| 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 |
| 19.1-a1 |
19.1-a |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{4} \) |
$18.04173$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.002652106$ |
$87.67404983$ |
5.026214859 |
\( -\frac{18434434191632}{390963} a^{3} + \frac{87572035744223}{390963} a^{2} + \frac{3050476507270}{130321} a - \frac{94551298943712}{130321} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 3 a\) , \( a\) , \( -6 a^{3} + \frac{50}{3} a^{2} + \frac{163}{3} a - 119\) , \( 23 a^{3} - \frac{260}{3} a^{2} - \frac{559}{3} a + 685\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+3a\right){x}^{2}+\left(-6a^{3}+\frac{50}{3}a^{2}+\frac{163}{3}a-119\right){x}+23a^{3}-\frac{260}{3}a^{2}-\frac{559}{3}a+685$ |
| 19.1-a2 |
19.1-a |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$18.04173$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.001326053$ |
$350.6961993$ |
5.026214859 |
\( -\frac{57314}{361} a^{3} + \frac{2327074}{361} a^{2} - \frac{2357391}{361} a - \frac{9926829}{361} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 3 a\) , \( a\) , \( -a^{3} - \frac{5}{3} a^{2} + \frac{38}{3} a + 26\) , \( \frac{1}{3} a^{3} - 5 a^{2} + \frac{2}{3} a + 48\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+3a\right){x}^{2}+\left(-a^{3}-\frac{5}{3}a^{2}+\frac{38}{3}a+26\right){x}+\frac{1}{3}a^{3}-5a^{2}+\frac{2}{3}a+48$ |
| 19.1-b1 |
19.1-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$18.04173$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$576.9355257$ |
2.064437623 |
\( -\frac{57314}{361} a^{3} + \frac{2327074}{361} a^{2} - \frac{2357391}{361} a - \frac{9926829}{361} \) |
\( \bigl[\frac{1}{3} a^{2} - \frac{1}{3} a - 2\) , \( -\frac{1}{3} a^{3} + \frac{10}{3} a + 4\) , \( \frac{1}{3} a^{3} - \frac{7}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{16}{3} a^{2} + 7 a + 27\) , \( 3 a^{3} - 19 a^{2} + 7 a + 68\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{7}{3}a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{10}{3}a+4\right){x}^{2}+\left(\frac{1}{3}a^{3}-\frac{16}{3}a^{2}+7a+27\right){x}+3a^{3}-19a^{2}+7a+68$ |
| 19.1-b2 |
19.1-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{4} \) |
$18.04173$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$144.2338814$ |
2.064437623 |
\( -\frac{18434434191632}{390963} a^{3} + \frac{87572035744223}{390963} a^{2} + \frac{3050476507270}{130321} a - \frac{94551298943712}{130321} \) |
\( \bigl[\frac{1}{3} a^{2} + \frac{2}{3} a - 2\) , \( -\frac{1}{3} a^{3} + \frac{10}{3} a + 4\) , \( 0\) , \( -\frac{56}{3} a^{3} + 85 a^{2} + \frac{485}{3} a - 646\) , \( -\frac{1883}{3} a^{3} - 10 a^{2} + \frac{13955}{3} a - 1005\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-2\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{10}{3}a+4\right){x}^{2}+\left(-\frac{56}{3}a^{3}+85a^{2}+\frac{485}{3}a-646\right){x}-\frac{1883}{3}a^{3}-10a^{2}+\frac{13955}{3}a-1005$ |
| 19.2-a1 |
19.2-a |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$18.04173$ |
$(1/3a^3-a^2-7/3a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.001326053$ |
$350.6961993$ |
5.026214859 |
\( \frac{57314}{361} a^{3} + \frac{113428}{19} a^{2} - \frac{2124815}{361} a - \frac{10014460}{361} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{10}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{7}{3} a + 3\) , \( \frac{1}{3} a^{2} + \frac{2}{3} a - 2\) , \( -2 a^{3} - a^{2} + 24 a + 34\) , \( -4 a^{3} - \frac{8}{3} a^{2} + \frac{146}{3} a + 67\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{10}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{7}{3}a+3\right){x}^{2}+\left(-2a^{3}-a^{2}+24a+34\right){x}-4a^{3}-\frac{8}{3}a^{2}+\frac{146}{3}a+67$ |
| 19.2-a2 |
19.2-a |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{4} \) |
$18.04173$ |
$(1/3a^3-a^2-7/3a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.002652106$ |
$87.67404983$ |
5.026214859 |
\( \frac{18434434191632}{390963} a^{3} + \frac{1698354377333}{20577} a^{2} - \frac{128992198435360}{390963} a - \frac{68454955252245}{130321} \) |
\( \bigl[a + 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{8}{3} a + 2\) , \( a + 1\) , \( \frac{2}{3} a^{3} - \frac{32}{3} a - 11\) , \( -a^{3} - \frac{32}{3} a^{2} + \frac{71}{3} a + 62\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{8}{3}a+2\right){x}^{2}+\left(\frac{2}{3}a^{3}-\frac{32}{3}a-11\right){x}-a^{3}-\frac{32}{3}a^{2}+\frac{71}{3}a+62$ |
| 19.2-b1 |
19.2-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$18.04173$ |
$(1/3a^3-a^2-7/3a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$576.9355257$ |
2.064437623 |
\( \frac{57314}{361} a^{3} + \frac{113428}{19} a^{2} - \frac{2124815}{361} a - \frac{10014460}{361} \) |
\( \bigl[\frac{1}{3} a^{2} - \frac{1}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{10}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 1\) , \( -\frac{4}{3} a^{3} - 2 a^{2} + \frac{31}{3} a + 18\) , \( -\frac{13}{3} a^{3} - \frac{26}{3} a^{2} + 29 a + 50\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{10}{3}a-2\right){x}^{2}+\left(-\frac{4}{3}a^{3}-2a^{2}+\frac{31}{3}a+18\right){x}-\frac{13}{3}a^{3}-\frac{26}{3}a^{2}+29a+50$ |
| 19.2-b2 |
19.2-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{4} \) |
$18.04173$ |
$(1/3a^3-a^2-7/3a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$144.2338814$ |
2.064437623 |
\( \frac{18434434191632}{390963} a^{3} + \frac{1698354377333}{20577} a^{2} - \frac{128992198435360}{390963} a - \frac{68454955252245}{130321} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{11}{3} a - 3\) , \( \frac{1}{3} a^{2} + \frac{2}{3} a - 2\) , \( -\frac{61}{3} a^{3} + \frac{367}{3} a^{2} - 39 a - 447\) , \( \frac{22808}{3} a^{3} - \frac{109892}{3} a^{2} - 2602 a + 120166\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+1\right){x}{y}+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{11}{3}a-3\right){x}^{2}+\left(-\frac{61}{3}a^{3}+\frac{367}{3}a^{2}-39a-447\right){x}+\frac{22808}{3}a^{3}-\frac{109892}{3}a^{2}-2602a+120166$ |
| 25.2-a1 |
25.2-a |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{12} \) |
$18.67139$ |
$(1/3a^3-a^2-7/3a+5), (1/3a^3+2/3a^2-2a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.195160173$ |
$185.4745894$ |
3.108574925 |
\( -\frac{393466}{75} a^{2} + \frac{393466}{75} a + \frac{21791541}{125} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 1\) , \( -\frac{1}{3} a^{3} + \frac{10}{3} a + 2\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 1\) , \( -2 a^{3} + 16 a - 3\) , \( -\frac{16}{3} a^{3} - \frac{52}{3} a^{2} + \frac{104}{3} a + 114\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{10}{3}a+2\right){x}^{2}+\left(-2a^{3}+16a-3\right){x}-\frac{16}{3}a^{3}-\frac{52}{3}a^{2}+\frac{104}{3}a+114$ |
| 25.2-a2 |
25.2-a |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$18.67139$ |
$(1/3a^3-a^2-7/3a+5), (1/3a^3+2/3a^2-2a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$0.390320347$ |
$370.9491788$ |
3.108574925 |
\( -\frac{20192}{75} a^{2} + \frac{20192}{75} a + \frac{14561}{5} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 1\) , \( -\frac{1}{3} a^{3} + \frac{10}{3} a + 2\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 1\) , \( -\frac{1}{3} a^{3} + \frac{13}{3} a + 2\) , \( a + 1\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{10}{3}a+2\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{13}{3}a+2\right){x}+a+1$ |
| 25.2-b1 |
25.2-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$18.67139$ |
$(1/3a^3-a^2-7/3a+5), (1/3a^3+2/3a^2-2a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$0.390320347$ |
$370.9491788$ |
3.108574925 |
\( -\frac{20192}{75} a^{2} + \frac{20192}{75} a + \frac{14561}{5} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{7}{3} a - 3\) , \( -\frac{1}{3} a^{2} + \frac{4}{3} a + 3\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a\) , \( \frac{4}{3} a^{3} + 2 a^{2} - \frac{22}{3} a - 11\) , \( \frac{8}{3} a^{3} + \frac{13}{3} a^{2} - 17 a - 29\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{7}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a\right){y}={x}^{3}+\left(-\frac{1}{3}a^{2}+\frac{4}{3}a+3\right){x}^{2}+\left(\frac{4}{3}a^{3}+2a^{2}-\frac{22}{3}a-11\right){x}+\frac{8}{3}a^{3}+\frac{13}{3}a^{2}-17a-29$ |
| 25.2-b2 |
25.2-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{12} \) |
$18.67139$ |
$(1/3a^3-a^2-7/3a+5), (1/3a^3+2/3a^2-2a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.195160173$ |
$185.4745894$ |
3.108574925 |
\( -\frac{393466}{75} a^{2} + \frac{393466}{75} a + \frac{21791541}{125} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{7}{3} a - 3\) , \( -\frac{1}{3} a^{2} + \frac{4}{3} a + 3\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a\) , \( 3 a^{3} - 3 a^{2} - 14 a - 6\) , \( \frac{19}{3} a^{3} - \frac{37}{3} a^{2} - 20 a + 20\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{7}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a\right){y}={x}^{3}+\left(-\frac{1}{3}a^{2}+\frac{4}{3}a+3\right){x}^{2}+\left(3a^{3}-3a^{2}-14a-6\right){x}+\frac{19}{3}a^{3}-\frac{37}{3}a^{2}-20a+20$ |
| 29.1-a1 |
29.1-a |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( - 29^{5} \) |
$19.02102$ |
$(1/3a^3-2/3a^2-8/3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.936112396$ |
$35.63026353$ |
4.773990006 |
\( -\frac{5180611509923}{20511149} a^{3} - \frac{9262473956333}{61533447} a^{2} + \frac{193234926305165}{61533447} a + \frac{89530803983057}{20511149} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{7}{3} a - 2\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 3 a\) , \( 0\) , \( -\frac{4}{3} a^{3} + \frac{34}{3} a^{2} + 6 a - 59\) , \( -2 a^{3} + \frac{52}{3} a^{2} + \frac{32}{3} a - 104\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{7}{3}a-2\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+3a\right){x}^{2}+\left(-\frac{4}{3}a^{3}+\frac{34}{3}a^{2}+6a-59\right){x}-2a^{3}+\frac{52}{3}a^{2}+\frac{32}{3}a-104$ |
| 29.1-b1 |
29.1-b |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( -29 \) |
$19.02102$ |
$(1/3a^3-2/3a^2-8/3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$567.3583374$ |
4.060335497 |
\( -\frac{74542}{87} a^{3} + \frac{63640}{87} a^{2} + \frac{274155}{29} a + \frac{41657}{29} \) |
\( \bigl[\frac{1}{3} a^{2} - \frac{1}{3} a - 2\) , \( 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a\) , \( -1\) , \( -a^{3} + \frac{16}{3} a^{2} - \frac{1}{3} a - 22\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a\right){y}={x}^{3}+{x}^{2}-{x}-a^{3}+\frac{16}{3}a^{2}-\frac{1}{3}a-22$ |
| 29.1-c1 |
29.1-c |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( -29 \) |
$19.02102$ |
$(1/3a^3-2/3a^2-8/3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.033530764$ |
$2520.075179$ |
2.418919544 |
\( -\frac{74542}{87} a^{3} + \frac{63640}{87} a^{2} + \frac{274155}{29} a + \frac{41657}{29} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{8}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 1\) , \( -\frac{4}{3} a^{3} + a^{2} + \frac{40}{3} a + 2\) , \( -\frac{1}{3} a^{3} - 3 a^{2} + \frac{16}{3} a + 31\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{8}{3}a-2\right){x}^{2}+\left(-\frac{4}{3}a^{3}+a^{2}+\frac{40}{3}a+2\right){x}-\frac{1}{3}a^{3}-3a^{2}+\frac{16}{3}a+31$ |
| 29.1-d1 |
29.1-d |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( - 29^{5} \) |
$19.02102$ |
$(1/3a^3-2/3a^2-8/3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$244.5789847$ |
1.750344832 |
\( -\frac{5180611509923}{20511149} a^{3} - \frac{9262473956333}{61533447} a^{2} + \frac{193234926305165}{61533447} a + \frac{89530803983057}{20511149} \) |
\( \bigl[1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a + 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a + 1\) , \( -7 a^{3} + \frac{52}{3} a^{2} + \frac{170}{3} a - 137\) , \( \frac{56}{3} a^{3} - \frac{298}{3} a^{2} - \frac{487}{3} a + 761\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a+1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a+1\right){x}^{2}+\left(-7a^{3}+\frac{52}{3}a^{2}+\frac{170}{3}a-137\right){x}+\frac{56}{3}a^{3}-\frac{298}{3}a^{2}-\frac{487}{3}a+761$ |
| 29.2-a1 |
29.2-a |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( - 29^{5} \) |
$19.02102$ |
$(1/3a^2+2/3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.936112396$ |
$35.63026353$ |
4.773990006 |
\( \frac{5180611509923}{20511149} a^{3} - \frac{55887977545640}{61533447} a^{2} - \frac{128084474803192}{61533447} a + \frac{145674343256078}{20511149} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a\) , \( a - 1\) , \( \frac{1}{3} a^{2} - \frac{1}{3} a - 3\) , \( \frac{10}{3} a^{3} + \frac{13}{3} a^{2} - \frac{92}{3} a - 44\) , \( \frac{29}{3} a^{3} + \frac{37}{3} a^{2} - 92 a - 140\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a\right){x}{y}+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(\frac{10}{3}a^{3}+\frac{13}{3}a^{2}-\frac{92}{3}a-44\right){x}+\frac{29}{3}a^{3}+\frac{37}{3}a^{2}-92a-140$ |
| 29.2-b1 |
29.2-b |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( -29 \) |
$19.02102$ |
$(1/3a^2+2/3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$567.3583374$ |
4.060335497 |
\( \frac{74542}{87} a^{3} - \frac{159986}{87} a^{2} - \frac{726119}{87} a + \frac{312178}{29} \) |
\( \bigl[\frac{1}{3} a^{2} - \frac{1}{3} a - 2\) , \( 1\) , \( \frac{1}{3} a^{3} - \frac{10}{3} a - 3\) , \( -a - 1\) , \( \frac{4}{3} a^{3} + 2 a^{2} - \frac{34}{3} a - 18\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{10}{3}a-3\right){y}={x}^{3}+{x}^{2}+\left(-a-1\right){x}+\frac{4}{3}a^{3}+2a^{2}-\frac{34}{3}a-18$ |
| 29.2-c1 |
29.2-c |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( -29 \) |
$19.02102$ |
$(1/3a^2+2/3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.033530764$ |
$2520.075179$ |
2.418919544 |
\( \frac{74542}{87} a^{3} - \frac{159986}{87} a^{2} - \frac{726119}{87} a + \frac{312178}{29} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{10}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 2 a + 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a\) , \( -\frac{4}{3} a^{3} + \frac{1}{3} a^{2} + 13 a + 14\) , \( -\frac{4}{3} a^{3} - \frac{1}{3} a^{2} + \frac{41}{3} a + 17\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{10}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+2a+1\right){x}^{2}+\left(-\frac{4}{3}a^{3}+\frac{1}{3}a^{2}+13a+14\right){x}-\frac{4}{3}a^{3}-\frac{1}{3}a^{2}+\frac{41}{3}a+17$ |
| 29.2-d1 |
29.2-d |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( - 29^{5} \) |
$19.02102$ |
$(1/3a^2+2/3a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$244.5789847$ |
1.750344832 |
\( \frac{5180611509923}{20511149} a^{3} - \frac{55887977545640}{61533447} a^{2} - \frac{128084474803192}{61533447} a + \frac{145674343256078}{20511149} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{8}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{10}{3} a - 2\) , \( \frac{20}{3} a^{3} - \frac{10}{3} a^{2} - \frac{202}{3} a - 70\) , \( -\frac{56}{3} a^{3} - \frac{130}{3} a^{2} + 304 a + 518\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}-\frac{10}{3}a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{8}{3}a-2\right){x}^{2}+\left(\frac{20}{3}a^{3}-\frac{10}{3}a^{2}-\frac{202}{3}a-70\right){x}-\frac{56}{3}a^{3}-\frac{130}{3}a^{2}+304a+518$ |
| 45.1-a1 |
45.1-a |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{6} \cdot 5^{3} \) |
$20.09489$ |
$(1/3a^3-a^2-7/3a+5), (-1/3a^3-2/3a^2+2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$249.2057619$ |
1.783456653 |
\( -\frac{127544209388146}{2025} a^{3} - \frac{76097939491738}{2025} a^{2} + \frac{1588020003101324}{2025} a + \frac{5457660858943}{5} \) |
\( \bigl[a\) , \( \frac{1}{3} a^{3} - \frac{7}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 1\) , \( 15 a^{3} - \frac{169}{3} a^{2} - \frac{107}{3} a + 150\) , \( \frac{545}{3} a^{3} - \frac{2726}{3} a^{2} + 20 a + 3087\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{7}{3}a-2\right){x}^{2}+\left(15a^{3}-\frac{169}{3}a^{2}-\frac{107}{3}a+150\right){x}+\frac{545}{3}a^{3}-\frac{2726}{3}a^{2}+20a+3087$ |
| 45.1-b1 |
45.1-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{2} \) |
$20.09489$ |
$(1/3a^3-a^2-7/3a+5), (-1/3a^3-2/3a^2+2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.079492147$ |
$2377.323800$ |
5.409748036 |
\( -\frac{277198315}{9} a^{3} + \frac{6674269307}{45} a^{2} + \frac{585393851}{45} a - \frac{22255914518}{45} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{11}{3} a + 2\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a\) , \( -\frac{35}{3} a^{3} + \frac{92}{3} a^{2} + 94 a - 249\) , \( \frac{158}{3} a^{3} - \frac{440}{3} a^{2} - 424 a + 1167\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{11}{3}a+2\right){x}^{2}+\left(-\frac{35}{3}a^{3}+\frac{92}{3}a^{2}+94a-249\right){x}+\frac{158}{3}a^{3}-\frac{440}{3}a^{2}-424a+1167$ |
| 45.1-b2 |
45.1-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{8} \cdot 5^{4} \) |
$20.09489$ |
$(1/3a^3-a^2-7/3a+5), (-1/3a^3-2/3a^2+2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.158984294$ |
$594.3309501$ |
5.409748036 |
\( \frac{3389819352217579}{675} a^{3} - \frac{7315176972120997}{405} a^{2} - \frac{83973907895880206}{2025} a + \frac{286618049138193949}{2025} \) |
\( \bigl[a\) , \( \frac{1}{3} a^{2} - \frac{4}{3} a - 3\) , \( 0\) , \( -\frac{61}{3} a^{3} + 93 a^{2} + \frac{514}{3} a - 714\) , \( 654 a^{3} - \frac{170}{3} a^{2} - \frac{14581}{3} a + 1552\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(\frac{1}{3}a^{2}-\frac{4}{3}a-3\right){x}^{2}+\left(-\frac{61}{3}a^{3}+93a^{2}+\frac{514}{3}a-714\right){x}+654a^{3}-\frac{170}{3}a^{2}-\frac{14581}{3}a+1552$ |
| 45.1-c1 |
45.1-c |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{8} \cdot 5^{4} \) |
$20.09489$ |
$(1/3a^3-a^2-7/3a+5), (-1/3a^3-2/3a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$42.04561641$ |
1.203608355 |
\( \frac{3389819352217579}{675} a^{3} - \frac{7315176972120997}{405} a^{2} - \frac{83973907895880206}{2025} a + \frac{286618049138193949}{2025} \) |
\( \bigl[\frac{1}{3} a^{2} - \frac{1}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 2 a + 1\) , \( \frac{1}{3} a^{3} - \frac{10}{3} a - 3\) , \( \frac{8}{3} a^{3} - 18 a^{2} + \frac{121}{3} a - 32\) , \( -70 a^{3} + \frac{916}{3} a^{2} + \frac{710}{3} a - 1456\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{10}{3}a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+2a+1\right){x}^{2}+\left(\frac{8}{3}a^{3}-18a^{2}+\frac{121}{3}a-32\right){x}-70a^{3}+\frac{916}{3}a^{2}+\frac{710}{3}a-1456$ |
| 45.1-c2 |
45.1-c |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{2} \) |
$20.09489$ |
$(1/3a^3-a^2-7/3a+5), (-1/3a^3-2/3a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$168.1824656$ |
1.203608355 |
\( -\frac{277198315}{9} a^{3} + \frac{6674269307}{45} a^{2} + \frac{585393851}{45} a - \frac{22255914518}{45} \) |
\( \bigl[\frac{1}{3} a^{2} - \frac{1}{3} a - 2\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{8}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{10}{3} a - 2\) , \( -\frac{4}{3} a^{3} + \frac{8}{3} a^{2} + \frac{59}{3} a - 43\) , \( -\frac{20}{3} a^{3} + \frac{79}{3} a^{2} + \frac{121}{3} a - 170\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{10}{3}a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{8}{3}a-2\right){x}^{2}+\left(-\frac{4}{3}a^{3}+\frac{8}{3}a^{2}+\frac{59}{3}a-43\right){x}-\frac{20}{3}a^{3}+\frac{79}{3}a^{2}+\frac{121}{3}a-170$ |
| 45.1-d1 |
45.1-d |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{6} \cdot 5^{3} \) |
$20.09489$ |
$(1/3a^3-a^2-7/3a+5), (-1/3a^3-2/3a^2+2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$1.075928766$ |
$49.18570479$ |
4.544730582 |
\( -\frac{127544209388146}{2025} a^{3} - \frac{76097939491738}{2025} a^{2} + \frac{1588020003101324}{2025} a + \frac{5457660858943}{5} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{7}{3} a - 3\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a - 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a\) , \( \frac{5}{3} a^{3} + \frac{1}{3} a^{2} - 13 a - 12\) , \( \frac{7}{3} a^{3} + \frac{8}{3} a^{2} - 17 a - 24\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{7}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a-1\right){x}^{2}+\left(\frac{5}{3}a^{3}+\frac{1}{3}a^{2}-13a-12\right){x}+\frac{7}{3}a^{3}+\frac{8}{3}a^{2}-17a-24$ |
| 45.4-a1 |
45.4-a |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
45.4 |
\( 3^{2} \cdot 5 \) |
\( - 3^{6} \cdot 5^{3} \) |
$20.09489$ |
$(1/3a^3+2/3a^2-2a-4), (a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$249.2057619$ |
1.783456653 |
\( \frac{127544209388146}{2025} a^{3} - \frac{458730567656176}{2025} a^{2} - \frac{70212766396894}{135} a + \frac{79882900046519}{45} \) |
\( \bigl[a + 1\) , \( -\frac{1}{3} a^{3} + \frac{13}{3} a + 2\) , \( \frac{1}{3} a^{2} - \frac{1}{3} a - 3\) , \( -\frac{46}{3} a^{3} - 15 a^{2} + \frac{352}{3} a + 106\) , \( -\frac{620}{3} a^{3} - 425 a^{2} + \frac{4319}{3} a + 2791\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{13}{3}a+2\right){x}^{2}+\left(-\frac{46}{3}a^{3}-15a^{2}+\frac{352}{3}a+106\right){x}-\frac{620}{3}a^{3}-425a^{2}+\frac{4319}{3}a+2791$ |
| 45.4-b1 |
45.4-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
45.4 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{2} \) |
$20.09489$ |
$(1/3a^3+2/3a^2-2a-4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.079492147$ |
$2377.323800$ |
5.409748036 |
\( \frac{277198315}{9} a^{3} + \frac{2516294582}{45} a^{2} - \frac{651730516}{3} a - 364049843 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{10}{3} a - 3\) , \( 1\) , \( a + 1\) , \( \frac{32}{3} a^{3} - \frac{14}{3} a^{2} - 109 a - 118\) , \( -\frac{124}{3} a^{3} + \frac{25}{3} a^{2} + 440 a + 513\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{10}{3}a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(\frac{32}{3}a^{3}-\frac{14}{3}a^{2}-109a-118\right){x}-\frac{124}{3}a^{3}+\frac{25}{3}a^{2}+440a+513$ |
| 45.4-b2 |
45.4-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
45.4 |
\( 3^{2} \cdot 5 \) |
\( - 3^{8} \cdot 5^{4} \) |
$20.09489$ |
$(1/3a^3+2/3a^2-2a-4), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.158984294$ |
$594.3309501$ |
5.409748036 |
\( -\frac{3389819352217579}{675} a^{3} - \frac{6067510690646774}{2025} a^{2} + \frac{8441153563142131}{135} a + \frac{3916393654185811}{45} \) |
\( \bigl[a + 1\) , \( \frac{1}{3} a^{2} - \frac{1}{3} a - 4\) , \( 0\) , \( \frac{61}{3} a^{3} + 32 a^{2} - \frac{889}{3} a - 470\) , \( -654 a^{3} + \frac{5716}{3} a^{2} + \frac{9035}{3} a - 2711\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-4\right){x}^{2}+\left(\frac{61}{3}a^{3}+32a^{2}-\frac{889}{3}a-470\right){x}-654a^{3}+\frac{5716}{3}a^{2}+\frac{9035}{3}a-2711$ |
| 45.4-c1 |
45.4-c |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
45.4 |
\( 3^{2} \cdot 5 \) |
\( - 3^{8} \cdot 5^{4} \) |
$20.09489$ |
$(1/3a^3+2/3a^2-2a-4), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$42.04561641$ |
1.203608355 |
\( -\frac{3389819352217579}{675} a^{3} - \frac{6067510690646774}{2025} a^{2} + \frac{8441153563142131}{135} a + \frac{3916393654185811}{45} \) |
\( \bigl[\frac{1}{3} a^{2} - \frac{1}{3} a - 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + 3\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a\) , \( -\frac{7}{3} a^{3} - \frac{32}{3} a^{2} - 16 a - 3\) , \( \frac{211}{3} a^{3} + \frac{284}{3} a^{2} - 641 a - 980\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+3\right){x}^{2}+\left(-\frac{7}{3}a^{3}-\frac{32}{3}a^{2}-16a-3\right){x}+\frac{211}{3}a^{3}+\frac{284}{3}a^{2}-641a-980$ |
| 45.4-c2 |
45.4-c |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
45.4 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{2} \) |
$20.09489$ |
$(1/3a^3+2/3a^2-2a-4), (a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$168.1824656$ |
1.203608355 |
\( \frac{277198315}{9} a^{3} + \frac{2516294582}{45} a^{2} - \frac{651730516}{3} a - 364049843 \) |
\( \bigl[\frac{1}{3} a^{2} - \frac{1}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a + 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a + 1\) , \( \frac{4}{3} a^{3} - \frac{4}{3} a^{2} - 22 a - 21\) , \( \frac{20}{3} a^{3} + \frac{19}{3} a^{2} - 74 a - 109\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a+1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a+1\right){x}^{2}+\left(\frac{4}{3}a^{3}-\frac{4}{3}a^{2}-22a-21\right){x}+\frac{20}{3}a^{3}+\frac{19}{3}a^{2}-74a-109$ |
| 45.4-d1 |
45.4-d |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
45.4 |
\( 3^{2} \cdot 5 \) |
\( - 3^{6} \cdot 5^{3} \) |
$20.09489$ |
$(1/3a^3+2/3a^2-2a-4), (a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$1.075928766$ |
$49.18570479$ |
4.544730582 |
\( \frac{127544209388146}{2025} a^{3} - \frac{458730567656176}{2025} a^{2} - \frac{70212766396894}{135} a + \frac{79882900046519}{45} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 1\) , \( \frac{1}{3} a^{3} - \frac{7}{3} a - 3\) , \( \frac{1}{3} a^{3} - \frac{10}{3} a - 3\) , \( 2 a^{3} + \frac{20}{3} a^{2} - \frac{38}{3} a - 44\) , \( \frac{17}{3} a^{3} + \frac{43}{3} a^{2} - 41 a - 101\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{10}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{7}{3}a-3\right){x}^{2}+\left(2a^{3}+\frac{20}{3}a^{2}-\frac{38}{3}a-44\right){x}+\frac{17}{3}a^{3}+\frac{43}{3}a^{2}-41a-101$ |
| 59.1-a1 |
59.1-a |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( - 59^{4} \) |
$20.78694$ |
$(1/3a^3-5/3a^2-5/3a+11)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.246893261$ |
$347.3072904$ |
4.909277729 |
\( \frac{12386631541461220250}{36352083} a^{3} - \frac{44550250760436925210}{36352083} a^{2} - \frac{102282142550085957370}{36352083} a + \frac{116369067556707039273}{12117361} \) |
\( \bigl[\frac{1}{3} a^{2} + \frac{2}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 4 a + 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 1\) , \( -\frac{13}{3} a^{3} + \frac{32}{3} a^{2} + \frac{116}{3} a - 75\) , \( 12 a^{3} - 50 a^{2} - 97 a + 397\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+4a+1\right){x}^{2}+\left(-\frac{13}{3}a^{3}+\frac{32}{3}a^{2}+\frac{116}{3}a-75\right){x}+12a^{3}-50a^{2}-97a+397$ |
| 59.1-a2 |
59.1-a |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( 59^{2} \) |
$20.78694$ |
$(1/3a^3-5/3a^2-5/3a+11)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.061723315$ |
$1389.229161$ |
4.909277729 |
\( -\frac{341579152}{3481} a^{3} + \frac{1454657420}{3481} a^{2} + \frac{2873574200}{3481} a - \frac{11284910347}{3481} \) |
\( \bigl[\frac{1}{3} a^{2} + \frac{2}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + 4 a + 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 1\) , \( -a^{3} - a^{2} + 12 a + 15\) , \( -\frac{2}{3} a^{3} - 2 a^{2} + \frac{26}{3} a + 22\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+4a+1\right){x}^{2}+\left(-a^{3}-a^{2}+12a+15\right){x}-\frac{2}{3}a^{3}-2a^{2}+\frac{26}{3}a+22$ |
| 59.1-b1 |
59.1-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( - 59^{4} \) |
$20.78694$ |
$(1/3a^3-5/3a^2-5/3a+11)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$84.21374683$ |
4.821447654 |
\( \frac{12386631541461220250}{36352083} a^{3} - \frac{44550250760436925210}{36352083} a^{2} - \frac{102282142550085957370}{36352083} a + \frac{116369067556707039273}{12117361} \) |
\( \bigl[\frac{1}{3} a^{2} + \frac{2}{3} a - 2\) , \( \frac{1}{3} a^{2} - \frac{4}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{7}{3} a - 3\) , \( -22 a^{3} + \frac{310}{3} a^{2} + \frac{47}{3} a - 349\) , \( -35 a^{3} + 166 a^{2} + 27 a - 578\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{7}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{2}-\frac{4}{3}a-2\right){x}^{2}+\left(-22a^{3}+\frac{310}{3}a^{2}+\frac{47}{3}a-349\right){x}-35a^{3}+166a^{2}+27a-578$ |
| 59.1-b2 |
59.1-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( 59^{2} \) |
$20.78694$ |
$(1/3a^3-5/3a^2-5/3a+11)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$336.8549873$ |
4.821447654 |
\( -\frac{341579152}{3481} a^{3} + \frac{1454657420}{3481} a^{2} + \frac{2873574200}{3481} a - \frac{11284910347}{3481} \) |
\( \bigl[\frac{1}{3} a^{2} + \frac{2}{3} a - 2\) , \( \frac{1}{3} a^{2} - \frac{4}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{7}{3} a - 3\) , \( \frac{14}{3} a^{3} - 25 a^{2} + \frac{7}{3} a + 86\) , \( \frac{25}{3} a^{3} - \frac{122}{3} a^{2} - \frac{8}{3} a + 132\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{7}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{2}-\frac{4}{3}a-2\right){x}^{2}+\left(\frac{14}{3}a^{3}-25a^{2}+\frac{7}{3}a+86\right){x}+\frac{25}{3}a^{3}-\frac{122}{3}a^{2}-\frac{8}{3}a+132$ |
| 59.2-a1 |
59.2-a |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( - 59^{4} \) |
$20.78694$ |
$(1/3a^2+2/3a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.246893261$ |
$347.3072904$ |
4.909277729 |
\( -\frac{12386631541461220250}{36352083} a^{3} - \frac{7390356136053264460}{36352083} a^{2} + \frac{51407583148858715680}{12117361} a + \frac{71553813633686485163}{12117361} \) |
\( \bigl[\frac{1}{3} a^{2} + \frac{2}{3} a - 2\) , \( -\frac{1}{3} a^{2} + \frac{4}{3} a + 2\) , \( \frac{1}{3} a^{2} - \frac{1}{3} a - 3\) , \( 4 a^{3} + \frac{7}{3} a^{2} - \frac{130}{3} a - 61\) , \( -\frac{23}{3} a^{3} - \frac{1}{3} a^{2} + 94 a + 119\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{2}+\frac{4}{3}a+2\right){x}^{2}+\left(4a^{3}+\frac{7}{3}a^{2}-\frac{130}{3}a-61\right){x}-\frac{23}{3}a^{3}-\frac{1}{3}a^{2}+94a+119$ |
| 59.2-a2 |
59.2-a |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( 59^{2} \) |
$20.78694$ |
$(1/3a^2+2/3a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.061723315$ |
$1389.229161$ |
4.909277729 |
\( \frac{341579152}{3481} a^{3} + \frac{429919964}{3481} a^{2} - \frac{4758151584}{3481} a - \frac{7298257879}{3481} \) |
\( \bigl[\frac{1}{3} a^{2} + \frac{2}{3} a - 2\) , \( -\frac{1}{3} a^{2} + \frac{4}{3} a + 2\) , \( \frac{1}{3} a^{2} - \frac{1}{3} a - 3\) , \( \frac{2}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 6\) , \( \frac{14}{3} a^{2} - \frac{14}{3} a - 20\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{2}+\frac{4}{3}a+2\right){x}^{2}+\left(\frac{2}{3}a^{3}+\frac{2}{3}a^{2}-\frac{10}{3}a-6\right){x}+\frac{14}{3}a^{2}-\frac{14}{3}a-20$ |
| 59.2-b1 |
59.2-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( - 59^{4} \) |
$20.78694$ |
$(1/3a^2+2/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$84.21374683$ |
4.821447654 |
\( -\frac{12386631541461220250}{36352083} a^{3} - \frac{7390356136053264460}{36352083} a^{2} + \frac{51407583148858715680}{12117361} a + \frac{71553813633686485163}{12117361} \) |
\( \bigl[\frac{1}{3} a^{2} + \frac{2}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{10}{3} a + 4\) , \( \frac{1}{3} a^{2} + \frac{2}{3} a - 3\) , \( \frac{62}{3} a^{3} + \frac{116}{3} a^{2} - \frac{436}{3} a - 251\) , \( \frac{68}{3} a^{3} + \frac{116}{3} a^{2} - \frac{520}{3} a - 286\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{10}{3}a+4\right){x}^{2}+\left(\frac{62}{3}a^{3}+\frac{116}{3}a^{2}-\frac{436}{3}a-251\right){x}+\frac{68}{3}a^{3}+\frac{116}{3}a^{2}-\frac{520}{3}a-286$ |
| 59.2-b2 |
59.2-b |
$2$ |
$2$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( 59^{2} \) |
$20.78694$ |
$(1/3a^2+2/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$336.8549873$ |
4.821447654 |
\( \frac{341579152}{3481} a^{3} + \frac{429919964}{3481} a^{2} - \frac{4758151584}{3481} a - \frac{7298257879}{3481} \) |
\( \bigl[\frac{1}{3} a^{2} + \frac{2}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{10}{3} a + 4\) , \( \frac{1}{3} a^{2} + \frac{2}{3} a - 3\) , \( -6 a^{3} - \frac{29}{3} a^{2} + \frac{134}{3} a + 69\) , \( -\frac{17}{3} a^{3} - \frac{29}{3} a^{2} + \frac{124}{3} a + 66\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{10}{3}a+4\right){x}^{2}+\left(-6a^{3}-\frac{29}{3}a^{2}+\frac{134}{3}a+69\right){x}-\frac{17}{3}a^{3}-\frac{29}{3}a^{2}+\frac{124}{3}a+66$ |
| 71.1-a1 |
71.1-a |
$4$ |
$6$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{4} \) |
$21.27362$ |
$(1/3a^3+a^2-7/3a-8)$ |
$2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$2.425234342$ |
$501.2309281$ |
7.732920170 |
\( -\frac{32193461005}{15123} a^{2} + \frac{32193461005}{15123} a + \frac{116485001975}{5041} \) |
\( \bigl[\frac{1}{3} a^{2} - \frac{1}{3} a - 2\) , \( \frac{1}{3} a^{2} - \frac{1}{3} a - 4\) , \( 0\) , \( \frac{4}{3} a^{2} - \frac{4}{3} a - 12\) , \( -\frac{7}{3} a^{2} + \frac{7}{3} a + 26\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-2\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-4\right){x}^{2}+\left(\frac{4}{3}a^{2}-\frac{4}{3}a-12\right){x}-\frac{7}{3}a^{2}+\frac{7}{3}a+26$ |
| 71.1-a2 |
71.1-a |
$4$ |
$6$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{12} \) |
$21.27362$ |
$(1/3a^3+a^2-7/3a-8)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$21.82710908$ |
$6.188036150$ |
7.732920170 |
\( -\frac{434940509188445}{384300851763} a^{2} + \frac{434940509188445}{384300851763} a + \frac{886743214400250}{128100283921} \) |
\( \bigl[\frac{1}{3} a^{2} - \frac{1}{3} a - 2\) , \( \frac{1}{3} a^{2} - \frac{1}{3} a - 4\) , \( 0\) , \( -2 a^{2} + 2 a - 7\) , \( -\frac{32}{3} a^{2} + \frac{32}{3} a + 45\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-2\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-4\right){x}^{2}+\left(-2a^{2}+2a-7\right){x}-\frac{32}{3}a^{2}+\frac{32}{3}a+45$ |
| 71.1-a3 |
71.1-a |
$4$ |
$6$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{2} \) |
$21.27362$ |
$(1/3a^3+a^2-7/3a-8)$ |
$2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.606308585$ |
$2004.923712$ |
7.732920170 |
\( \frac{52635}{71} a^{2} - \frac{52635}{71} a - \frac{437300}{71} \) |
\( \bigl[\frac{1}{3} a^{2} - \frac{1}{3} a - 2\) , \( \frac{1}{3} a^{2} - \frac{1}{3} a - 4\) , \( 0\) , \( -\frac{1}{3} a^{2} + \frac{1}{3} a + 3\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-2\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-4\right){x}^{2}+\left(-\frac{1}{3}a^{2}+\frac{1}{3}a+3\right){x}$ |
| 71.1-a4 |
71.1-a |
$4$ |
$6$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{6} \) |
$21.27362$ |
$(1/3a^3+a^2-7/3a-8)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$5.456777271$ |
$24.75214460$ |
7.732920170 |
\( \frac{1968562982965}{357911} a^{2} - \frac{1968562982965}{357911} a - \frac{8160986946575}{357911} \) |
\( \bigl[1\) , \( 1\) , \( \frac{1}{3} a^{2} - \frac{1}{3} a - 2\) , \( -\frac{14}{3} a^{2} + \frac{14}{3} a + 46\) , \( \frac{5}{3} a^{2} - \frac{5}{3} a - 24\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-2\right){y}={x}^{3}+{x}^{2}+\left(-\frac{14}{3}a^{2}+\frac{14}{3}a+46\right){x}+\frac{5}{3}a^{2}-\frac{5}{3}a-24$ |
| 71.1-b1 |
71.1-b |
$4$ |
$6$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{4} \) |
$21.27362$ |
$(1/3a^3+a^2-7/3a-8)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.849519304$ |
$72.90812161$ |
7.720212309 |
\( -\frac{32193461005}{15123} a^{2} + \frac{32193461005}{15123} a + \frac{116485001975}{5041} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{10}{3} a - 3\) , \( \frac{1}{3} a^{2} - \frac{4}{3} a - 2\) , \( 0\) , \( -16 a^{3} + \frac{248}{3} a^{2} - \frac{20}{3} a - 288\) , \( -\frac{227}{3} a^{3} + 394 a^{2} - \frac{118}{3} a - 1377\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{10}{3}a-3\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{2}-\frac{4}{3}a-2\right){x}^{2}+\left(-16a^{3}+\frac{248}{3}a^{2}-\frac{20}{3}a-288\right){x}-\frac{227}{3}a^{3}+394a^{2}-\frac{118}{3}a-1377$ |
| 71.1-b2 |
71.1-b |
$4$ |
$6$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{12} \) |
$21.27362$ |
$(1/3a^3+a^2-7/3a-8)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$16.64567374$ |
$8.100902402$ |
7.720212309 |
\( -\frac{434940509188445}{384300851763} a^{2} + \frac{434940509188445}{384300851763} a + \frac{886743214400250}{128100283921} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{10}{3} a - 3\) , \( \frac{1}{3} a^{2} - \frac{4}{3} a - 2\) , \( 0\) , \( 199 a^{3} - 949 a^{2} - 90 a + 3082\) , \( \frac{25477}{3} a^{3} - 41036 a^{2} - \frac{7999}{3} a + 134920\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{10}{3}a-3\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{2}-\frac{4}{3}a-2\right){x}^{2}+\left(199a^{3}-949a^{2}-90a+3082\right){x}+\frac{25477}{3}a^{3}-41036a^{2}-\frac{7999}{3}a+134920$ |
| 71.1-b3 |
71.1-b |
$4$ |
$6$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{6} \) |
$21.27362$ |
$(1/3a^3+a^2-7/3a-8)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$4.161418436$ |
$32.40360960$ |
7.720212309 |
\( \frac{1968562982965}{357911} a^{2} - \frac{1968562982965}{357911} a - \frac{8160986946575}{357911} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{7}{3} a - 2\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 4 a\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a\) , \( 27 a^{3} - \frac{442}{3} a^{2} + \frac{103}{3} a + 552\) , \( 455 a^{3} - 2192 a^{2} - 144 a + 7224\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{7}{3}a-2\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-4a\right){x}^{2}+\left(27a^{3}-\frac{442}{3}a^{2}+\frac{103}{3}a+552\right){x}+455a^{3}-2192a^{2}-144a+7224$ |
| 71.1-b4 |
71.1-b |
$4$ |
$6$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
71.1 |
\( 71 \) |
\( 71^{2} \) |
$21.27362$ |
$(1/3a^3+a^2-7/3a-8)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.462379826$ |
$291.6324864$ |
7.720212309 |
\( \frac{52635}{71} a^{2} - \frac{52635}{71} a - \frac{437300}{71} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 3 a + 1\) , \( 0\) , \( -4 a^{3} - \frac{26}{3} a^{2} + \frac{83}{3} a + 57\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-3a+1\right){x}^{2}+\left(-4a^{3}-\frac{26}{3}a^{2}+\frac{83}{3}a+57\right){x}$ |
| 80.1-a1 |
80.1-a |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$21.59336$ |
$(1/3a^3-a^2-7/3a+5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.155739123$ |
$381.4871364$ |
5.102268972 |
\( \frac{25376162573}{600} a^{3} - \frac{91247100961}{600} a^{2} - \frac{52391325463}{150} a + \frac{4766453581}{4} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - 2 a + 1\) , \( -\frac{1}{3} a^{3} + \frac{13}{3} a + 4\) , \( a\) , \( \frac{11}{3} a^{2} + \frac{7}{3} a - 5\) , \( \frac{1}{3} a^{3} + 11 a^{2} - \frac{25}{3} a - 40\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-2a+1\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{13}{3}a+4\right){x}^{2}+\left(\frac{11}{3}a^{2}+\frac{7}{3}a-5\right){x}+\frac{1}{3}a^{3}+11a^{2}-\frac{25}{3}a-40$ |
| 80.1-b1 |
80.1-b |
$1$ |
$1$ |
4.4.19525.1 |
$4$ |
$[4, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$21.59336$ |
$(1/3a^3-a^2-7/3a+5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{2} \) |
$1$ |
$28.98248692$ |
1.866734856 |
\( \frac{25376162573}{600} a^{3} - \frac{91247100961}{600} a^{2} - \frac{52391325463}{150} a + \frac{4766453581}{4} \) |
\( \bigl[a + 1\) , \( \frac{1}{3} a^{2} - \frac{1}{3} a - 4\) , \( \frac{1}{3} a^{2} + \frac{2}{3} a - 3\) , \( -\frac{31}{3} a^{3} - \frac{56}{3} a^{2} + 72 a + 117\) , \( -113 a^{3} - \frac{620}{3} a^{2} + \frac{2366}{3} a + 1323\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{2}+\frac{2}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{2}-\frac{1}{3}a-4\right){x}^{2}+\left(-\frac{31}{3}a^{3}-\frac{56}{3}a^{2}+72a+117\right){x}-113a^{3}-\frac{620}{3}a^{2}+\frac{2366}{3}a+1323$ |
*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.
