| 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 |
| 25.1-a1 |
25.1-a |
$4$ |
$10$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$11.95160$ |
$(1/2a^3+1/2a^2-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-40$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.4[2] |
$4$ |
\( 2 \) |
$1$ |
$77.62503566$ |
1.735748564 |
\( -95178240 a^{2} + 688737600 \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{2} - 2\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( -\frac{33}{2} a^{3} + \frac{47}{2} a^{2} + 116 a - 182\) , \( -93 a^{3} + 138 a^{2} + 661 a - 1053\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-2\right){x}^{2}+\left(-\frac{33}{2}a^{3}+\frac{47}{2}a^{2}+116a-182\right){x}-93a^{3}+138a^{2}+661a-1053$ |
| 25.1-a2 |
25.1-a |
$4$ |
$10$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$11.95160$ |
$(1/2a^3+1/2a^2-3a-5)$ |
0 |
$\Z/10\Z$ |
$\textsf{potential}$ |
$-40$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.1[2] |
$4$ |
\( 2 \) |
$1$ |
$1940.625891$ |
1.735748564 |
\( -95178240 a^{2} + 688737600 \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{2} a^{2} + 2\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( 16 a^{3} - 44 a^{2} - 41 a + 113\) , \( -\frac{259}{2} a^{3} + 347 a^{2} + 356 a - 955\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+2\right){x}^{2}+\left(16a^{3}-44a^{2}-41a+113\right){x}-\frac{259}{2}a^{3}+347a^{2}+356a-955$ |
| 25.1-a3 |
25.1-a |
$4$ |
$10$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$11.95160$ |
$(1/2a^3+1/2a^2-3a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-40$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.4[2] |
$4$ |
\( 2 \) |
$1$ |
$77.62503566$ |
1.735748564 |
\( 95178240 a^{2} - 263044800 \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{2} - 2\) , \( 1\) , \( -9 a^{3} - \frac{39}{2} a^{2} + 21 a + 38\) , \( -\frac{151}{2} a^{3} - 201 a^{2} + 200 a + 532\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{2}-2\right){x}^{2}+\left(-9a^{3}-\frac{39}{2}a^{2}+21a+38\right){x}-\frac{151}{2}a^{3}-201a^{2}+200a+532$ |
| 25.1-a4 |
25.1-a |
$4$ |
$10$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$11.95160$ |
$(1/2a^3+1/2a^2-3a-5)$ |
0 |
$\Z/10\Z$ |
$\textsf{potential}$ |
$-40$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.1[2] |
$4$ |
\( 2 \) |
$1$ |
$1940.625891$ |
1.735748564 |
\( 95178240 a^{2} - 263044800 \) |
\( \bigl[a\) , \( \frac{1}{2} a^{2} - 3\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{55}{2} a^{3} + 42 a^{2} - 198 a - 317\) , \( -\frac{421}{2} a^{3} - 349 a^{2} + 1521 a + 2525\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-3\right){x}^{2}+\left(\frac{55}{2}a^{3}+42a^{2}-198a-317\right){x}-\frac{421}{2}a^{3}-349a^{2}+1521a+2525$ |
| 25.1-b1 |
25.1-b |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$11.95160$ |
$(1/2a^3+1/2a^2-3a-5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.2.2[2] |
$1$ |
\( 2 \) |
$0.031683597$ |
$1152.278159$ |
3.265403157 |
\( 8000 \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 3\) , \( \frac{1}{2} a^{3} - 3 a + 1\) , \( -4 a^{3} - 13 a^{2} + 8 a + 38\) , \( -19 a^{3} - \frac{105}{2} a^{2} + 51 a + 147\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{3}-3a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+3\right){x}^{2}+\left(-4a^{3}-13a^{2}+8a+38\right){x}-19a^{3}-\frac{105}{2}a^{2}+51a+147$ |
| 25.1-b2 |
25.1-b |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$11.95160$ |
$(1/2a^3+1/2a^2-3a-5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.2.2[2] |
$1$ |
\( 2 \) |
$0.031683597$ |
$1152.278159$ |
3.265403157 |
\( 8000 \) |
\( \bigl[a\) , \( \frac{1}{2} a^{2} + a - 2\) , \( a + 1\) , \( 8 a^{3} + 13 a^{2} - 56 a - 92\) , \( \frac{63}{2} a^{3} + \frac{105}{2} a^{2} - 227 a - 378\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+a-2\right){x}^{2}+\left(8a^{3}+13a^{2}-56a-92\right){x}+\frac{63}{2}a^{3}+\frac{105}{2}a^{2}-227a-378$ |
| 29.1-a1 |
29.1-a |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{4} \) |
$12.17540$ |
$(1/2a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$94.11493115$ |
2.104473837 |
\( -\frac{18141312}{707281} a^{3} - \frac{353227136}{707281} a^{2} - \frac{276422400}{707281} a + \frac{1507649088}{707281} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} + a - 2\) , \( a + 1\) , \( 3 a^{3} - 6 a^{2} - 21 a + 44\) , \( \frac{5}{2} a^{3} - 5 a^{2} - 19 a + 33\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+a-2\right){x}^{2}+\left(3a^{3}-6a^{2}-21a+44\right){x}+\frac{5}{2}a^{3}-5a^{2}-19a+33$ |
| 29.1-a2 |
29.1-a |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$12.17540$ |
$(1/2a^2+a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$376.4597246$ |
2.104473837 |
\( \frac{477094016}{841} a^{3} + \frac{1293502336}{841} a^{2} - \frac{1284868352}{841} a - \frac{3517331904}{841} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( 1\) , \( 3 a^{3} - 3 a^{2} - 9 a + 9\) , \( 6 a^{3} - 11 a^{2} - 17 a + 30\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){x}^{2}+\left(3a^{3}-3a^{2}-9a+9\right){x}+6a^{3}-11a^{2}-17a+30$ |
| 29.1-b1 |
29.1-b |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$12.17540$ |
$(1/2a^2+a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.045328322$ |
$2556.217872$ |
2.590911100 |
\( \frac{477094016}{841} a^{3} + \frac{1293502336}{841} a^{2} - \frac{1284868352}{841} a - \frac{3517331904}{841} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} + a - 2\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( -4 a^{3} + \frac{9}{2} a^{2} + 28 a - 38\) , \( -3 a^{3} + \frac{7}{2} a^{2} + 21 a - 30\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+a-2\right){x}^{2}+\left(-4a^{3}+\frac{9}{2}a^{2}+28a-38\right){x}-3a^{3}+\frac{7}{2}a^{2}+21a-30$ |
| 29.1-b2 |
29.1-b |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{4} \) |
$12.17540$ |
$(1/2a^2+a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.090656644$ |
$639.0544681$ |
2.590911100 |
\( -\frac{18141312}{707281} a^{3} - \frac{353227136}{707281} a^{2} - \frac{276422400}{707281} a + \frac{1507649088}{707281} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( \frac{1}{2} a^{3} - 3 a + 1\) , \( \frac{1}{2} a^{3} + 3 a^{2} - 2 a - 8\) , \( -2 a^{3} + 10 a^{2} + 6 a - 29\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}-3a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){x}^{2}+\left(\frac{1}{2}a^{3}+3a^{2}-2a-8\right){x}-2a^{3}+10a^{2}+6a-29$ |
| 29.2-a1 |
29.2-a |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29^{2} \) |
$12.17540$ |
$(1/2a^3-1/2a^2-3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$376.4597246$ |
2.104473837 |
\( \frac{788847872}{841} a^{3} - \frac{1293502336}{841} a^{2} - \frac{5687275264}{841} a + \frac{9417691456}{841} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} - 4 a - 1\) , \( a + 1\) , \( \frac{5}{2} a^{3} + \frac{7}{2} a^{2} - 20 a - 27\) , \( 3 a^{3} + 5 a^{2} - 23 a - 37\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-4a-1\right){x}^{2}+\left(\frac{5}{2}a^{3}+\frac{7}{2}a^{2}-20a-27\right){x}+3a^{3}+5a^{2}-23a-37$ |
| 29.2-a2 |
29.2-a |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29^{4} \) |
$12.17540$ |
$(1/2a^3-1/2a^2-3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$94.11493115$ |
2.104473837 |
\( -\frac{192635136}{707281} a^{3} + \frac{353227136}{707281} a^{2} + \frac{1192093440}{707281} a - \frac{2024622272}{707281} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 3\) , \( \frac{1}{2} a^{3} - 3 a + 1\) , \( -\frac{3}{2} a^{3} + 4 a^{2} + 2 a - 6\) , \( -2 a^{3} + 5 a^{2} + 7 a - 17\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}-3a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+3\right){x}^{2}+\left(-\frac{3}{2}a^{3}+4a^{2}+2a-6\right){x}-2a^{3}+5a^{2}+7a-17$ |
| 29.2-b1 |
29.2-b |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29^{4} \) |
$12.17540$ |
$(1/2a^3-1/2a^2-3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.090656644$ |
$639.0544681$ |
2.590911100 |
\( -\frac{192635136}{707281} a^{3} + \frac{353227136}{707281} a^{2} + \frac{1192093440}{707281} a - \frac{2024622272}{707281} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} - 4 a - 1\) , \( 1\) , \( -\frac{3}{2} a^{3} - \frac{3}{2} a^{2} + 9 a + 16\) , \( -3 a^{3} - \frac{9}{2} a^{2} + 21 a + 35\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-4a-1\right){x}^{2}+\left(-\frac{3}{2}a^{3}-\frac{3}{2}a^{2}+9a+16\right){x}-3a^{3}-\frac{9}{2}a^{2}+21a+35$ |
| 29.2-b2 |
29.2-b |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29^{2} \) |
$12.17540$ |
$(1/2a^3-1/2a^2-3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.045328322$ |
$2556.217872$ |
2.590911100 |
\( \frac{788847872}{841} a^{3} - \frac{1293502336}{841} a^{2} - \frac{5687275264}{841} a + \frac{9417691456}{841} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 3\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( 2 a^{3} - \frac{13}{2} a^{2} - 5 a + 17\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} - 4 a + 15\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+3\right){x}^{2}+\left(2a^{3}-\frac{13}{2}a^{2}-5a+17\right){x}+\frac{3}{2}a^{3}-\frac{11}{2}a^{2}-4a+15$ |
| 29.3-a1 |
29.3-a |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.3 |
\( 29 \) |
\( 29^{2} \) |
$12.17540$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$376.4597246$ |
2.104473837 |
\( -\frac{788847872}{841} a^{3} - \frac{1293502336}{841} a^{2} + \frac{5687275264}{841} a + \frac{9417691456}{841} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{2} a^{3} + 4 a - 1\) , \( a + 1\) , \( -3 a^{3} + \frac{7}{2} a^{2} + 22 a - 27\) , \( -3 a^{3} + 5 a^{2} + 22 a - 37\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+4a-1\right){x}^{2}+\left(-3a^{3}+\frac{7}{2}a^{2}+22a-27\right){x}-3a^{3}+5a^{2}+22a-37$ |
| 29.3-a2 |
29.3-a |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.3 |
\( 29 \) |
\( 29^{4} \) |
$12.17540$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$94.11493115$ |
2.104473837 |
\( \frac{192635136}{707281} a^{3} + \frac{353227136}{707281} a^{2} - \frac{1192093440}{707281} a - \frac{2024622272}{707281} \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 3 a + 3\) , \( \frac{1}{2} a^{3} - 3 a + 1\) , \( \frac{3}{2} a^{3} + 4 a^{2} - 3 a - 6\) , \( \frac{3}{2} a^{3} + 5 a^{2} - 4 a - 17\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}-3a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+3a+3\right){x}^{2}+\left(\frac{3}{2}a^{3}+4a^{2}-3a-6\right){x}+\frac{3}{2}a^{3}+5a^{2}-4a-17$ |
| 29.3-b1 |
29.3-b |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.3 |
\( 29 \) |
\( 29^{4} \) |
$12.17540$ |
$(a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.090656644$ |
$639.0544681$ |
2.590911100 |
\( \frac{192635136}{707281} a^{3} + \frac{353227136}{707281} a^{2} - \frac{1192093440}{707281} a - \frac{2024622272}{707281} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{2} a^{3} + 4 a - 1\) , \( 1\) , \( a^{3} - \frac{3}{2} a^{2} - 7 a + 16\) , \( 3 a^{3} - \frac{9}{2} a^{2} - 21 a + 35\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+4a-1\right){x}^{2}+\left(a^{3}-\frac{3}{2}a^{2}-7a+16\right){x}+3a^{3}-\frac{9}{2}a^{2}-21a+35$ |
| 29.3-b2 |
29.3-b |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.3 |
\( 29 \) |
\( 29^{2} \) |
$12.17540$ |
$(a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.045328322$ |
$2556.217872$ |
2.590911100 |
\( -\frac{788847872}{841} a^{3} - \frac{1293502336}{841} a^{2} + \frac{5687275264}{841} a + \frac{9417691456}{841} \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 3 a + 3\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( -2 a^{3} - \frac{13}{2} a^{2} + 4 a + 17\) , \( -2 a^{3} - \frac{11}{2} a^{2} + 6 a + 15\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+3a+3\right){x}^{2}+\left(-2a^{3}-\frac{13}{2}a^{2}+4a+17\right){x}-2a^{3}-\frac{11}{2}a^{2}+6a+15$ |
| 29.4-a1 |
29.4-a |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29^{4} \) |
$12.17540$ |
$(-1/2a^2+a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$94.11493115$ |
2.104473837 |
\( \frac{18141312}{707281} a^{3} - \frac{353227136}{707281} a^{2} + \frac{276422400}{707281} a + \frac{1507649088}{707281} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} - a - 2\) , \( a + 1\) , \( -\frac{7}{2} a^{3} - 6 a^{2} + 24 a + 44\) , \( -\frac{5}{2} a^{3} - 5 a^{2} + 18 a + 33\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-a-2\right){x}^{2}+\left(-\frac{7}{2}a^{3}-6a^{2}+24a+44\right){x}-\frac{5}{2}a^{3}-5a^{2}+18a+33$ |
| 29.4-a2 |
29.4-a |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29^{2} \) |
$12.17540$ |
$(-1/2a^2+a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$376.4597246$ |
2.104473837 |
\( -\frac{477094016}{841} a^{3} + \frac{1293502336}{841} a^{2} + \frac{1284868352}{841} a - \frac{3517331904}{841} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 2 a + 3\) , \( 1\) , \( -\frac{7}{2} a^{3} - 3 a^{2} + 11 a + 9\) , \( -6 a^{3} - 11 a^{2} + 17 a + 30\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+2a+3\right){x}^{2}+\left(-\frac{7}{2}a^{3}-3a^{2}+11a+9\right){x}-6a^{3}-11a^{2}+17a+30$ |
| 29.4-b1 |
29.4-b |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29^{2} \) |
$12.17540$ |
$(-1/2a^2+a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.045328322$ |
$2556.217872$ |
2.590911100 |
\( -\frac{477094016}{841} a^{3} + \frac{1293502336}{841} a^{2} + \frac{1284868352}{841} a - \frac{3517331904}{841} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} - a - 2\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{7}{2} a^{3} + \frac{9}{2} a^{2} - 25 a - 38\) , \( \frac{5}{2} a^{3} + \frac{7}{2} a^{2} - 19 a - 30\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a\right){x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-a-2\right){x}^{2}+\left(\frac{7}{2}a^{3}+\frac{9}{2}a^{2}-25a-38\right){x}+\frac{5}{2}a^{3}+\frac{7}{2}a^{2}-19a-30$ |
| 29.4-b2 |
29.4-b |
$2$ |
$2$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29^{4} \) |
$12.17540$ |
$(-1/2a^2+a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.090656644$ |
$639.0544681$ |
2.590911100 |
\( \frac{18141312}{707281} a^{3} - \frac{353227136}{707281} a^{2} + \frac{276422400}{707281} a + \frac{1507649088}{707281} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 2 a + 3\) , \( \frac{1}{2} a^{3} - 3 a + 1\) , \( -a^{3} + 3 a^{2} + 4 a - 8\) , \( \frac{3}{2} a^{3} + 10 a^{2} - 3 a - 29\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}-3a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+2a+3\right){x}^{2}+\left(-a^{3}+3a^{2}+4a-8\right){x}+\frac{3}{2}a^{3}+10a^{2}-3a-29$ |
| 44.1-a1 |
44.1-a |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(1/2a^2+a-2), (a^2+a-4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$121.6466860$ |
2.720102591 |
\( \frac{186806457187065527217}{644204} a^{3} + \frac{1242268729854976999493}{2576816} a^{2} - \frac{10813953778068508135555}{5153632} a - \frac{17978281963641980467639}{5153632} \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{2} - a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( 9 a^{3} + 7 a^{2} - 47 a - 44\) , \( -10 a^{3} - 16 a^{2} + 61 a + 151\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-a+3\right){x}^{2}+\left(9a^{3}+7a^{2}-47a-44\right){x}-10a^{3}-16a^{2}+61a+151$ |
| 44.1-a2 |
44.1-a |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(1/2a^2+a-2), (a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$121.6466860$ |
2.720102591 |
\( -\frac{2444850}{11} a^{3} - \frac{6465825}{11} a^{2} + \frac{13730125}{22} a + \frac{35368141}{22} \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{2} - a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -a^{3} - 3 a^{2} + 3 a + 11\) , \( -a^{3} - \frac{5}{2} a^{2} + 3 a + 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-a+3\right){x}^{2}+\left(-a^{3}-3a^{2}+3a+11\right){x}-a^{3}-\frac{5}{2}a^{2}+3a+6$ |
| 44.1-b1 |
44.1-b |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(1/2a^2+a-2), (a^2+a-4)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
|
\( 2 \cdot 5 \) |
$1$ |
$0.401031874$ |
3.181808836 |
\( -\frac{180573546428986317635}{10307264} a^{3} - \frac{464347704777436882827}{10307264} a^{2} + \frac{65134388954518111809}{1288408} a + \frac{311720018028907303419}{2576816} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( -\frac{1}{2} a^{2} + a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 3\) , \( 18 a^{3} - 23 a^{2} - 174 a - 153\) , \( -1200 a^{3} - 2339 a^{2} + 8061 a + 14338\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+a+3\right){x}^{2}+\left(18a^{3}-23a^{2}-174a-153\right){x}-1200a^{3}-2339a^{2}+8061a+14338$ |
| 44.1-b2 |
44.1-b |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(1/2a^2+a-2), (a^2+a-4)$ |
$0 \le r \le 1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
|
\( 2 \) |
$1$ |
$250.6449213$ |
3.181808836 |
\( \frac{102657698955035}{44} a^{3} + \frac{170669220228365}{44} a^{2} - \frac{371419044029915}{22} a - \frac{617487039616167}{22} \) |
\( \bigl[\frac{1}{2} a^{2} - 2\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 4 a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -3 a^{3} + \frac{3}{2} a^{2} + 20 a - 12\) , \( -41 a^{3} + \frac{129}{2} a^{2} + 295 a - 473\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+4a+3\right){x}^{2}+\left(-3a^{3}+\frac{3}{2}a^{2}+20a-12\right){x}-41a^{3}+\frac{129}{2}a^{2}+295a-473$ |
| 44.1-c1 |
44.1-c |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(1/2a^2+a-2), (a^2+a-4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$78.70372532$ |
1.759868799 |
\( -\frac{180573546428986317635}{10307264} a^{3} - \frac{464347704777436882827}{10307264} a^{2} + \frac{65134388954518111809}{1288408} a + \frac{311720018028907303419}{2576816} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 3\) , \( -\frac{1}{2} a^{2} - a + 4\) , \( a + 1\) , \( -\frac{83}{2} a^{3} - \frac{177}{2} a^{2} + 972 a - 1174\) , \( 315 a^{3} + 2922 a^{2} - 17210 a + 19020\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-a+4\right){x}^{2}+\left(-\frac{83}{2}a^{3}-\frac{177}{2}a^{2}+972a-1174\right){x}+315a^{3}+2922a^{2}-17210a+19020$ |
| 44.1-c2 |
44.1-c |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(1/2a^2+a-2), (a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$78.70372532$ |
1.759868799 |
\( \frac{102657698955035}{44} a^{3} + \frac{170669220228365}{44} a^{2} - \frac{371419044029915}{22} a - \frac{617487039616167}{22} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( \frac{1}{2} a^{2} - 2\) , \( -5 a^{3} - 15 a^{2} + 10 a + 41\) , \( \frac{131}{2} a^{3} + 175 a^{2} - 183 a - 485\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{2}-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){x}^{2}+\left(-5a^{3}-15a^{2}+10a+41\right){x}+\frac{131}{2}a^{3}+175a^{2}-183a-485$ |
| 44.1-d1 |
44.1-d |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(1/2a^2+a-2), (a^2+a-4)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \) |
$0.589031151$ |
$886.2775173$ |
1.867725211 |
\( -\frac{2444850}{11} a^{3} - \frac{6465825}{11} a^{2} + \frac{13730125}{22} a + \frac{35368141}{22} \) |
\( \bigl[\frac{1}{2} a^{2} - 2\) , \( \frac{1}{2} a^{3} - 2 a - 1\) , \( a\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a^{2} - a - 17\) , \( \frac{5}{2} a^{3} - \frac{3}{2} a^{2} - 12 a - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{3}-2a-1\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{9}{2}a^{2}-a-17\right){x}+\frac{5}{2}a^{3}-\frac{3}{2}a^{2}-12a-5$ |
| 44.1-d2 |
44.1-d |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(1/2a^2+a-2), (a^2+a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \cdot 5 \) |
$2.945155759$ |
$1.418044027$ |
1.867725211 |
\( \frac{186806457187065527217}{644204} a^{3} + \frac{1242268729854976999493}{2576816} a^{2} - \frac{10813953778068508135555}{5153632} a - \frac{17978281963641980467639}{5153632} \) |
\( \bigl[\frac{1}{2} a^{2} - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( 191 a^{3} + \frac{447}{2} a^{2} - 828 a - 123\) , \( -\frac{7231}{2} a^{3} + \frac{11383}{2} a^{2} + 25834 a - 42070\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+3\right){x}^{2}+\left(191a^{3}+\frac{447}{2}a^{2}-828a-123\right){x}-\frac{7231}{2}a^{3}+\frac{11383}{2}a^{2}+25834a-42070$ |
| 44.2-a1 |
44.2-a |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(1/2a^3-1/2a^2-3a+3), (a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$121.6466860$ |
2.720102591 |
\( -\frac{15608075}{44} a^{3} + \frac{6465825}{11} a^{2} + \frac{56603625}{22} a - \frac{93948359}{22} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( -a^{3} + \frac{1}{2} a^{2} + 6 a - 6\) , \( -a^{3} + \frac{1}{2} a^{2} + 7 a - 9\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-2\right){x}^{2}+\left(-a^{3}+\frac{1}{2}a^{2}+6a-6\right){x}-a^{3}+\frac{1}{2}a^{2}+7a-9$ |
| 44.2-a2 |
44.2-a |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(1/2a^3-1/2a^2-3a+3), (a^2+a-4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$121.6466860$ |
2.720102591 |
\( -\frac{1847243833089362829139}{10307264} a^{3} - \frac{1242268729854976999493}{2576816} a^{2} + \frac{2552828184275040051945}{5153632} a + \frac{6867092633457559522221}{5153632} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( 4 a^{3} - \frac{19}{2} a^{2} - 44 a + 39\) , \( a^{3} + 14 a^{2} + 13 a + 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-2\right){x}^{2}+\left(4a^{3}-\frac{19}{2}a^{2}-44a+39\right){x}+a^{3}+14a^{2}+13a+1$ |
| 44.2-b1 |
44.2-b |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(1/2a^3-1/2a^2-3a+3), (a^2+a-4)$ |
$0 \le r \le 1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
|
\( 2 \) |
$1$ |
$250.6449213$ |
3.181808836 |
\( -\frac{31722973582405}{22} a^{3} - \frac{170669220228365}{44} a^{2} + \frac{87680142539395}{22} a + \frac{117929530762829}{11} \) |
\( \bigl[\frac{1}{2} a^{2} - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( \frac{3}{2} a^{3} - \frac{3}{2} a^{2} - 4 a + 3\) , \( 25 a^{3} - \frac{133}{2} a^{2} - 69 a + 182\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){x}^{2}+\left(\frac{3}{2}a^{3}-\frac{3}{2}a^{2}-4a+3\right){x}+25a^{3}-\frac{133}{2}a^{2}-69a+182$ |
| 44.2-b2 |
44.2-b |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(1/2a^3-1/2a^2-3a+3), (a^2+a-4)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
|
\( 2 \cdot 5 \) |
$1$ |
$0.401031874$ |
3.181808836 |
\( -\frac{281183083468886505669}{10307264} a^{3} + \frac{464347704777436882827}{10307264} a^{2} + \frac{512061398417822917321}{2576816} a - \frac{1698298487829369807297}{5153632} \) |
\( \bigl[\frac{1}{2} a^{2} + a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( \frac{1}{2} a^{2} + a - 2\) , \( -33 a^{3} + 23 a^{2} + 162 a - 383\) , \( \frac{861}{2} a^{3} + 2339 a^{2} - 183 a - 9052\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-3\right){x}{y}+\left(\frac{1}{2}a^{2}+a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){x}^{2}+\left(-33a^{3}+23a^{2}+162a-383\right){x}+\frac{861}{2}a^{3}+2339a^{2}-183a-9052$ |
| 44.2-c1 |
44.2-c |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(1/2a^3-1/2a^2-3a+3), (a^2+a-4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$78.70372532$ |
1.759868799 |
\( -\frac{281183083468886505669}{10307264} a^{3} + \frac{464347704777436882827}{10307264} a^{2} + \frac{512061398417822917321}{2576816} a - \frac{1698298487829369807297}{5153632} \) |
\( \bigl[\frac{1}{2} a^{2} + a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( \frac{723}{2} a^{3} + 84 a^{2} - 2089 a - 2043\) , \( -\frac{16043}{2} a^{3} - \frac{6019}{2} a^{2} + 47417 a + 50295\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-4\right){x}^{2}+\left(\frac{723}{2}a^{3}+84a^{2}-2089a-2043\right){x}-\frac{16043}{2}a^{3}-\frac{6019}{2}a^{2}+47417a+50295$ |
| 44.2-c2 |
44.2-c |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(1/2a^3-1/2a^2-3a+3), (a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$78.70372532$ |
1.759868799 |
\( -\frac{31722973582405}{22} a^{3} - \frac{170669220228365}{44} a^{2} + \frac{87680142539395}{22} a + \frac{117929530762829}{11} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( \frac{1}{2} a^{2} + a - 3\) , \( -\frac{21}{2} a^{3} + 18 a^{2} + 76 a - 126\) , \( 121 a^{3} - \frac{407}{2} a^{2} - 877 a + 1465\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+3\right){x}^{2}+\left(-\frac{21}{2}a^{3}+18a^{2}+76a-126\right){x}+121a^{3}-\frac{407}{2}a^{2}-877a+1465$ |
| 44.2-d1 |
44.2-d |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(1/2a^3-1/2a^2-3a+3), (a^2+a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \cdot 5 \) |
$2.945155759$ |
$1.418044027$ |
1.867725211 |
\( -\frac{1847243833089362829139}{10307264} a^{3} - \frac{1242268729854976999493}{2576816} a^{2} + \frac{2552828184275040051945}{5153632} a + \frac{6867092633457559522221}{5153632} \) |
\( \bigl[\frac{1}{2} a^{2} - 3\) , \( \frac{1}{2} a^{2} - a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( \frac{319}{2} a^{3} - \frac{447}{2} a^{2} - 1340 a + 2112\) , \( \frac{4141}{2} a^{3} - \frac{11387}{2} a^{2} - 5193 a + 14855\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-a-2\right){x}^{2}+\left(\frac{319}{2}a^{3}-\frac{447}{2}a^{2}-1340a+2112\right){x}+\frac{4141}{2}a^{3}-\frac{11387}{2}a^{2}-5193a+14855$ |
| 44.2-d2 |
44.2-d |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(1/2a^3-1/2a^2-3a+3), (a^2+a-4)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \) |
$0.589031151$ |
$886.2775173$ |
1.867725211 |
\( -\frac{15608075}{44} a^{3} + \frac{6465825}{11} a^{2} + \frac{56603625}{22} a - \frac{93948359}{22} \) |
\( \bigl[\frac{1}{2} a^{2} - 3\) , \( \frac{1}{2} a^{3} - 4 a - 1\) , \( \frac{1}{2} a^{3} - 3 a\) , \( -\frac{3}{2} a^{3} - \frac{9}{2} a^{2} + 9 a + 28\) , \( \frac{3}{2} a^{3} + \frac{3}{2} a^{2} - 14 a - 20\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-3\right){x}{y}+\left(\frac{1}{2}a^{3}-3a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-4a-1\right){x}^{2}+\left(-\frac{3}{2}a^{3}-\frac{9}{2}a^{2}+9a+28\right){x}+\frac{3}{2}a^{3}+\frac{3}{2}a^{2}-14a-20$ |
| 44.3-a1 |
44.3-a |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(a+1), (a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$121.6466860$ |
2.720102591 |
\( \frac{15608075}{44} a^{3} + \frac{6465825}{11} a^{2} - \frac{56603625}{22} a - \frac{93948359}{22} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a + 1\) , \( \frac{1}{2} a^{2} - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( a^{3} + \frac{1}{2} a^{2} - 8 a - 6\) , \( a^{3} + \frac{1}{2} a^{2} - 8 a - 9\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-2\right){x}^{2}+\left(a^{3}+\frac{1}{2}a^{2}-8a-6\right){x}+a^{3}+\frac{1}{2}a^{2}-8a-9$ |
| 44.3-a2 |
44.3-a |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(a+1), (a^2+a-4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$121.6466860$ |
2.720102591 |
\( \frac{1847243833089362829139}{10307264} a^{3} - \frac{1242268729854976999493}{2576816} a^{2} - \frac{2552828184275040051945}{5153632} a + \frac{6867092633457559522221}{5153632} \) |
\( \bigl[\frac{1}{2} a^{3} - 3 a + 1\) , \( \frac{1}{2} a^{2} - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( -4 a^{3} - \frac{19}{2} a^{2} + 42 a + 39\) , \( -a^{3} + 14 a^{2} - 14 a + 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-2\right){x}^{2}+\left(-4a^{3}-\frac{19}{2}a^{2}+42a+39\right){x}-a^{3}+14a^{2}-14a+1$ |
| 44.3-b1 |
44.3-b |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(a+1), (a^2+a-4)$ |
$0 \le r \le 1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
|
\( 2 \) |
$1$ |
$250.6449213$ |
3.181808836 |
\( \frac{31722973582405}{22} a^{3} - \frac{170669220228365}{44} a^{2} - \frac{87680142539395}{22} a + \frac{117929530762829}{11} \) |
\( \bigl[\frac{1}{2} a^{2} - 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( -\frac{3}{2} a^{3} - \frac{3}{2} a^{2} + 3 a + 3\) , \( -25 a^{3} - \frac{133}{2} a^{2} + 68 a + 182\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-2\right){x}^{2}+\left(-\frac{3}{2}a^{3}-\frac{3}{2}a^{2}+3a+3\right){x}-25a^{3}-\frac{133}{2}a^{2}+68a+182$ |
| 44.3-b2 |
44.3-b |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(a+1), (a^2+a-4)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
|
\( 2 \cdot 5 \) |
$1$ |
$0.401031874$ |
3.181808836 |
\( \frac{281183083468886505669}{10307264} a^{3} + \frac{464347704777436882827}{10307264} a^{2} - \frac{512061398417822917321}{2576816} a - \frac{1698298487829369807297}{5153632} \) |
\( \bigl[\frac{1}{2} a^{2} + a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( 34 a^{3} + \frac{45}{2} a^{2} - 167 a - 378\) , \( -\frac{1153}{2} a^{3} + \frac{4693}{2} a^{2} + 1106 a - 8757\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){x}^{2}+\left(34a^{3}+\frac{45}{2}a^{2}-167a-378\right){x}-\frac{1153}{2}a^{3}+\frac{4693}{2}a^{2}+1106a-8757$ |
| 44.3-c1 |
44.3-c |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(a+1), (a^2+a-4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$78.70372532$ |
1.759868799 |
\( \frac{281183083468886505669}{10307264} a^{3} + \frac{464347704777436882827}{10307264} a^{2} - \frac{512061398417822917321}{2576816} a - \frac{1698298487829369807297}{5153632} \) |
\( \bigl[\frac{1}{2} a^{2} + a - 2\) , \( \frac{1}{2} a^{2} - a - 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( -\frac{725}{2} a^{3} + 84 a^{2} + 2093 a - 2043\) , \( \frac{16043}{2} a^{3} - \frac{6019}{2} a^{2} - 47418 a + 50295\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-a-4\right){x}^{2}+\left(-\frac{725}{2}a^{3}+84a^{2}+2093a-2043\right){x}+\frac{16043}{2}a^{3}-\frac{6019}{2}a^{2}-47418a+50295$ |
| 44.3-c2 |
44.3-c |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(a+1), (a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$78.70372532$ |
1.759868799 |
\( \frac{31722973582405}{22} a^{3} - \frac{170669220228365}{44} a^{2} - \frac{87680142539395}{22} a + \frac{117929530762829}{11} \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 4 a + 3\) , \( \frac{1}{2} a^{2} - 3\) , \( \frac{19}{2} a^{3} + \frac{29}{2} a^{2} - 67 a - 106\) , \( -105 a^{3} - 175 a^{2} + 761 a + 1265\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+4a+3\right){x}^{2}+\left(\frac{19}{2}a^{3}+\frac{29}{2}a^{2}-67a-106\right){x}-105a^{3}-175a^{2}+761a+1265$ |
| 44.3-d1 |
44.3-d |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(a+1), (a^2+a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \cdot 5 \) |
$2.945155759$ |
$1.418044027$ |
1.867725211 |
\( \frac{1847243833089362829139}{10307264} a^{3} - \frac{1242268729854976999493}{2576816} a^{2} - \frac{2552828184275040051945}{5153632} a + \frac{6867092633457559522221}{5153632} \) |
\( \bigl[\frac{1}{2} a^{2} - 3\) , \( \frac{1}{2} a^{2} + a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -\frac{319}{2} a^{3} - \frac{447}{2} a^{2} + 1339 a + 2112\) , \( -2071 a^{3} - \frac{11387}{2} a^{2} + 5194 a + 14855\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+a-2\right){x}^{2}+\left(-\frac{319}{2}a^{3}-\frac{447}{2}a^{2}+1339a+2112\right){x}-2071a^{3}-\frac{11387}{2}a^{2}+5194a+14855$ |
| 44.3-d2 |
44.3-d |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(a+1), (a^2+a-4)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \) |
$0.589031151$ |
$886.2775173$ |
1.867725211 |
\( \frac{15608075}{44} a^{3} + \frac{6465825}{11} a^{2} - \frac{56603625}{22} a - \frac{93948359}{22} \) |
\( \bigl[\frac{1}{2} a^{2} - 3\) , \( -\frac{1}{2} a^{3} + 4 a - 1\) , \( \frac{1}{2} a^{3} - 3 a\) , \( 2 a^{3} - \frac{9}{2} a^{2} - 13 a + 28\) , \( -\frac{3}{2} a^{3} + \frac{3}{2} a^{2} + 14 a - 20\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-3\right){x}{y}+\left(\frac{1}{2}a^{3}-3a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+4a-1\right){x}^{2}+\left(2a^{3}-\frac{9}{2}a^{2}-13a+28\right){x}-\frac{3}{2}a^{3}+\frac{3}{2}a^{2}+14a-20$ |
| 44.4-a1 |
44.4-a |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(-1/2a^3+3a+1), (a^2+a-4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$121.6466860$ |
2.720102591 |
\( -\frac{186806457187065527217}{644204} a^{3} + \frac{1242268729854976999493}{2576816} a^{2} + \frac{10813953778068508135555}{5153632} a - \frac{17978281963641980467639}{5153632} \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{2} + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -10 a^{3} + 7 a^{2} + 51 a - 44\) , \( \frac{19}{2} a^{3} - 16 a^{2} - 60 a + 151\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+3\right){x}^{2}+\left(-10a^{3}+7a^{2}+51a-44\right){x}+\frac{19}{2}a^{3}-16a^{2}-60a+151$ |
| 44.4-a2 |
44.4-a |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(-1/2a^3+3a+1), (a^2+a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$121.6466860$ |
2.720102591 |
\( \frac{2444850}{11} a^{3} - \frac{6465825}{11} a^{2} - \frac{13730125}{22} a + \frac{35368141}{22} \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{2} + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -3 a^{2} + a + 11\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a^{2} - 2 a + 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+3\right){x}^{2}+\left(-3a^{2}+a+11\right){x}+\frac{1}{2}a^{3}-\frac{5}{2}a^{2}-2a+6$ |
| 44.4-b1 |
44.4-b |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{5} \) |
$12.82671$ |
$(-1/2a^3+3a+1), (a^2+a-4)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4[2] |
|
\( 2 \cdot 5 \) |
$1$ |
$0.401031874$ |
3.181808836 |
\( \frac{180573546428986317635}{10307264} a^{3} - \frac{464347704777436882827}{10307264} a^{2} - \frac{65134388954518111809}{1288408} a + \frac{311720018028907303419}{2576816} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( -\frac{1}{2} a^{2} + a + 3\) , \( \frac{1}{2} a^{2} + a - 3\) , \( -19 a^{3} - \frac{49}{2} a^{2} + 181 a - 143\) , \( 1176 a^{3} - \frac{4693}{2} a^{2} - 8209 a + 14708\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a-2\right){x}{y}+\left(\frac{1}{2}a^{2}+a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+a+3\right){x}^{2}+\left(-19a^{3}-\frac{49}{2}a^{2}+181a-143\right){x}+1176a^{3}-\frac{4693}{2}a^{2}-8209a+14708$ |
| 44.4-b2 |
44.4-b |
$2$ |
$5$ |
4.4.8000.1 |
$4$ |
$[4, 0]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11 \) |
$12.82671$ |
$(-1/2a^3+3a+1), (a^2+a-4)$ |
$0 \le r \le 1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1[2] |
|
\( 2 \) |
$1$ |
$250.6449213$ |
3.181808836 |
\( -\frac{102657698955035}{44} a^{3} + \frac{170669220228365}{44} a^{2} + \frac{371419044029915}{22} a - \frac{617487039616167}{22} \) |
\( \bigl[\frac{1}{2} a^{2} - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( \frac{5}{2} a^{3} + \frac{3}{2} a^{2} - 19 a - 12\) , \( \frac{81}{2} a^{3} + \frac{129}{2} a^{2} - 294 a - 473\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+3\right){x}^{2}+\left(\frac{5}{2}a^{3}+\frac{3}{2}a^{2}-19a-12\right){x}+\frac{81}{2}a^{3}+\frac{129}{2}a^{2}-294a-473$ |
*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.
