| 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 |
| 9.1-a1 |
9.1-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$8.89829$ |
$(1/3a^3-8/3a-2/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5Nn.2.2[2] |
$1$ |
\( 1 \) |
$1$ |
$378.9822621$ |
1.252192640 |
\( -\frac{27461}{243} a^{3} - \frac{149023}{243} a^{2} + \frac{171953}{243} a + \frac{985162}{243} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( a^{2} - 3\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( \frac{5}{3} a^{3} + 3 a^{2} - \frac{31}{3} a - \frac{46}{3}\) , \( \frac{5}{3} a^{3} + 2 a^{2} - \frac{31}{3} a - \frac{34}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{4}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{4}{3}\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(\frac{5}{3}a^{3}+3a^{2}-\frac{31}{3}a-\frac{46}{3}\right){x}+\frac{5}{3}a^{3}+2a^{2}-\frac{31}{3}a-\frac{34}{3}$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{20} \) |
$8.89829$ |
$(1/3a^3-8/3a-2/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5Nn.2.2[2] |
$1$ |
\( 2 \) |
$1$ |
$189.4911310$ |
1.252192640 |
\( \frac{17984592881}{59049} a^{3} - \frac{3640839358}{6561} a^{2} - \frac{36754267676}{19683} a + \frac{202884647407}{59049} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( a^{2} - 3\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( -\frac{20}{3} a^{3} - 2 a^{2} + \frac{124}{3} a + \frac{49}{3}\) , \( \frac{25}{3} a^{3} + 2 a^{2} - \frac{170}{3} a - \frac{74}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{4}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{4}{3}\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-\frac{20}{3}a^{3}-2a^{2}+\frac{124}{3}a+\frac{49}{3}\right){x}+\frac{25}{3}a^{3}+2a^{2}-\frac{170}{3}a-\frac{74}{3}$ |
| 9.2-a1 |
9.2-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{20} \) |
$8.89829$ |
$(-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5Nn.2.2[2] |
$1$ |
\( 2 \) |
$1$ |
$189.4911310$ |
1.252192640 |
\( \frac{66381494242}{177147} a^{3} + \frac{3640839358}{6561} a^{2} - \frac{270887955341}{177147} a - \frac{263642306174}{177147} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{1}{3}\) , \( -a^{2} + a + 5\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{1}{3}\) , \( -\frac{28}{3} a^{3} + 30 a^{2} - \frac{10}{3} a - \frac{103}{3}\) , \( 51 a^{3} - 178 a^{2} + 33 a + 227\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{1}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{1}{3}\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-\frac{28}{3}a^{3}+30a^{2}-\frac{10}{3}a-\frac{103}{3}\right){x}+51a^{3}-178a^{2}+33a+227$ |
| 9.2-a2 |
9.2-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{10} \) |
$8.89829$ |
$(-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5Nn.2.2[2] |
$1$ |
\( 1 \) |
$1$ |
$378.9822621$ |
1.252192640 |
\( \frac{101288}{729} a^{3} + \frac{149023}{243} a^{2} - \frac{610384}{729} a - \frac{884464}{729} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{5}{3} a + \frac{8}{3}\) , \( 0\) , \( \frac{2}{3} a^{3} - a^{2} - \frac{4}{3} a + \frac{5}{3}\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{4}{3}\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}-a^{2}+\frac{5}{3}a+\frac{8}{3}\right){x}^{2}+\left(\frac{2}{3}a^{3}-a^{2}-\frac{4}{3}a+\frac{5}{3}\right){x}$ |
| 25.1-a1 |
25.1-a |
$1$ |
$1$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$10.11041$ |
$(2/3a^3-10/3a-1/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.017315585$ |
$1199.632820$ |
2.196280302 |
\( \frac{8282}{5} a^{3} - \frac{52011}{5} a^{2} + 5433 a + \frac{80824}{5} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( a^{2} + a - 4\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + \frac{1}{3}\) , \( \frac{10}{3} a^{3} + 3 a^{2} - \frac{41}{3} a - \frac{17}{3}\) , \( 4 a^{3} + 8 a^{2} - 16 a - 24\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+\frac{1}{3}\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(\frac{10}{3}a^{3}+3a^{2}-\frac{41}{3}a-\frac{17}{3}\right){x}+4a^{3}+8a^{2}-16a-24$ |
| 25.1-b1 |
25.1-b |
$1$ |
$1$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$10.11041$ |
$(2/3a^3-10/3a-1/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.017315585$ |
$1199.632820$ |
2.196280302 |
\( \frac{145432}{15} a^{3} + \frac{52011}{5} a^{2} - \frac{186577}{3} a - \frac{1041239}{15} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 5\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{11}{3}\) , \( a^{2} - 2 a - 5\) , \( -\frac{8}{3} a^{3} - 2 a^{2} + \frac{46}{3} a + \frac{40}{3}\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{11}{3}\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(a^{2}-2a-5\right){x}-\frac{8}{3}a^{3}-2a^{2}+\frac{46}{3}a+\frac{40}{3}$ |
| 29.1-a1 |
29.1-a |
$2$ |
$3$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$10.29973$ |
$(1/3a^3-2/3a-8/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$126.0142097$ |
1.665450674 |
\( -\frac{405021824397549340}{87} a^{3} - \frac{116382822171561015}{29} a^{2} + \frac{2590043207928526325}{87} a + \frac{2392655189902841486}{87} \) |
\( \bigl[a^{2} + a - 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a + \frac{2}{3}\) , \( a^{2} + a - 3\) , \( -\frac{61}{3} a^{3} - 31 a^{2} + \frac{242}{3} a + \frac{251}{3}\) , \( -\frac{416}{3} a^{3} - 215 a^{2} + \frac{1678}{3} a + \frac{1786}{3}\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a+\frac{2}{3}\right){x}^{2}+\left(-\frac{61}{3}a^{3}-31a^{2}+\frac{242}{3}a+\frac{251}{3}\right){x}-\frac{416}{3}a^{3}-215a^{2}+\frac{1678}{3}a+\frac{1786}{3}$ |
| 29.1-a2 |
29.1-a |
$2$ |
$3$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{3} \) |
$10.29973$ |
$(1/3a^3-2/3a-8/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$126.0142097$ |
1.665450674 |
\( \frac{479602472672746}{73167} a^{3} + \frac{248047721770401}{24389} a^{2} - \frac{1938100892208245}{73167} a - \frac{2067629828346671}{73167} \) |
\( \bigl[a\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{5}{3} a + \frac{11}{3}\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{1}{3}\) , \( -74 a^{3} + 254 a^{2} - 43 a - 321\) , \( \frac{2237}{3} a^{3} - 2596 a^{2} + \frac{1415}{3} a + \frac{9926}{3}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{1}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-a^{2}+\frac{5}{3}a+\frac{11}{3}\right){x}^{2}+\left(-74a^{3}+254a^{2}-43a-321\right){x}+\frac{2237}{3}a^{3}-2596a^{2}+\frac{1415}{3}a+\frac{9926}{3}$ |
| 29.1-b1 |
29.1-b |
$1$ |
$1$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$10.29973$ |
$(1/3a^3-2/3a-8/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.066923655$ |
$671.2139007$ |
2.374722369 |
\( -\frac{947365}{87} a^{3} + \frac{605414}{29} a^{2} + \frac{5899730}{87} a - \frac{10989853}{87} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a + \frac{2}{3}\) , \( a^{2} - 3\) , \( -a^{3} + 3 a + 1\) , \( -a^{3} + 3 a^{2} - 4\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a+\frac{2}{3}\right){x}^{2}+\left(-a^{3}+3a+1\right){x}-a^{3}+3a^{2}-4$ |
| 29.1-c1 |
29.1-c |
$2$ |
$3$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{3} \) |
$10.29973$ |
$(1/3a^3-2/3a-8/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.027018594$ |
$538.6246620$ |
2.308035528 |
\( -\frac{11714327}{73167} a^{3} + \frac{3104056}{24389} a^{2} + \frac{120115789}{73167} a + \frac{171277273}{73167} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a + \frac{1}{3}\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{2}{3} a + \frac{8}{3}\) , \( a^{2} + a - 4\) , \( -a^{3} - 2 a^{2} + 3 a + 6\) , \( \frac{2}{3} a^{3} + 2 a^{2} - \frac{7}{3} a - \frac{22}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+\frac{1}{3}\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-a^{2}+\frac{2}{3}a+\frac{8}{3}\right){x}^{2}+\left(-a^{3}-2a^{2}+3a+6\right){x}+\frac{2}{3}a^{3}+2a^{2}-\frac{7}{3}a-\frac{22}{3}$ |
| 29.1-c2 |
29.1-c |
$2$ |
$3$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$10.29973$ |
$(1/3a^3-2/3a-8/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.081055783$ |
$538.6246620$ |
2.308035528 |
\( -\frac{4443097}{87} a^{3} + \frac{1357306}{29} a^{2} + \frac{57118865}{87} a + \frac{45994796}{87} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a + \frac{4}{3}\) , \( -\frac{1}{3} a^{3} + \frac{8}{3} a - \frac{4}{3}\) , \( 1\) , \( \frac{8}{3} a^{3} - 5 a^{2} - \frac{7}{3} a + \frac{17}{3}\) , \( \frac{16}{3} a^{3} - 15 a^{2} + \frac{1}{3} a + \frac{52}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+\frac{4}{3}\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{8}{3}a-\frac{4}{3}\right){x}^{2}+\left(\frac{8}{3}a^{3}-5a^{2}-\frac{7}{3}a+\frac{17}{3}\right){x}+\frac{16}{3}a^{3}-15a^{2}+\frac{1}{3}a+\frac{52}{3}$ |
| 29.1-d1 |
29.1-d |
$1$ |
$1$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{5} \) |
$10.29973$ |
$(1/3a^3-2/3a-8/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5Nn.2.2[2] |
$1$ |
\( 1 \) |
$1$ |
$88.95160728$ |
1.175617532 |
\( -\frac{846452936217216}{20511149} a^{3} - \frac{730103522587178}{20511149} a^{2} + \frac{5413701131095303}{20511149} a + \frac{5001491726712970}{20511149} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( a^{2} + a - 4\) , \( 1\) , \( 4 a^{3} + 4 a^{2} - 25 a - 26\) , \( -\frac{29}{3} a^{3} - 9 a^{2} + \frac{169}{3} a + \frac{142}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{4}{3}\right){x}{y}+{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(4a^{3}+4a^{2}-25a-26\right){x}-\frac{29}{3}a^{3}-9a^{2}+\frac{169}{3}a+\frac{142}{3}$ |
| 29.2-a1 |
29.2-a |
$2$ |
$3$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$10.29973$ |
$(2/3a^3+a^2-10/3a-16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$126.0142097$ |
1.665450674 |
\( -\frac{33442546748576150}{29} a^{3} + \frac{116382822171561015}{29} a^{2} - \frac{21098628237379125}{29} a - \frac{148328941525828343}{29} \) |
\( \bigl[a^{2} + a - 4\) , \( \frac{1}{3} a^{3} - a^{2} - \frac{5}{3} a + \frac{10}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + \frac{4}{3}\) , \( -\frac{44}{3} a^{3} + 28 a^{2} + \frac{268}{3} a - \frac{518}{3}\) , \( -\frac{362}{3} a^{3} + 232 a^{2} + \frac{2242}{3} a - \frac{4247}{3}\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+\frac{4}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-a^{2}-\frac{5}{3}a+\frac{10}{3}\right){x}^{2}+\left(-\frac{44}{3}a^{3}+28a^{2}+\frac{268}{3}a-\frac{518}{3}\right){x}-\frac{362}{3}a^{3}+232a^{2}+\frac{2242}{3}a-\frac{4247}{3}$ |
| 29.2-a2 |
29.2-a |
$2$ |
$3$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29^{3} \) |
$10.29973$ |
$(2/3a^3+a^2-10/3a-16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$126.0142097$ |
1.665450674 |
\( \frac{128286191540280}{24389} a^{3} - \frac{248047721770401}{24389} a^{2} - \frac{794734781419895}{24389} a + \frac{1511638253800750}{24389} \) |
\( \bigl[a^{2} - 3\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{8}{3} a - \frac{10}{3}\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( -46 a^{3} - 32 a^{2} + 294 a + 225\) , \( \frac{361}{3} a^{3} + 115 a^{2} - \frac{2312}{3} a - \frac{2348}{3}\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{8}{3}a-\frac{10}{3}\right){x}^{2}+\left(-46a^{3}-32a^{2}+294a+225\right){x}+\frac{361}{3}a^{3}+115a^{2}-\frac{2312}{3}a-\frac{2348}{3}$ |
| 29.2-b1 |
29.2-b |
$1$ |
$1$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$10.29973$ |
$(2/3a^3+a^2-10/3a-16/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.066923655$ |
$671.2139007$ |
2.374722369 |
\( -\frac{1165144}{87} a^{3} - \frac{605414}{29} a^{2} + \frac{4662815}{87} a + \frac{5138546}{87} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( -a^{2} + a + 5\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + \frac{1}{3}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{8}{3} a + \frac{2}{3}\) , \( -\frac{7}{3} a^{3} - a^{2} + \frac{53}{3} a + \frac{35}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+\frac{1}{3}\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{8}{3}a+\frac{2}{3}\right){x}-\frac{7}{3}a^{3}-a^{2}+\frac{53}{3}a+\frac{35}{3}$ |
| 29.2-c1 |
29.2-c |
$2$ |
$3$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$10.29973$ |
$(2/3a^3+a^2-10/3a-16/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.081055783$ |
$538.6246620$ |
2.308035528 |
\( \frac{5834057}{87} a^{3} - \frac{1357306}{29} a^{2} - \frac{64073665}{87} a + \frac{92919212}{87} \) |
\( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a - \frac{2}{3}\) , \( a^{2} - 4\) , \( \frac{2}{3} a^{3} + 2 a^{2} - \frac{13}{3} a - \frac{37}{3}\) , \( a^{3} + 2 a^{2} - 6 a - 14\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a-\frac{2}{3}\right){x}^{2}+\left(\frac{2}{3}a^{3}+2a^{2}-\frac{13}{3}a-\frac{37}{3}\right){x}+a^{3}+2a^{2}-6a-14$ |
| 29.2-c2 |
29.2-c |
$2$ |
$3$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29^{3} \) |
$10.29973$ |
$(2/3a^3+a^2-10/3a-16/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.027018594$ |
$538.6246620$ |
2.308035528 |
\( \frac{5696335}{73167} a^{3} - \frac{3104056}{24389} a^{2} - \frac{90025829}{73167} a + \frac{272497447}{73167} \) |
\( \bigl[a\) , \( -\frac{1}{3} a^{3} + \frac{8}{3} a - \frac{4}{3}\) , \( a^{2} + a - 3\) , \( -a^{3} + 5 a - 3\) , \( \frac{1}{3} a^{3} - 3 a^{2} - \frac{11}{3} a + \frac{43}{3}\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{8}{3}a-\frac{4}{3}\right){x}^{2}+\left(-a^{3}+5a-3\right){x}+\frac{1}{3}a^{3}-3a^{2}-\frac{11}{3}a+\frac{43}{3}$ |
| 29.2-d1 |
29.2-d |
$1$ |
$1$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29^{5} \) |
$10.29973$ |
$(2/3a^3+a^2-10/3a-16/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5Nn.2.2[2] |
$1$ |
\( 1 \) |
$1$ |
$88.95160728$ |
1.175617532 |
\( -\frac{209272945351749}{20511149} a^{3} + \frac{730103522587178}{20511149} a^{2} - \frac{135071723250478}{20511149} a - \frac{932259985706165}{20511149} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( -a^{2} - a + 5\) , \( 1\) , \( a^{3} - 4 a^{2} + 7\) , \( -4 a^{3} + 9 a^{2} + 12 a - 28\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{4}{3}\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(a^{3}-4a^{2}+7\right){x}-4a^{3}+9a^{2}+12a-28$ |
| 31.1-a1 |
31.1-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{2} \) |
$10.38596$ |
$(2/3a^3+a^2-7/3a-13/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.062716034$ |
$31.30135761$ |
2.534032361 |
\( -\frac{136431389853426643}{2883} a^{3} + \frac{158242724911892276}{961} a^{2} - \frac{85969372865366998}{2883} a - \frac{604965888910105204}{2883} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( \frac{1}{3} a^{3} - a^{2} - \frac{5}{3} a + \frac{16}{3}\) , \( a\) , \( \frac{49}{3} a^{3} + 10 a^{2} - \frac{338}{3} a - \frac{281}{3}\) , \( \frac{250}{3} a^{3} + 57 a^{2} - \frac{1733}{3} a - \frac{1553}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{3}a^{3}-a^{2}-\frac{5}{3}a+\frac{16}{3}\right){x}^{2}+\left(\frac{49}{3}a^{3}+10a^{2}-\frac{338}{3}a-\frac{281}{3}\right){x}+\frac{250}{3}a^{3}+57a^{2}-\frac{1733}{3}a-\frac{1553}{3}$ |
| 31.1-a2 |
31.1-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$10.38596$ |
$(2/3a^3+a^2-7/3a-13/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.531358017$ |
$125.2054304$ |
2.534032361 |
\( \frac{62544305}{31} a^{3} + \frac{230097301}{31} a^{2} - \frac{457462975}{31} a - \frac{356181225}{31} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( \frac{1}{3} a^{3} - a^{2} - \frac{5}{3} a + \frac{16}{3}\) , \( a\) , \( -2 a^{3} - 5 a^{2} + 4 a + 13\) , \( -18 a^{3} - 30 a^{2} + 68 a + 77\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{3}a^{3}-a^{2}-\frac{5}{3}a+\frac{16}{3}\right){x}^{2}+\left(-2a^{3}-5a^{2}+4a+13\right){x}-18a^{3}-30a^{2}+68a+77$ |
| 31.1-b1 |
31.1-b |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{10} \) |
$10.38596$ |
$(2/3a^3+a^2-7/3a-13/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.398104330$ |
$42.01599443$ |
2.210669417 |
\( -\frac{2361068591750282913760}{819628286980801} a^{3} - \frac{2035629411874586215938}{819628286980801} a^{2} + \frac{15098661409412079713873}{819628286980801} a + \frac{13949664696500439382594}{819628286980801} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - \frac{11}{3}\) , \( 0\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( \frac{11}{3} a^{3} - \frac{28}{3} a - \frac{25}{3}\) , \( -\frac{31}{3} a^{3} + 54 a^{2} - \frac{70}{3} a - \frac{235}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-\frac{11}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){y}={x}^{3}+\left(\frac{11}{3}a^{3}-\frac{28}{3}a-\frac{25}{3}\right){x}-\frac{31}{3}a^{3}+54a^{2}-\frac{70}{3}a-\frac{235}{3}$ |
| 31.1-b2 |
31.1-b |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{5} \) |
$10.38596$ |
$(2/3a^3+a^2-7/3a-13/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.199052165$ |
$168.0639777$ |
2.210669417 |
\( \frac{170747689728}{28629151} a^{3} + \frac{218487362503}{28629151} a^{2} - \frac{2659323624028}{28629151} a + \frac{2971473426440}{28629151} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - \frac{11}{3}\) , \( 0\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( \frac{11}{3} a^{3} - 5 a^{2} - \frac{13}{3} a + \frac{5}{3}\) , \( -\frac{17}{3} a^{3} + 28 a^{2} - \frac{32}{3} a - \frac{122}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-\frac{11}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){y}={x}^{3}+\left(\frac{11}{3}a^{3}-5a^{2}-\frac{13}{3}a+\frac{5}{3}\right){x}-\frac{17}{3}a^{3}+28a^{2}-\frac{32}{3}a-\frac{122}{3}$ |
| 31.2-a1 |
31.2-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( - 31^{2} \) |
$10.38596$ |
$(1/3a^3+a^2-5/3a-20/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.062716034$ |
$31.30135761$ |
2.534032361 |
\( -\frac{183572074047606330}{961} a^{3} - \frac{158242724911892276}{961} a^{2} + \frac{1173902477615531721}{961} a + \frac{1084434283807197967}{961} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a + \frac{2}{3}\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( a^{3} - 11 a^{2} + 25 a - 19\) , \( \frac{55}{3} a^{3} - 78 a^{2} + \frac{238}{3} a - \frac{8}{3}\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a+\frac{2}{3}\right){x}^{2}+\left(a^{3}-11a^{2}+25a-19\right){x}+\frac{55}{3}a^{3}-78a^{2}+\frac{238}{3}a-\frac{8}{3}$ |
| 31.2-a2 |
31.2-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$10.38596$ |
$(1/3a^3+a^2-5/3a-20/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.531358017$ |
$125.2054304$ |
2.534032361 |
\( -\frac{187205836}{93} a^{3} - \frac{230097301}{31} a^{2} + \frac{1370253530}{93} a + \frac{4769244701}{93} \) |
\( \bigl[a + 1\) , \( \frac{1}{3} a^{3} - \frac{8}{3} a + \frac{1}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + \frac{1}{3}\) , \( \frac{5}{3} a^{3} - 7 a^{2} + \frac{8}{3} a + \frac{14}{3}\) , \( \frac{22}{3} a^{3} - 28 a^{2} + \frac{34}{3} a + \frac{82}{3}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+\frac{1}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{8}{3}a+\frac{1}{3}\right){x}^{2}+\left(\frac{5}{3}a^{3}-7a^{2}+\frac{8}{3}a+\frac{14}{3}\right){x}+\frac{22}{3}a^{3}-28a^{2}+\frac{34}{3}a+\frac{82}{3}$ |
| 31.2-b1 |
31.2-b |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( - 31^{5} \) |
$10.38596$ |
$(1/3a^3+a^2-5/3a-20/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.199052165$ |
$168.0639777$ |
2.210669417 |
\( -\frac{1511829468707}{85887453} a^{3} - \frac{218487362503}{28629151} a^{2} + \frac{12975902869699}{85887453} a + \frac{12789506529010}{85887453} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - \frac{8}{3}\) , \( -\frac{1}{3} a^{3} + \frac{8}{3} a + \frac{2}{3}\) , \( a^{2} + a - 3\) , \( \frac{41}{3} a^{3} + 17 a^{2} - \frac{223}{3} a - \frac{241}{3}\) , \( -\frac{16}{3} a^{3} + 5 a^{2} + \frac{191}{3} a + \frac{137}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-\frac{8}{3}\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{8}{3}a+\frac{2}{3}\right){x}^{2}+\left(\frac{41}{3}a^{3}+17a^{2}-\frac{223}{3}a-\frac{241}{3}\right){x}-\frac{16}{3}a^{3}+5a^{2}+\frac{191}{3}a+\frac{137}{3}$ |
| 31.2-b2 |
31.2-b |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{10} \) |
$10.38596$ |
$(1/3a^3+a^2-5/3a-20/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.398104330$ |
$42.01599443$ |
2.210669417 |
\( -\frac{584752637571865793423}{819628286980801} a^{3} + \frac{2035629411874586215938}{819628286980801} a^{2} - \frac{369555262801336177958}{819628286980801} a - \frac{2594684056192419440511}{819628286980801} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - \frac{8}{3}\) , \( -\frac{1}{3} a^{3} + \frac{8}{3} a + \frac{2}{3}\) , \( a^{2} + a - 3\) , \( \frac{31}{3} a^{3} + 12 a^{2} - \frac{158}{3} a - \frac{146}{3}\) , \( -39 a^{3} - 21 a^{2} + 278 a + 223\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-\frac{8}{3}\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{8}{3}a+\frac{2}{3}\right){x}^{2}+\left(\frac{31}{3}a^{3}+12a^{2}-\frac{158}{3}a-\frac{146}{3}\right){x}-39a^{3}-21a^{2}+278a+223$ |
| 59.1-a1 |
59.1-a |
$1$ |
$1$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( 59 \) |
$11.25597$ |
$(-1/3a^3+a^2+2/3a-13/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.350620670$ |
$149.0834776$ |
2.763371514 |
\( -\frac{18982}{59} a^{3} - \frac{9536}{59} a^{2} + \frac{62715}{59} a + \frac{25417}{59} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( -1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{1}{3}\) , \( \frac{2}{3} a^{3} + a^{2} - \frac{10}{3} a - \frac{10}{3}\) , \( \frac{2}{3} a^{3} + a^{2} - \frac{10}{3} a - \frac{13}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{1}{3}\right){y}={x}^{3}-{x}^{2}+\left(\frac{2}{3}a^{3}+a^{2}-\frac{10}{3}a-\frac{10}{3}\right){x}+\frac{2}{3}a^{3}+a^{2}-\frac{10}{3}a-\frac{13}{3}$ |
| 59.2-a1 |
59.2-a |
$1$ |
$1$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( 59 \) |
$11.25597$ |
$(a^3+a^2-6a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.350620670$ |
$149.0834776$ |
2.763371514 |
\( -\frac{26535}{59} a^{3} + \frac{9536}{59} a^{2} + \frac{164870}{59} a - \frac{67960}{59} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{1}{3}\) , \( -2 a^{2} + 2 a + 5\) , \( \frac{4}{3} a^{3} - 5 a^{2} + \frac{4}{3} a + \frac{19}{3}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{1}{3}\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-2a^{2}+2a+5\right){x}+\frac{4}{3}a^{3}-5a^{2}+\frac{4}{3}a+\frac{19}{3}$ |
| 79.1-a1 |
79.1-a |
$1$ |
$1$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$11.67427$ |
$(2/3a^3+a^2-10/3a-19/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$180.3765033$ |
2.383922969 |
\( \frac{2519040}{79} a^{3} - \frac{5242880}{79} a^{2} - \frac{13864960}{79} a + \frac{27791360}{79} \) |
\( \bigl[0\) , \( \frac{1}{3} a^{3} - a^{2} - \frac{5}{3} a + \frac{10}{3}\) , \( a^{2} + a - 3\) , \( \frac{8}{3} a^{3} + 4 a^{2} - \frac{34}{3} a - \frac{22}{3}\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{2}{3} a + \frac{2}{3}\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-a^{2}-\frac{5}{3}a+\frac{10}{3}\right){x}^{2}+\left(\frac{8}{3}a^{3}+4a^{2}-\frac{34}{3}a-\frac{22}{3}\right){x}-\frac{1}{3}a^{3}-a^{2}+\frac{2}{3}a+\frac{2}{3}$ |
| 79.1-b1 |
79.1-b |
$4$ |
$6$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$11.67427$ |
$(2/3a^3+a^2-10/3a-19/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$715.0674799$ |
2.362649456 |
\( \frac{205899841}{79} a^{3} + \frac{7418233}{79} a^{2} - \frac{1304528660}{79} a - \frac{140099014}{79} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - \frac{11}{3}\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{11}{3}\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( \frac{91}{3} a^{3} + 30 a^{2} - \frac{542}{3} a - \frac{506}{3}\) , \( -133 a^{3} - 107 a^{2} + 876 a + 802\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-\frac{11}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{4}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{11}{3}\right){x}^{2}+\left(\frac{91}{3}a^{3}+30a^{2}-\frac{542}{3}a-\frac{506}{3}\right){x}-133a^{3}-107a^{2}+876a+802$ |
| 79.1-b2 |
79.1-b |
$4$ |
$6$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( - 79^{6} \) |
$11.67427$ |
$(2/3a^3+a^2-10/3a-19/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$357.5337399$ |
2.362649456 |
\( \frac{1235293430109944}{729262366563} a^{3} + \frac{2040290222541221}{243087455521} a^{2} + \frac{7097382629795747}{729262366563} a + \frac{3212820559356182}{729262366563} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{2}{3} a + \frac{11}{3}\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( \frac{2}{3} a^{3} - 2 a^{2} - \frac{28}{3} a - \frac{7}{3}\) , \( -4 a^{3} - 3 a^{2} + 29 a + 28\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-a^{2}+\frac{2}{3}a+\frac{11}{3}\right){x}^{2}+\left(\frac{2}{3}a^{3}-2a^{2}-\frac{28}{3}a-\frac{7}{3}\right){x}-4a^{3}-3a^{2}+29a+28$ |
| 79.1-b3 |
79.1-b |
$4$ |
$6$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( - 79^{3} \) |
$11.67427$ |
$(2/3a^3+a^2-10/3a-19/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$715.0674799$ |
2.362649456 |
\( \frac{70942189}{493039} a^{3} - \frac{130052573}{493039} a^{2} - \frac{476822190}{493039} a + \frac{880737855}{493039} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{2}{3} a + \frac{11}{3}\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( -a^{3} - 2 a^{2} + 4 a + 6\) , \( -\frac{2}{3} a^{3} - a^{2} + \frac{10}{3} a + \frac{10}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-a^{2}+\frac{2}{3}a+\frac{11}{3}\right){x}^{2}+\left(-a^{3}-2a^{2}+4a+6\right){x}-\frac{2}{3}a^{3}-a^{2}+\frac{10}{3}a+\frac{10}{3}$ |
| 79.1-b4 |
79.1-b |
$4$ |
$6$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( - 79^{2} \) |
$11.67427$ |
$(2/3a^3+a^2-10/3a-19/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$357.5337399$ |
2.362649456 |
\( -\frac{528436005447435440}{18723} a^{3} - \frac{151845825619255915}{6241} a^{2} + \frac{3379255148104516477}{18723} a + \frac{3121721034458358025}{18723} \) |
\( \bigl[a + 1\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - \frac{11}{3}\) , \( -6 a^{3} + 13 a^{2} + 46 a - 93\) , \( \frac{145}{3} a^{3} - 98 a^{2} - \frac{818}{3} a + \frac{1606}{3}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-\frac{11}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}^{2}+\left(-6a^{3}+13a^{2}+46a-93\right){x}+\frac{145}{3}a^{3}-98a^{2}-\frac{818}{3}a+\frac{1606}{3}$ |
| 79.2-a1 |
79.2-a |
$1$ |
$1$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( -79 \) |
$11.67427$ |
$(-1/3a^3+a^2+5/3a-7/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$180.3765033$ |
2.383922969 |
\( \frac{11530240}{237} a^{3} + \frac{5242880}{79} a^{2} - \frac{53841920}{237} a - \frac{54210560}{237} \) |
\( \bigl[0\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{8}{3} a - \frac{8}{3}\) , \( a^{2} + a - 4\) , \( -\frac{1}{3} a^{3} + 2 a^{2} - \frac{7}{3} a + \frac{2}{3}\) , \( -\frac{2}{3} a^{3} + \frac{7}{3} a - \frac{2}{3}\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{8}{3}a-\frac{8}{3}\right){x}^{2}+\left(-\frac{1}{3}a^{3}+2a^{2}-\frac{7}{3}a+\frac{2}{3}\right){x}-\frac{2}{3}a^{3}+\frac{7}{3}a-\frac{2}{3}$ |
| 79.2-b1 |
79.2-b |
$4$ |
$6$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( - 79^{6} \) |
$11.67427$ |
$(-1/3a^3+a^2+5/3a-7/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$357.5337399$ |
2.362649456 |
\( \frac{1206539933672404}{243087455521} a^{3} - \frac{2040290222541221}{243087455521} a^{2} - \frac{10457316261810509}{243087455521} a + \frac{20228327646292139}{243087455521} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} + \frac{8}{3} a - \frac{1}{3}\) , \( a^{2} - 4\) , \( -\frac{2}{3} a^{3} + \frac{28}{3} a - \frac{35}{3}\) , \( 2 a^{2} - 9 a + 10\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{8}{3}a-\frac{1}{3}\right){x}^{2}+\left(-\frac{2}{3}a^{3}+\frac{28}{3}a-\frac{35}{3}\right){x}+2a^{2}-9a+10$ |
| 79.2-b2 |
79.2-b |
$4$ |
$6$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( - 79^{3} \) |
$11.67427$ |
$(-1/3a^3+a^2+5/3a-7/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$715.0674799$ |
2.362649456 |
\( \frac{220767895}{1479117} a^{3} + \frac{130052573}{493039} a^{2} - \frac{737505740}{1479117} a - \frac{861264578}{1479117} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} + \frac{8}{3} a - \frac{1}{3}\) , \( a^{2} - 4\) , \( -\frac{2}{3} a^{3} + \frac{13}{3} a - \frac{5}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a - \frac{1}{3}\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{8}{3}a-\frac{1}{3}\right){x}^{2}+\left(-\frac{2}{3}a^{3}+\frac{13}{3}a-\frac{5}{3}\right){x}-\frac{1}{3}a^{3}+\frac{5}{3}a-\frac{1}{3}$ |
| 79.2-b3 |
79.2-b |
$4$ |
$6$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( -79 \) |
$11.67427$ |
$(-1/3a^3+a^2+5/3a-7/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$715.0674799$ |
2.362649456 |
\( \frac{335251835}{237} a^{3} - \frac{7418233}{79} a^{2} - \frac{851170810}{237} a - \frac{502452439}{237} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - \frac{8}{3}\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{8}{3} a + \frac{8}{3}\) , \( a^{2} - 3\) , \( \frac{25}{3} a^{3} - 16 a^{2} - \frac{17}{3} a + \frac{43}{3}\) , \( -39 a^{3} + 159 a^{2} - 45 a - 215\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-\frac{8}{3}\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-a^{2}+\frac{8}{3}a+\frac{8}{3}\right){x}^{2}+\left(\frac{25}{3}a^{3}-16a^{2}-\frac{17}{3}a+\frac{43}{3}\right){x}-39a^{3}+159a^{2}-45a-215$ |
| 79.2-b4 |
79.2-b |
$4$ |
$6$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( - 79^{2} \) |
$11.67427$ |
$(-1/3a^3+a^2+5/3a-7/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$357.5337399$ |
2.362649456 |
\( -\frac{43632824290799922}{6241} a^{3} + \frac{151845825619255915}{6241} a^{2} - \frac{27527585501780149}{6241} a - \frac{193526241562172002}{6241} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a + \frac{4}{3}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{2}{3} a - \frac{16}{3}\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{11}{3}\) , \( -6 a^{3} - 12 a^{2} + 12 a + 22\) , \( \frac{145}{3} a^{3} + 70 a^{2} - \frac{647}{3} a - \frac{674}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+\frac{4}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{11}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{2}{3}a-\frac{16}{3}\right){x}^{2}+\left(-6a^{3}-12a^{2}+12a+22\right){x}+\frac{145}{3}a^{3}+70a^{2}-\frac{647}{3}a-\frac{674}{3}$ |
| 81.1-a1 |
81.1-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{12} \) |
$11.71081$ |
$(1/3a^3-8/3a-2/3), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$60.42569051$ |
1.597216809 |
\( \frac{1482100363031141}{81} a^{3} - \frac{106136572658321}{3} a^{2} - \frac{3060531346398946}{27} a + \frac{17463907730489617}{81} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( 0\) , \( a\) , \( \frac{23}{3} a^{3} - 30 a^{2} + \frac{56}{3} a + \frac{53}{3}\) , \( -\frac{479}{3} a^{3} + 546 a^{2} - \frac{173}{3} a - \frac{2270}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{4}{3}\right){x}{y}+a{y}={x}^{3}+\left(\frac{23}{3}a^{3}-30a^{2}+\frac{56}{3}a+\frac{53}{3}\right){x}-\frac{479}{3}a^{3}+546a^{2}-\frac{173}{3}a-\frac{2270}{3}$ |
| 81.1-a2 |
81.1-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$11.71081$ |
$(1/3a^3-8/3a-2/3), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$241.7027620$ |
1.597216809 |
\( -1069232 a^{3} + \frac{20963441}{9} a^{2} + \frac{59010259}{9} a - \frac{40147549}{3} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( 0\) , \( a\) , \( \frac{38}{3} a^{3} - 45 a^{2} + \frac{26}{3} a + \frac{173}{3}\) , \( -103 a^{3} + 358 a^{2} - 64 a - 458\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{4}{3}\right){x}{y}+a{y}={x}^{3}+\left(\frac{38}{3}a^{3}-45a^{2}+\frac{26}{3}a+\frac{173}{3}\right){x}-103a^{3}+358a^{2}-64a-458$ |
| 81.1-b1 |
81.1-b |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$11.71081$ |
$(1/3a^3-8/3a-2/3), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$241.7027620$ |
1.597216809 |
\( -\frac{38937886}{27} a^{3} - \frac{20963441}{9} a^{2} + \frac{162004973}{27} a + \frac{194616344}{27} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a + \frac{2}{3}\) , \( a\) , \( 6 a^{3} + 5 a^{2} - 42 a - 41\) , \( -20 a^{3} - 19 a^{2} + 124 a + 118\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a+\frac{2}{3}\right){x}^{2}+\left(6a^{3}+5a^{2}-42a-41\right){x}-20a^{3}-19a^{2}+124a+118$ |
| 81.1-b2 |
81.1-b |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{12} \) |
$11.71081$ |
$(1/3a^3-8/3a-2/3), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$60.42569051$ |
1.597216809 |
\( \frac{5540896326826957}{243} a^{3} + \frac{106136572658321}{3} a^{2} - \frac{22391204962011386}{243} a - \frac{23887243038713624}{243} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a + \frac{2}{3}\) , \( a\) , \( -14 a^{3} - 25 a^{2} + 43 a + 49\) , \( -\frac{430}{3} a^{3} - 202 a^{2} + \frac{1955}{3} a + \frac{2012}{3}\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a+\frac{2}{3}\right){x}^{2}+\left(-14a^{3}-25a^{2}+43a+49\right){x}-\frac{430}{3}a^{3}-202a^{2}+\frac{1955}{3}a+\frac{2012}{3}$ |
| 81.2-a1 |
81.2-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
81.2 |
\( 3^{4} \) |
\( - 3^{32} \) |
$11.71081$ |
$(1/3a^3-8/3a-2/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5Nn.3.2[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$165.0358834$ |
2.181175630 |
\( \frac{17984592881}{59049} a^{3} - \frac{3640839358}{6561} a^{2} - \frac{36754267676}{19683} a + \frac{202884647407}{59049} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} + a - 3\) , \( a + 1\) , \( -\frac{493}{3} a^{3} - 138 a^{2} + \frac{3155}{3} a + \frac{2867}{3}\) , \( 1508 a^{3} + 1295 a^{2} - 9642 a - 8874\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-\frac{493}{3}a^{3}-138a^{2}+\frac{3155}{3}a+\frac{2867}{3}\right){x}+1508a^{3}+1295a^{2}-9642a-8874$ |
| 81.2-a2 |
81.2-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
81.2 |
\( 3^{4} \) |
\( 3^{22} \) |
$11.71081$ |
$(1/3a^3-8/3a-2/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5Nn.3.2[2] |
$1$ |
\( 2 \) |
$1$ |
$330.0717668$ |
2.181175630 |
\( -\frac{27461}{243} a^{3} - \frac{149023}{243} a^{2} + \frac{171953}{243} a + \frac{985162}{243} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{2}{3} a - \frac{8}{3}\) , \( \frac{1}{3} a^{3} - a^{2} - \frac{2}{3} a + \frac{13}{3}\) , \( 1\) , \( 14 a^{3} + 18 a^{2} - 75 a - 74\) , \( \frac{97}{3} a^{3} + 37 a^{2} - \frac{521}{3} a - \frac{512}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{2}{3}a-\frac{8}{3}\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{3}a^{3}-a^{2}-\frac{2}{3}a+\frac{13}{3}\right){x}^{2}+\left(14a^{3}+18a^{2}-75a-74\right){x}+\frac{97}{3}a^{3}+37a^{2}-\frac{521}{3}a-\frac{512}{3}$ |
| 81.3-a1 |
81.3-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
81.3 |
\( 3^{4} \) |
\( - 3^{32} \) |
$11.71081$ |
$(-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5Nn.3.2[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$165.0358834$ |
2.181175630 |
\( \frac{66381494242}{177147} a^{3} + \frac{3640839358}{6561} a^{2} - \frac{270887955341}{177147} a - \frac{263642306174}{177147} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{11}{3}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{2}{3} a - \frac{13}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + \frac{1}{3}\) , \( -\frac{130}{3} a^{3} + 141 a^{2} - \frac{46}{3} a - \frac{538}{3}\) , \( 328 a^{3} - 1137 a^{2} + 194 a + 1463\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{11}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+\frac{1}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{2}{3}a-\frac{13}{3}\right){x}^{2}+\left(-\frac{130}{3}a^{3}+141a^{2}-\frac{46}{3}a-\frac{538}{3}\right){x}+328a^{3}-1137a^{2}+194a+1463$ |
| 81.3-a2 |
81.3-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
81.3 |
\( 3^{4} \) |
\( 3^{22} \) |
$11.71081$ |
$(-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5Nn.3.2[2] |
$1$ |
\( 2 \) |
$1$ |
$330.0717668$ |
2.181175630 |
\( \frac{101288}{729} a^{3} + \frac{149023}{243} a^{2} - \frac{610384}{729} a - \frac{884464}{729} \) |
\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{11}{3}\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{2}{3} a - \frac{13}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + \frac{1}{3}\) , \( \frac{35}{3} a^{3} - 44 a^{2} + \frac{29}{3} a + \frac{182}{3}\) , \( 80 a^{3} - 280 a^{2} + 52 a + 357\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+a^{2}-\frac{5}{3}a-\frac{11}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a+\frac{1}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+a^{2}+\frac{2}{3}a-\frac{13}{3}\right){x}^{2}+\left(\frac{35}{3}a^{3}-44a^{2}+\frac{29}{3}a+\frac{182}{3}\right){x}+80a^{3}-280a^{2}+52a+357$ |
| 99.1-a1 |
99.1-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{2} \cdot 11^{2} \) |
$12.00828$ |
$(1/3a^3+a^2-5/3a-11/3), (1/3a^3-8/3a-2/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$367.2701294$ |
2.426989329 |
\( -\frac{7419489698}{363} a^{3} - \frac{11512179388}{363} a^{2} + \frac{29983098625}{363} a + \frac{31989046202}{363} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( \frac{1}{3} a^{3} - a^{2} - \frac{2}{3} a + \frac{10}{3}\) , \( 0\) , \( a^{2} - 2 a\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{4}{3}\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}-a^{2}-\frac{2}{3}a+\frac{10}{3}\right){x}^{2}+\left(a^{2}-2a\right){x}$ |
| 99.1-a2 |
99.1-a |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( - 3^{4} \cdot 11 \) |
$12.00828$ |
$(1/3a^3+a^2-5/3a-11/3), (1/3a^3-8/3a-2/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$91.81753236$ |
2.426989329 |
\( \frac{500065603144517219}{99} a^{3} + \frac{86209380532813855}{11} a^{2} - \frac{673601689954094411}{33} a - \frac{2155822423848772208}{99} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( \frac{1}{3} a^{3} - a^{2} - \frac{2}{3} a + \frac{10}{3}\) , \( 0\) , \( -4 a^{2} + 8 a\) , \( -\frac{38}{3} a^{3} + 33 a^{2} + \frac{61}{3} a - \frac{209}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{4}{3}\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}-a^{2}-\frac{2}{3}a+\frac{10}{3}\right){x}^{2}+\left(-4a^{2}+8a\right){x}-\frac{38}{3}a^{3}+33a^{2}+\frac{61}{3}a-\frac{209}{3}$ |
| 99.1-b1 |
99.1-b |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{2} \cdot 11^{2} \) |
$12.00828$ |
$(1/3a^3+a^2-5/3a-11/3), (1/3a^3-8/3a-2/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$194.8847350$ |
1.287834578 |
\( \frac{126340991}{363} a^{3} - \frac{439647050}{363} a^{2} + \frac{79073246}{363} a + \frac{562074610}{363} \) |
\( \bigl[a\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{1}{3}\) , \( 0\) , \( \frac{5}{3} a^{3} + 2 a^{2} - \frac{25}{3} a - \frac{22}{3}\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{1}{3}\right){x}^{2}+\left(\frac{5}{3}a^{3}+2a^{2}-\frac{25}{3}a-\frac{22}{3}\right){x}$ |
| 99.1-b2 |
99.1-b |
$2$ |
$2$ |
4.4.5725.1 |
$4$ |
$[4, 0]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( - 3^{4} \cdot 11 \) |
$12.00828$ |
$(1/3a^3+a^2-5/3a-11/3), (1/3a^3-8/3a-2/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$48.72118375$ |
1.287834578 |
\( -\frac{404610303065758}{99} a^{3} + \frac{469359187787779}{33} a^{2} - \frac{85088914179124}{33} a - \frac{1794581231821157}{99} \) |
\( \bigl[a\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{1}{3}\) , \( 0\) , \( -\frac{20}{3} a^{3} - 8 a^{2} + \frac{100}{3} a + \frac{88}{3}\) , \( -14 a^{3} - 20 a^{2} + 59 a + 55\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a+\frac{1}{3}\right){x}^{2}+\left(-\frac{20}{3}a^{3}-8a^{2}+\frac{100}{3}a+\frac{88}{3}\right){x}-14a^{3}-20a^{2}+59a+55$ |
*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.
