+31/6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.201154978$ |
$351.7147644$ |
3.095576241 |
\( -\frac{1087216113}{22} a^{3} + \frac{2221371056}{11} a^{2} + \frac{754251858}{11} a - \frac{14441157887}{22} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} - a^{2} + \frac{7}{3} a + \frac{41}{6}\) , \( 1\) , \( -\frac{7}{3} a^{3} - 59 a^{2} + \frac{173}{3} a + \frac{773}{3}\) , \( \frac{263}{3} a^{3} - 138 a^{2} - \frac{910}{3} a + \frac{821}{3}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{41}{6}\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{6}a^{3}-a^{2}+\frac{7}{3}a+\frac{41}{6}\right){x}^{2}+\left(-\frac{7}{3}a^{3}-59a^{2}+\frac{173}{3}a+\frac{773}{3}\right){x}+\frac{263}{3}a^{3}-138a^{2}-\frac{910}{3}a+\frac{821}{3}$ |
| 11.2-a3 |
11.2-a |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$16.45738$ |
$(1/6a^3-a^2-1/3a+31/6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.600577489$ |
$1406.859057$ |
3.095576241 |
\( \frac{5636725301}{242} a^{3} + \frac{6386985120}{121} a^{2} - \frac{18600594704}{121} a - \frac{70767974511}{242} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( -\frac{1}{6} a^{3} - a^{2} + \frac{1}{3} a + \frac{41}{6}\) , \( 0\) , \( \frac{1}{6} a^{3} - \frac{10}{3} a + \frac{7}{6}\) , \( \frac{1}{2} a^{3} + a^{2} - 4 a - \frac{9}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){x}{y}={x}^{3}+\left(-\frac{1}{6}a^{3}-a^{2}+\frac{1}{3}a+\frac{41}{6}\right){x}^{2}+\left(\frac{1}{6}a^{3}-\frac{10}{3}a+\frac{7}{6}\right){x}+\frac{1}{2}a^{3}+a^{2}-4a-\frac{9}{2}$ |
| 11.2-a4 |
11.2-a |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$16.45738$ |
$(1/6a^3-a^2-1/3a+31/6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.300288744$ |
$1406.859057$ |
3.095576241 |
\( \frac{891578993041014491}{66} a^{3} + \frac{336710867092897954}{11} a^{2} - \frac{2942019691428708002}{33} a - \frac{11192713258196419471}{66} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( -\frac{1}{6} a^{3} - a^{2} + \frac{1}{3} a + \frac{41}{6}\) , \( 0\) , \( -\frac{3}{2} a^{3} - 5 a^{2} + \frac{19}{2}\) , \( \frac{37}{3} a^{3} + 33 a^{2} - \frac{176}{3} a - \frac{392}{3}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){x}{y}={x}^{3}+\left(-\frac{1}{6}a^{3}-a^{2}+\frac{1}{3}a+\frac{41}{6}\right){x}^{2}+\left(-\frac{3}{2}a^{3}-5a^{2}+\frac{19}{2}\right){x}+\frac{37}{3}a^{3}+33a^{2}-\frac{176}{3}a-\frac{392}{3}$ |
| 11.2-b1 |
11.2-b |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$16.45738$ |
$(1/6a^3-a^2-1/3a+31/6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$2.610142249$ |
$47.29414455$ |
3.618123622 |
\( \frac{891578993041014491}{66} a^{3} + \frac{336710867092897954}{11} a^{2} - \frac{2942019691428708002}{33} a - \frac{11192713258196419471}{66} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{7}{3} a - \frac{43}{6}\) , \( a\) , \( \frac{491}{6} a^{3} - 344 a^{2} - \frac{320}{3} a + \frac{6797}{6}\) , \( \frac{2171}{2} a^{3} - 4563 a^{2} - 1401 a + \frac{29867}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{41}{6}\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{6}a^{3}+a^{2}+\frac{7}{3}a-\frac{43}{6}\right){x}^{2}+\left(\frac{491}{6}a^{3}-344a^{2}-\frac{320}{3}a+\frac{6797}{6}\right){x}+\frac{2171}{2}a^{3}-4563a^{2}-1401a+\frac{29867}{2}$ |
| 11.2-b2 |
11.2-b |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$16.45738$ |
$(1/6a^3-a^2-1/3a+31/6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.305071124$ |
$756.7063129$ |
3.618123622 |
\( \frac{5636725301}{242} a^{3} + \frac{6386985120}{121} a^{2} - \frac{18600594704}{121} a - \frac{70767974511}{242} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} + \frac{1}{3} a + \frac{5}{6}\) , \( 1\) , \( \frac{22}{3} a^{3} - 21 a^{2} - \frac{62}{3} a + \frac{205}{3}\) , \( -\frac{193}{6} a^{3} + 102 a^{2} + \frac{202}{3} a - \frac{1825}{6}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{41}{6}\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{1}{3}a+\frac{5}{6}\right){x}^{2}+\left(\frac{22}{3}a^{3}-21a^{2}-\frac{62}{3}a+\frac{205}{3}\right){x}-\frac{193}{6}a^{3}+102a^{2}+\frac{202}{3}a-\frac{1825}{6}$ |
| 11.2-b3 |
11.2-b |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$16.45738$ |
$(1/6a^3-a^2-1/3a+31/6)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.652535562$ |
$756.7063129$ |
3.618123622 |
\( -\frac{3082224043}{87846} a^{3} - \frac{746018190}{14641} a^{2} + \frac{16157491552}{43923} a + \frac{51758123999}{87846} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( a^{2} - 7\) , \( a^{2} - 6\) , \( \frac{4}{3} a^{3} + 2 a^{2} - \frac{41}{3} a - \frac{11}{3}\) , \( -\frac{1}{6} a^{3} + 5 a^{2} + \frac{13}{3} a - \frac{205}{6}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(\frac{4}{3}a^{3}+2a^{2}-\frac{41}{3}a-\frac{11}{3}\right){x}-\frac{1}{6}a^{3}+5a^{2}+\frac{13}{3}a-\frac{205}{6}$ |
| 11.2-b4 |
11.2-b |
$4$ |
$4$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$16.45738$ |
$(1/6a^3-a^2-1/3a+31/6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.652535562$ |
$756.7063129$ |
3.618123622 |
\( -\frac{1087216113}{22} a^{3} + \frac{2221371056}{11} a^{2} + \frac{754251858}{11} a - \frac{14441157887}{22} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( \frac{1}{6} a^{3} - a^{2} - \frac{7}{3} a + \frac{43}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{7}{6}\) , \( -3 a^{3} - 9 a^{2} + 20 a + 63\) , \( -\frac{26}{3} a^{3} - 22 a^{2} + \frac{166}{3} a + \frac{379}{3}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{7}{6}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-a^{2}-\frac{7}{3}a+\frac{43}{6}\right){x}^{2}+\left(-3a^{3}-9a^{2}+20a+63\right){x}-\frac{26}{3}a^{3}-22a^{2}+\frac{166}{3}a+\frac{379}{3}$ |
| 20.1-a1 |
20.1-a |
$2$ |
$2$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$17.73436$ |
$(1/2a^3+a^2-5a-21/2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.445305190$ |
$359.4527298$ |
4.691496469 |
\( -\frac{214001}{60} a^{3} + \frac{305383}{20} a^{2} + \frac{54853}{60} a - \frac{124942}{3} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( \frac{1}{6} a^{3} - \frac{7}{3} a + \frac{1}{6}\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( -\frac{7}{6} a^{3} - a^{2} + \frac{31}{3} a + \frac{71}{6}\) , \( \frac{413}{6} a^{3} + 103 a^{2} - \frac{2147}{3} a - \frac{6973}{6}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{7}{3}a+\frac{1}{6}\right){x}^{2}+\left(-\frac{7}{6}a^{3}-a^{2}+\frac{31}{3}a+\frac{71}{6}\right){x}+\frac{413}{6}a^{3}+103a^{2}-\frac{2147}{3}a-\frac{6973}{6}$ |
| 20.1-a2 |
20.1-a |
$2$ |
$2$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$17.73436$ |
$(1/2a^3+a^2-5a-21/2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.222652595$ |
$359.4527298$ |
4.691496469 |
\( \frac{1346657}{240} a^{3} + \frac{1161901}{80} a^{2} - \frac{1362329}{48} a - \frac{3661819}{60} \) |
\( \bigl[1\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a - \frac{1}{6}\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{7}{6}\) , \( -\frac{25}{3} a^{3} - 21 a^{2} + \frac{170}{3} a + \frac{347}{3}\) , \( \frac{269}{6} a^{3} + 82 a^{2} - \frac{839}{3} a - \frac{2905}{6}\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{7}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a-\frac{1}{6}\right){x}^{2}+\left(-\frac{25}{3}a^{3}-21a^{2}+\frac{170}{3}a+\frac{347}{3}\right){x}+\frac{269}{6}a^{3}+82a^{2}-\frac{839}{3}a-\frac{2905}{6}$ |
| 20.1-b1 |
20.1-b |
$2$ |
$2$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{10} \) |
$17.73436$ |
$(1/2a^3+a^2-5a-21/2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.130085753$ |
$190.0896298$ |
3.623848354 |
\( \frac{4461364253}{1500} a^{3} + \frac{3377251529}{500} a^{2} - \frac{5864955929}{300} a - \frac{13968231781}{375} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( -a^{2} - a + 6\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{6}\) , \( 25 a^{3} - 73 a^{2} - 208 a + 583\) , \( -\frac{965}{3} a^{3} + 816 a^{2} + \frac{9913}{3} a - \frac{24872}{3}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{41}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{6}\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(25a^{3}-73a^{2}-208a+583\right){x}-\frac{965}{3}a^{3}+816a^{2}+\frac{9913}{3}a-\frac{24872}{3}$ |
| 20.1-b2 |
20.1-b |
$2$ |
$2$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{5} \) |
$17.73436$ |
$(1/2a^3+a^2-5a-21/2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.260171506$ |
$380.1792596$ |
3.623848354 |
\( -\frac{385810183859}{50} a^{3} - \frac{565777507637}{50} a^{2} + \frac{4001928738953}{50} a + \frac{3202354723143}{25} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{1}{3} a - \frac{49}{6}\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{7}{6}\) , \( \frac{15}{2} a^{3} + 35 a^{2} - 87 a - \frac{723}{2}\) , \( -\frac{671}{6} a^{3} - 103 a^{2} + \frac{3434}{3} a + \frac{7489}{6}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{7}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+a^{2}+\frac{1}{3}a-\frac{49}{6}\right){x}^{2}+\left(\frac{15}{2}a^{3}+35a^{2}-87a-\frac{723}{2}\right){x}-\frac{671}{6}a^{3}-103a^{2}+\frac{3434}{3}a+\frac{7489}{6}$ |
| 20.1-c1 |
20.1-c |
$2$ |
$2$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{5} \) |
$17.73436$ |
$(1/2a^3+a^2-5a-21/2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.314721022$ |
$263.5098702$ |
4.469381246 |
\( -\frac{385810183859}{50} a^{3} - \frac{565777507637}{50} a^{2} + \frac{4001928738953}{50} a + \frac{3202354723143}{25} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{35}{6}\) , \( 0\) , \( \frac{43}{6} a^{3} - 16 a^{2} - \frac{40}{3} a + \frac{133}{6}\) , \( -\frac{55}{2} a^{3} + 136 a^{2} + 5 a - \frac{855}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{41}{6}\right){x}{y}={x}^{3}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{35}{6}\right){x}^{2}+\left(\frac{43}{6}a^{3}-16a^{2}-\frac{40}{3}a+\frac{133}{6}\right){x}-\frac{55}{2}a^{3}+136a^{2}+5a-\frac{855}{2}$ |
| 20.1-c2 |
20.1-c |
$2$ |
$2$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{10} \) |
$17.73436$ |
$(1/2a^3+a^2-5a-21/2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.157360511$ |
$131.7549351$ |
4.469381246 |
\( \frac{4461364253}{1500} a^{3} + \frac{3377251529}{500} a^{2} - \frac{5864955929}{300} a - \frac{13968231781}{375} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( 33 a^{3} - 9 a^{2} - 298 a + 137\) , \( \frac{675}{2} a^{3} - 575 a^{2} - 3184 a + \frac{11145}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{35}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{35}{6}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}+a^{2}-\frac{4}{3}a-\frac{41}{6}\right){x}^{2}+\left(33a^{3}-9a^{2}-298a+137\right){x}+\frac{675}{2}a^{3}-575a^{2}-3184a+\frac{11145}{2}$ |
| 20.1-d1 |
20.1-d |
$2$ |
$2$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$17.73436$ |
$(1/2a^3+a^2-5a-21/2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.045563058$ |
$923.3538492$ |
2.466169251 |
\( -\frac{214001}{60} a^{3} + \frac{305383}{20} a^{2} + \frac{54853}{60} a - \frac{124942}{3} \) |
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} - a^{2} + \frac{1}{3} a + \frac{35}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{6}\) , \( \frac{3}{2} a^{3} - a^{2} - 10 a + \frac{19}{2}\) , \( \frac{5}{6} a^{3} + 3 a^{2} - \frac{23}{3} a - \frac{73}{6}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{41}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}-a^{2}+\frac{1}{3}a+\frac{35}{6}\right){x}^{2}+\left(\frac{3}{2}a^{3}-a^{2}-10a+\frac{19}{2}\right){x}+\frac{5}{6}a^{3}+3a^{2}-\frac{23}{3}a-\frac{73}{6}$ |
| 20.1-d2 |
20.1-d |
$2$ |
$2$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$17.73436$ |
$(1/2a^3+a^2-5a-21/2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.091126116$ |
$923.3538492$ |
2.466169251 |
\( \frac{1346657}{240} a^{3} + \frac{1161901}{80} a^{2} - \frac{1362329}{48} a - \frac{3661819}{60} \) |
\( \bigl[a\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{4}{3} a - \frac{43}{6}\) , \( 1\) , \( \frac{5}{6} a^{3} - \frac{47}{3} a - \frac{73}{6}\) , \( -\frac{21}{2} a^{3} - 19 a^{2} + 84 a + \frac{275}{2}\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-\frac{1}{6}a^{3}+a^{2}+\frac{4}{3}a-\frac{43}{6}\right){x}^{2}+\left(\frac{5}{6}a^{3}-\frac{47}{3}a-\frac{73}{6}\right){x}-\frac{21}{2}a^{3}-19a^{2}+84a+\frac{275}{2}$ |
| 20.2-a1 |
20.2-a |
$2$ |
$2$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$17.73436$ |
$(1/2a^3+a^2-5a-21/2), (-1/2a^3-a^2+4a+15/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.445305190$ |
$359.4527298$ |
4.691496469 |
\( -\frac{42859}{4} a^{3} - \frac{305383}{20} a^{2} + \frac{453349}{4} a + \frac{3604837}{20} \) |
\( \bigl[a\) , \( -a^{2} + a + 8\) , \( a\) , \( -\frac{5}{6} a^{3} - a^{2} + \frac{17}{3} a + \frac{79}{6}\) , \( \frac{145}{6} a^{3} - 104 a^{2} - \frac{85}{3} a + \frac{2077}{6}\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+8\right){x}^{2}+\left(-\frac{5}{6}a^{3}-a^{2}+\frac{17}{3}a+\frac{79}{6}\right){x}+\frac{145}{6}a^{3}-104a^{2}-\frac{85}{3}a+\frac{2077}{6}$ |
| 20.2-a2 |
20.2-a |
$2$ |
$2$ |
4.4.18625.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$17.73436$ |
$(1/2a^3+a^2-5a-21/2), (-1/2a^3-a^2+4a+15/2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.222652595$ |
$359.4527298$ |
4.691496469 |
\( \frac{95065}{16} a^{3} - \frac{1161901}{80} a^{2} - \frac{5123137}{80} a + \frac{12572529}{80} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -\frac{19}{3} a^{3} + 21 a^{2} + \frac{179}{3} a - \frac{592}{3}\) , \( \frac{89}{2} a^{3} - 83 a^{2} - 436 a + \frac{1507}{2}\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-\frac{19}{3}a^{3}+21a^{2}+\frac{179}{3}a-\frac{592}{3}\right){x}+\frac{89}{2}a^{3}-83a^{2}-436a+\frac{1507}{2}$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
