| 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 |
\( \frac{4425908224139}{15} a^{3} + \frac{3342835384389}{5} a^{2} - \frac{29209317541288}{15} a - \frac{55559399005201}{15} \) |
\( \bigl[1\) , \( -a^{2} + a + 7\) , \( 1\) , \( -\frac{121}{3} a^{3} - 19 a^{2} + \frac{1229}{3} a + \frac{806}{3}\) , \( \frac{7238}{3} a^{3} + 3325 a^{2} - \frac{74980}{3} a - \frac{113659}{3}\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-\frac{121}{3}a^{3}-19a^{2}+\frac{1229}{3}a+\frac{806}{3}\right){x}+\frac{7238}{3}a^{3}+3325a^{2}-\frac{74980}{3}a-\frac{113659}{3}$ |
*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.
