| 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 |
$2$ |
$2$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{28} \) |
$7.91094$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$200.6730253$ |
1.491590850 |
\( \frac{52090799555}{14348907} a^{3} - \frac{111328161884}{14348907} a^{2} - \frac{239205084749}{14348907} a + \frac{154844862850}{4782969} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -\frac{61}{3} a^{3} + \frac{124}{3} a^{2} + \frac{286}{3} a - 160\) , \( \frac{257}{3} a^{3} - \frac{542}{3} a^{2} - \frac{1205}{3} a + 700\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-\frac{61}{3}a^{3}+\frac{124}{3}a^{2}+\frac{286}{3}a-160\right){x}+\frac{257}{3}a^{3}-\frac{542}{3}a^{2}-\frac{1205}{3}a+700$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$7.91094$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$401.3460506$ |
1.491590850 |
\( \frac{859306}{6561} a^{3} - \frac{1313461}{6561} a^{2} - \frac{5534131}{6561} a + \frac{1611986}{729} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -\frac{11}{3} a^{3} + \frac{14}{3} a^{2} + \frac{56}{3} a - 15\) , \( -\frac{22}{3} a^{3} + \frac{37}{3} a^{2} + \frac{106}{3} a - 45\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-\frac{11}{3}a^{3}+\frac{14}{3}a^{2}+\frac{56}{3}a-15\right){x}-\frac{22}{3}a^{3}+\frac{37}{3}a^{2}+\frac{106}{3}a-45$ |
| 9.2-a1 |
9.2-a |
$2$ |
$2$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{14} \) |
$7.91094$ |
$(1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$401.3460506$ |
1.491590850 |
\( \frac{2984}{2187} a^{3} + \frac{16489}{243} a^{2} + \frac{76337}{243} a + \frac{108367}{81} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( -a^{2} + a + 5\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -\frac{10}{3} a^{3} - \frac{11}{3} a^{2} + \frac{49}{3} a + 21\) , \( -5 a^{3} - 5 a^{2} + 25 a + 28\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-4\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-\frac{10}{3}a^{3}-\frac{11}{3}a^{2}+\frac{49}{3}a+21\right){x}-5a^{3}-5a^{2}+25a+28$ |
| 9.2-a2 |
9.2-a |
$2$ |
$2$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{28} \) |
$7.91094$ |
$(1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$200.6730253$ |
1.491590850 |
\( \frac{2451598141}{1594323} a^{3} + \frac{12390993020}{4782969} a^{2} - \frac{6379516283}{1594323} a - \frac{1489118393}{531441} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{4}{3} a + 3\) , \( a^{2} - 4\) , \( \frac{2}{3} a^{3} - \frac{32}{3} a^{2} + \frac{16}{3} a + 19\) , \( -\frac{5}{3} a^{3} + \frac{53}{3} a^{2} - \frac{1}{3} a - 25\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{2}{3}a^{2}+\frac{4}{3}a+3\right){x}^{2}+\left(\frac{2}{3}a^{3}-\frac{32}{3}a^{2}+\frac{16}{3}a+19\right){x}-\frac{5}{3}a^{3}+\frac{53}{3}a^{2}-\frac{1}{3}a-25$ |
| 25.1-a1 |
25.1-a |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{10} \) |
$8.98856$ |
$(-a^2+a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$108.7523764$ |
1.616700096 |
\( -\frac{9898}{3} a^{3} + \frac{21718}{3} a^{2} + \frac{16798}{3} a - 11561 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a\) , \( \frac{1}{3} a^{3} - \frac{4}{3} a^{2} - \frac{4}{3} a + 3\) , \( a + 1\) , \( -3 a^{3} - 2 a^{2} + 18 a + 20\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{4}{3} a + 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{4}{3}a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{4}{3}a^{2}-\frac{4}{3}a+3\right){x}^{2}+\left(-3a^{3}-2a^{2}+18a+20\right){x}-\frac{1}{3}a^{3}-\frac{2}{3}a^{2}+\frac{4}{3}a+2$ |
| 25.1-a2 |
25.1-a |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{10} \) |
$8.98856$ |
$(-a^2+a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$108.7523764$ |
1.616700096 |
\( -\frac{11405}{3} a^{3} + \frac{45821}{3} a^{2} - \frac{9907}{3} a - 25798 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( \frac{22}{3} a^{3} - \frac{40}{3} a^{2} - \frac{100}{3} a + 52\) , \( \frac{26}{3} a^{3} - \frac{44}{3} a^{2} - \frac{122}{3} a + 55\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(\frac{22}{3}a^{3}-\frac{40}{3}a^{2}-\frac{100}{3}a+52\right){x}+\frac{26}{3}a^{3}-\frac{44}{3}a^{2}-\frac{122}{3}a+55$ |
| 25.1-b1 |
25.1-b |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{4} \) |
$8.98856$ |
$(-a^2+a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.021477794$ |
$426.2423810$ |
1.633120637 |
\( -\frac{11405}{3} a^{3} + \frac{45821}{3} a^{2} - \frac{9907}{3} a - 25798 \) |
\( \bigl[a^{2} - 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 5\) , \( a\) , \( a^{3} - 6 a^{2} + 5 a + 14\) , \( -\frac{10}{3} a^{3} + \frac{40}{3} a^{2} - \frac{5}{3} a - 23\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-5\right){x}^{2}+\left(a^{3}-6a^{2}+5a+14\right){x}-\frac{10}{3}a^{3}+\frac{40}{3}a^{2}-\frac{5}{3}a-23$ |
| 25.1-b2 |
25.1-b |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{4} \) |
$8.98856$ |
$(-a^2+a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.064433383$ |
$426.2423810$ |
1.633120637 |
\( -\frac{9898}{3} a^{3} + \frac{21718}{3} a^{2} + \frac{16798}{3} a - 11561 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a + 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( -a^{3} - 3 a^{2} + 10 a + 12\) , \( \frac{8}{3} a^{3} - \frac{14}{3} a^{2} - \frac{26}{3} a - 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{4}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{10}{3}a-5\right){x}^{2}+\left(-a^{3}-3a^{2}+10a+12\right){x}+\frac{8}{3}a^{3}-\frac{14}{3}a^{2}-\frac{26}{3}a-2$ |
| 25.2-a1 |
25.2-a |
$12$ |
$24$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{26} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$2.536723725$ |
1.810110619 |
\( \frac{6021271375086041}{29296875} a^{3} - \frac{329116334098622852}{732421875} a^{2} - \frac{696368383757163521}{732421875} a + \frac{433071474158603996}{244140625} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( 0\) , \( -20 a^{3} + 105 a^{2} + 70 a - 564\) , \( -238 a^{3} + 908 a^{2} + 924 a - 4429\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-4\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{10}{3}a-5\right){x}^{2}+\left(-20a^{3}+105a^{2}+70a-564\right){x}-238a^{3}+908a^{2}+924a-4429$ |
| 25.2-a2 |
25.2-a |
$12$ |
$24$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{4} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$649.4012736$ |
1.810110619 |
\( \frac{52709425624671842354}{75} a^{3} + \frac{90696785844887564419}{75} a^{2} - \frac{24441557922375925243}{15} a - \frac{58120569280828197826}{25} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( 0\) , \( -\frac{10}{3} a^{3} + \frac{25}{3} a^{2} - \frac{5}{3} a - 74\) , \( 13 a^{3} - 25 a^{2} + 14 a + 245\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-4\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{10}{3}a-5\right){x}^{2}+\left(-\frac{10}{3}a^{3}+\frac{25}{3}a^{2}-\frac{5}{3}a-74\right){x}+13a^{3}-25a^{2}+14a+245$ |
| 25.2-a3 |
25.2-a |
$12$ |
$24$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{16} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$40.58757960$ |
1.810110619 |
\( -\frac{644587659271686}{15625} a^{3} + \frac{395572907532291}{3125} a^{2} + \frac{421063408509693}{15625} a - \frac{2804698593183502}{15625} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( 0\) , \( \frac{10}{3} a^{3} - \frac{25}{3} a^{2} + \frac{5}{3} a - 14\) , \( \frac{53}{3} a^{3} - \frac{155}{3} a^{2} + \frac{4}{3} a + 31\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-4\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{10}{3}a-5\right){x}^{2}+\left(\frac{10}{3}a^{3}-\frac{25}{3}a^{2}+\frac{5}{3}a-14\right){x}+\frac{53}{3}a^{3}-\frac{155}{3}a^{2}+\frac{4}{3}a+31$ |
| 25.2-a4 |
25.2-a |
$12$ |
$24$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{8} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$649.4012736$ |
1.810110619 |
\( \frac{21721622919}{125} a^{3} + \frac{37406399448}{125} a^{2} - \frac{50372257683}{125} a - \frac{71902341809}{125} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( 0\) , \( -4\) , \( \frac{2}{3} a^{3} - \frac{5}{3} a^{2} + \frac{1}{3} a + 6\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-4\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{10}{3}a-5\right){x}^{2}-4{x}+\frac{2}{3}a^{3}-\frac{5}{3}a^{2}+\frac{1}{3}a+6$ |
| 25.2-a5 |
25.2-a |
$12$ |
$24$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{4} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$649.4012736$ |
1.810110619 |
\( -\frac{193604}{75} a^{3} - \frac{374419}{75} a^{2} + \frac{87493}{15} a + \frac{255651}{25} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-4\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{10}{3}a-5\right){x}^{2}+{x}$ |
| 25.2-a6 |
25.2-a |
$12$ |
$24$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{4} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$649.4012736$ |
1.810110619 |
\( \frac{130054800410127559012}{75} a^{3} - \frac{54692202375937393157}{15} a^{2} - \frac{608849114527317979249}{75} a + \frac{353839298933599467969}{25} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -\frac{20}{3} a^{3} + \frac{5}{3} a^{2} + \frac{125}{3} a - 50\) , \( \frac{73}{3} a^{3} - \frac{52}{3} a^{2} - \frac{445}{3} a + 165\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){y}={x}^{3}+{x}^{2}+\left(-\frac{20}{3}a^{3}+\frac{5}{3}a^{2}+\frac{125}{3}a-50\right){x}+\frac{73}{3}a^{3}-\frac{52}{3}a^{2}-\frac{445}{3}a+165$ |
| 25.2-a7 |
25.2-a |
$12$ |
$24$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{16} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$40.58757960$ |
1.810110619 |
\( -\frac{183851555200156}{3125} a^{3} - \frac{414019102388989}{15625} a^{2} + \frac{5834318332580171}{15625} a + \frac{5704229205357599}{15625} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( \frac{20}{3} a^{3} - \frac{5}{3} a^{2} - \frac{125}{3} a - 40\) , \( 37 a^{3} + 2 a^{2} - 235 a - 209\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){y}={x}^{3}+{x}^{2}+\left(\frac{20}{3}a^{3}-\frac{5}{3}a^{2}-\frac{125}{3}a-40\right){x}+37a^{3}+2a^{2}-235a-209$ |
| 25.2-a8 |
25.2-a |
$12$ |
$24$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{8} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$649.4012736$ |
1.810110619 |
\( \frac{53602375039}{125} a^{3} - \frac{112730397406}{125} a^{2} - \frac{250923734149}{125} a + \frac{87527214224}{25} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -5\) , \( \frac{4}{3} a^{3} - \frac{1}{3} a^{2} - \frac{25}{3} a - 4\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){y}={x}^{3}+{x}^{2}-5{x}+\frac{4}{3}a^{3}-\frac{1}{3}a^{2}-\frac{25}{3}a-4$ |
| 25.2-a9 |
25.2-a |
$12$ |
$24$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{4} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$649.4012736$ |
1.810110619 |
\( -\frac{495262}{75} a^{3} + \frac{212657}{15} a^{2} + \frac{2317999}{75} a - \frac{1371394}{25} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){y}={x}^{3}+{x}^{2}$ |
| 25.2-a10 |
25.2-a |
$12$ |
$24$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{26} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$2.536723725$ |
1.810110619 |
\( \frac{59589852387140609}{732421875} a^{3} + \frac{118994697334331218}{732421875} a^{2} - \frac{28823632660000603}{146484375} a - \frac{74567740514840683}{244140625} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( 5 a^{3} - 90 a^{2} - 10 a + 105\) , \( -19 a^{3} - 736 a^{2} + 114 a + 1008\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){y}={x}^{3}+{x}^{2}+\left(5a^{3}-90a^{2}-10a+105\right){x}-19a^{3}-736a^{2}+114a+1008$ |
| 25.2-a11 |
25.2-a |
$12$ |
$24$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{14} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$2.536723725$ |
1.810110619 |
\( -\frac{51933001703146062336369233}{1875} a^{3} + \frac{159352151378730649585590788}{1875} a^{2} + \frac{33924171594876146468112929}{1875} a - \frac{75322789485234143767597452}{625} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{4}{3} a + 3\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( \frac{31}{3} a^{3} - \frac{142}{3} a^{2} - \frac{19}{3} a + 83\) , \( -\frac{880}{3} a^{3} + \frac{1594}{3} a^{2} + \frac{5065}{3} a - 2676\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{1}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{1}{3}a\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{2}{3}a^{2}+\frac{4}{3}a+3\right){x}^{2}+\left(\frac{31}{3}a^{3}-\frac{142}{3}a^{2}-\frac{19}{3}a+83\right){x}-\frac{880}{3}a^{3}+\frac{1594}{3}a^{2}+\frac{5065}{3}a-2676$ |
| 25.2-a12 |
25.2-a |
$12$ |
$24$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{14} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$2.536723725$ |
1.810110619 |
\( -\frac{74062563550520567545750049}{1875} a^{3} - \frac{33356586125064019703471506}{1875} a^{2} + \frac{470058089419790373060364199}{1875} a + \frac{153192331243755387937872027}{625} \) |
\( \bigl[a + 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a - 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 4\) , \( \frac{28}{3} a^{3} + \frac{77}{3} a^{2} - \frac{214}{3} a - 170\) , \( -\frac{221}{3} a^{3} - \frac{598}{3} a^{2} - \frac{451}{3} a - 122\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{4}{3}a-1\right){x}^{2}+\left(\frac{28}{3}a^{3}+\frac{77}{3}a^{2}-\frac{214}{3}a-170\right){x}-\frac{221}{3}a^{3}-\frac{598}{3}a^{2}-\frac{451}{3}a-122$ |
| 25.2-b1 |
25.2-b |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.013627408$ |
$828.5780201$ |
2.014274375 |
\( -\frac{10846208}{75} a^{3} + \frac{22851584}{75} a^{2} + \frac{50745344}{75} a - \frac{5910528}{5} \) |
\( \bigl[0\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 5\) , \( a^{2} - 3\) , \( -\frac{4}{3} a^{3} + \frac{10}{3} a^{2} + \frac{7}{3} a\) , \( a^{3} - 3 a^{2} - a + 2\bigr] \) |
${y}^2+\left(a^{2}-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-5\right){x}^{2}+\left(-\frac{4}{3}a^{3}+\frac{10}{3}a^{2}+\frac{7}{3}a\right){x}+a^{3}-3a^{2}-a+2$ |
| 25.2-b2 |
25.2-b |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.040882224$ |
$828.5780201$ |
2.014274375 |
\( \frac{6335684608}{15} a^{3} + \frac{2853441536}{15} a^{2} - \frac{40211083264}{15} a - 2620960768 \) |
\( \bigl[0\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + \frac{1}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -a + 1\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a - 1\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+\frac{1}{3}a-4\right){x}^{2}+\left(-a+1\right){x}+\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{4}{3}a-1$ |
| 25.2-c1 |
25.2-c |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.013627408$ |
$828.5780201$ |
2.014274375 |
\( -\frac{4390912}{75} a^{3} - \frac{7614464}{75} a^{2} + \frac{10203136}{75} a + 196608 \) |
\( \bigl[0\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + \frac{1}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( \frac{1}{3} a^{3} - \frac{4}{3} a^{2} - \frac{7}{3} a + 9\) , \( -a^{3} + 2 a^{2} + 3 a - 9\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+\frac{1}{3}a-4\right){x}^{2}+\left(\frac{1}{3}a^{3}-\frac{4}{3}a^{2}-\frac{7}{3}a+9\right){x}-a^{3}+2a^{2}+3a-9$ |
| 25.2-c2 |
25.2-c |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a^2+a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.040882224$ |
$828.5780201$ |
2.014274375 |
\( \frac{4442611712}{15} a^{3} - \frac{13631737856}{15} a^{2} - \frac{2902102016}{15} a + 1288683520 \) |
\( \bigl[0\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{7}{3} a + 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{7}{3} a\) , \( \frac{2}{3} a^{3} + \frac{1}{3} a^{2} - \frac{14}{3} a - 4\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{2}{3}a^{2}+\frac{7}{3}a+3\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+\frac{7}{3}a\right){x}+\frac{2}{3}a^{3}+\frac{1}{3}a^{2}-\frac{14}{3}a-4$ |
| 25.3-a1 |
25.3-a |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{10} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$108.7523764$ |
1.616700096 |
\( -\frac{13556}{3} a^{3} + \frac{1736}{3} a^{2} + \frac{77018}{3} a + 12361 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a\) , \( a^{2} - 5\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( -\frac{7}{3} a^{3} + \frac{19}{3} a^{2} + \frac{13}{3} a - 11\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{4}{3} a - 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{4}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{1}{3}a\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-\frac{7}{3}a^{3}+\frac{19}{3}a^{2}+\frac{13}{3}a-11\right){x}-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+\frac{4}{3}a-2$ |
| 25.3-a2 |
25.3-a |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{10} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$108.7523764$ |
1.616700096 |
\( -\frac{18442}{3} a^{3} - \frac{15974}{3} a^{2} + \frac{129295}{3} a + 47469 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{10}{3} a + 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( 2 a^{3} + 3 a^{2} - a - 2\) , \( \frac{17}{3} a^{3} + \frac{28}{3} a^{2} - \frac{35}{3} a - 17\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{1}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{2}{3}a^{2}+\frac{10}{3}a+3\right){x}^{2}+\left(2a^{3}+3a^{2}-a-2\right){x}+\frac{17}{3}a^{3}+\frac{28}{3}a^{2}-\frac{35}{3}a-17$ |
| 25.3-b1 |
25.3-b |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{4} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.021477794$ |
$426.2423810$ |
1.633120637 |
\( -\frac{18442}{3} a^{3} - \frac{15974}{3} a^{2} + \frac{129295}{3} a + 47469 \) |
\( \bigl[a^{2} - a - 4\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + \frac{1}{3} a - 4\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( 2 a^{2} - 4 a - 3\) , \( -\frac{2}{3} a^{3} + \frac{2}{3} a^{2} + \frac{8}{3} a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{1}{3}a\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}+\frac{1}{3}a-4\right){x}^{2}+\left(2a^{2}-4a-3\right){x}-\frac{2}{3}a^{3}+\frac{2}{3}a^{2}+\frac{8}{3}a-1$ |
| 25.3-b2 |
25.3-b |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{4} \) |
$8.98856$ |
$(-1/3a^3-2/3a^2+4/3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.064433383$ |
$426.2423810$ |
1.633120637 |
\( -\frac{13556}{3} a^{3} + \frac{1736}{3} a^{2} + \frac{77018}{3} a + 12361 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a + 1\) , \( -a^{2} + 2 a + 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{13}{3} a - 3\) , \( \frac{10}{3} a^{3} + \frac{2}{3} a^{2} - \frac{64}{3} a - 21\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{4}{3}a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-4\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{13}{3}a-3\right){x}+\frac{10}{3}a^{3}+\frac{2}{3}a^{2}-\frac{64}{3}a-21$ |
| 45.1-a1 |
45.1-a |
$2$ |
$2$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{4} \cdot 5^{8} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.451118733$ |
$24.99201932$ |
2.681654982 |
\( -\frac{792065426166497}{16875} a^{3} - \frac{356720079831814}{16875} a^{2} + \frac{5027100082617284}{16875} a + \frac{1638332535318959}{5625} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{10}{3} a + 5\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 4\) , \( -\frac{5}{3} a^{3} - \frac{22}{3} a^{2} + \frac{113}{3} a - 15\) , \( \frac{113}{3} a^{3} - \frac{398}{3} a^{2} + \frac{88}{3} a + 138\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{2}{3}a^{2}+\frac{10}{3}a+5\right){x}^{2}+\left(-\frac{5}{3}a^{3}-\frac{22}{3}a^{2}+\frac{113}{3}a-15\right){x}+\frac{113}{3}a^{3}-\frac{398}{3}a^{2}+\frac{88}{3}a+138$ |
| 45.1-a2 |
45.1-a |
$2$ |
$2$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{4} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.902237467$ |
$49.98403864$ |
2.681654982 |
\( \frac{10440094}{225} a^{3} + \frac{33468116}{225} a^{2} - \frac{151088869}{225} a - \frac{15875717}{75} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{4}{3} a + 4\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a + 1\) , \( -\frac{25}{3} a^{3} - \frac{65}{3} a^{2} + \frac{70}{3} a + 42\) , \( -\frac{163}{3} a^{3} - \frac{338}{3} a^{2} + \frac{400}{3} a + 211\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{2}{3}a^{2}+\frac{4}{3}a+4\right){x}^{2}+\left(-\frac{25}{3}a^{3}-\frac{65}{3}a^{2}+\frac{70}{3}a+42\right){x}-\frac{163}{3}a^{3}-\frac{338}{3}a^{2}+\frac{400}{3}a+211$ |
| 45.1-b1 |
45.1-b |
$2$ |
$5$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{10} \cdot 5 \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 5 \) |
$0.015271155$ |
$472.5674111$ |
2.145637649 |
\( \frac{3070199}{3645} a^{3} - \frac{12265811}{3645} a^{2} - \frac{779416}{729} a + \frac{6988984}{1215} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 5\) , \( a\) , \( -\frac{19}{3} a^{3} - \frac{29}{3} a^{2} + \frac{46}{3} a + 22\) , \( \frac{86}{3} a^{3} + \frac{148}{3} a^{2} - \frac{200}{3} a - 96\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-\frac{19}{3}a^{3}-\frac{29}{3}a^{2}+\frac{46}{3}a+22\right){x}+\frac{86}{3}a^{3}+\frac{148}{3}a^{2}-\frac{200}{3}a-96$ |
| 45.1-b2 |
45.1-b |
$2$ |
$5$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{5} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$0.076355779$ |
$472.5674111$ |
2.145637649 |
\( -\frac{523550761}{1125} a^{3} + \frac{1101071989}{1125} a^{2} + \frac{98033836}{45} a - \frac{1424838641}{375} \) |
\( \bigl[1\) , \( -a^{2} + a + 3\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( \frac{14}{3} a^{3} - \frac{44}{3} a^{2} - \frac{8}{3} a + 21\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-a^{3}+2a^{2}+3a-3\right){x}+\frac{14}{3}a^{3}-\frac{44}{3}a^{2}-\frac{8}{3}a+21$ |
| 45.1-c1 |
45.1-c |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{6} \cdot 5^{3} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.007009552$ |
$1579.532167$ |
1.975107543 |
\( \frac{1892084596}{2025} a^{3} + \frac{519269111}{2025} a^{2} - \frac{2617475096}{405} a - \frac{4182618619}{675} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( a - 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 3\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-4\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{10}{3}a-4\right){x}+\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{10}{3}a-3$ |
| 45.1-c2 |
45.1-c |
$2$ |
$3$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5 \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.021028658$ |
$1579.532167$ |
1.975107543 |
\( -\frac{7676362614926}{45} a^{3} + \frac{16140773298014}{45} a^{2} + \frac{7187354966788}{9} a - \frac{20885041232011}{15} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{7}{3} a\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a + 1\) , \( 3 a^{3} - 7 a^{2} + 12\) , \( -\frac{19}{3} a^{3} + \frac{73}{3} a^{2} + \frac{10}{3} a - 33\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{4}{3}a+1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+\frac{7}{3}a\right){x}^{2}+\left(3a^{3}-7a^{2}+12\right){x}-\frac{19}{3}a^{3}+\frac{73}{3}a^{2}+\frac{10}{3}a-33$ |
| 45.2-a1 |
45.2-a |
$2$ |
$2$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( - 3^{4} \cdot 5^{2} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$56.41461516$ |
0.838653064 |
\( \frac{536576594211111125}{3} a^{3} - \frac{16923571210899618562}{45} a^{2} - \frac{12559866426726816242}{15} a + \frac{7299303267583919782}{5} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 4\) , \( a^{2} - a - 4\) , \( -\frac{140}{3} a^{3} - \frac{361}{3} a^{2} + \frac{368}{3} a + 218\) , \( \frac{1922}{3} a^{3} + \frac{3742}{3} a^{2} - \frac{4616}{3} a - 2355\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{10}{3}a-4\right){x}^{2}+\left(-\frac{140}{3}a^{3}-\frac{361}{3}a^{2}+\frac{368}{3}a+218\right){x}+\frac{1922}{3}a^{3}+\frac{3742}{3}a^{2}-\frac{4616}{3}a-2355$ |
| 45.2-a2 |
45.2-a |
$2$ |
$2$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{4} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$112.8292303$ |
0.838653064 |
\( -\frac{10334609816}{75} a^{3} + \frac{21720253496}{75} a^{2} + \frac{16129259167}{25} a - \frac{28098690072}{25} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 3\) , \( a^{2} - a - 4\) , \( -\frac{11}{3} a^{3} + \frac{26}{3} a^{2} + \frac{53}{3} a - 35\) , \( -14 a^{3} + 31 a^{2} + 60 a - 112\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-\frac{11}{3}a^{3}+\frac{26}{3}a^{2}+\frac{53}{3}a-35\right){x}-14a^{3}+31a^{2}+60a-112$ |
| 45.2-b1 |
45.2-b |
$4$ |
$4$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( - 3^{8} \cdot 5^{2} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$16.10591909$ |
1.915429661 |
\( \frac{232330021481019825017}{405} a^{3} - \frac{488511016617812682082}{405} a^{2} - \frac{362549549396455848119}{135} a + \frac{210699622166927331058}{45} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{1}{3} a\) , \( a^{2} - a - 4\) , \( \frac{23}{3} a^{3} + \frac{1}{3} a^{2} - \frac{23}{3} a - 19\) , \( -64 a^{3} - 50 a^{2} + 145 a + 84\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+\frac{1}{3}a\right){x}^{2}+\left(\frac{23}{3}a^{3}+\frac{1}{3}a^{2}-\frac{23}{3}a-19\right){x}-64a^{3}-50a^{2}+145a+84$ |
| 45.2-b2 |
45.2-b |
$4$ |
$4$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1030.778822$ |
1.915429661 |
\( -\frac{28617}{5} a^{3} + \frac{41392}{5} a^{2} + \frac{501511}{15} a - \frac{141777}{5} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{1}{3} a\) , \( a^{2} - a - 4\) , \( -\frac{2}{3} a^{3} - \frac{4}{3} a^{2} + \frac{2}{3} a + 1\) , \( \frac{5}{3} a^{3} + \frac{7}{3} a^{2} - \frac{14}{3} a - 6\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+\frac{1}{3}a\right){x}^{2}+\left(-\frac{2}{3}a^{3}-\frac{4}{3}a^{2}+\frac{2}{3}a+1\right){x}+\frac{5}{3}a^{3}+\frac{7}{3}a^{2}-\frac{14}{3}a-6$ |
| 45.2-b3 |
45.2-b |
$4$ |
$4$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$257.6947055$ |
1.915429661 |
\( \frac{5939483806}{25} a^{3} - \frac{110420098997}{225} a^{2} - \frac{86167121641}{75} a + \frac{49345941574}{25} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{1}{3} a\) , \( a^{2} - a - 4\) , \( a^{3} - 18 a^{2} + 4 a + 26\) , \( -18 a^{3} + 13 a^{2} + 26 a - 13\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+\frac{1}{3}a\right){x}^{2}+\left(a^{3}-18a^{2}+4a+26\right){x}-18a^{3}+13a^{2}+26a-13$ |
| 45.2-b4 |
45.2-b |
$4$ |
$4$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( - 3^{2} \cdot 5^{8} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$64.42367639$ |
1.915429661 |
\( -\frac{2529146615520395663}{1875} a^{3} + \frac{310419149294252894}{75} a^{2} + \frac{550704437439645633}{625} a - \frac{3668233537899864202}{625} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{2}{3} a - 5\) , \( a^{2} - 4\) , \( -\frac{86}{3} a^{3} + \frac{83}{3} a^{2} + \frac{422}{3} a - 71\) , \( -21 a^{3} + 156 a^{2} - 2 a - 852\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{4}{3}a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{2}{3}a-5\right){x}^{2}+\left(-\frac{86}{3}a^{3}+\frac{83}{3}a^{2}+\frac{422}{3}a-71\right){x}-21a^{3}+156a^{2}-2a-852$ |
| 45.2-c1 |
45.2-c |
$4$ |
$6$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5 \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$33.16474289$ |
0.986046370 |
\( -\frac{24435184947482614}{5} a^{3} + \frac{674796229834795304}{45} a^{2} + \frac{9577070261866006}{3} a - \frac{106321195278928257}{5} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( a + 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{2672}{3} a^{3} + \frac{5684}{3} a^{2} + \frac{12470}{3} a - 7391\) , \( -\frac{95620}{3} a^{3} + \frac{200878}{3} a^{2} + \frac{447763}{3} a - 259818\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{1}{3}a\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{2672}{3}a^{3}+\frac{5684}{3}a^{2}+\frac{12470}{3}a-7391\right){x}-\frac{95620}{3}a^{3}+\frac{200878}{3}a^{2}+\frac{447763}{3}a-259818$ |
| 45.2-c2 |
45.2-c |
$4$ |
$6$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$132.6589715$ |
0.986046370 |
\( -\frac{122179692}{5} a^{3} - \frac{359874356}{5} a^{2} + \frac{3806200784}{15} a + 334523697 \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a + 1\) , \( a^{2} - 4\) , \( a + 1\) , \( 10 a^{3} - 28 a^{2} - 7 a + 38\) , \( \frac{160}{3} a^{3} - \frac{481}{3} a^{2} - \frac{109}{3} a + 226\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{1}{3}a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(10a^{3}-28a^{2}-7a+38\right){x}+\frac{160}{3}a^{3}-\frac{481}{3}a^{2}-\frac{109}{3}a+226$ |
| 45.2-c3 |
45.2-c |
$4$ |
$6$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{12} \cdot 5^{3} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$33.16474289$ |
0.986046370 |
\( \frac{2483996508115693}{6075} a^{3} + \frac{12822595317166304}{18225} a^{2} - \frac{230367694085264}{243} a - \frac{2739003641213717}{2025} \) |
\( \bigl[a + 1\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{7}{3} a + 5\) , \( 0\) , \( -\frac{52}{3} a^{3} + \frac{136}{3} a^{2} + \frac{220}{3} a - 196\) , \( -14 a^{3} + 103 a^{2} + 11 a - 542\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{2}{3}a^{2}+\frac{7}{3}a+5\right){x}^{2}+\left(-\frac{52}{3}a^{3}+\frac{136}{3}a^{2}+\frac{220}{3}a-196\right){x}-14a^{3}+103a^{2}+11a-542$ |
| 45.2-c4 |
45.2-c |
$4$ |
$6$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{6} \cdot 5^{6} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$132.6589715$ |
0.986046370 |
\( \frac{447662906}{3375} a^{3} + \frac{85399252}{375} a^{2} - \frac{38409837}{125} a - \frac{10906647}{25} \) |
\( \bigl[a + 1\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{7}{3} a + 5\) , \( 0\) , \( \frac{13}{3} a^{3} - \frac{34}{3} a^{2} - \frac{55}{3} a + 49\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{2}{3}a^{2}+\frac{7}{3}a+5\right){x}^{2}+\left(\frac{13}{3}a^{3}-\frac{34}{3}a^{2}-\frac{55}{3}a+49\right){x}$ |
| 45.2-d1 |
45.2-d |
$4$ |
$10$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{4} \cdot 5^{5} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$4$ |
\( 2 \) |
$1$ |
$63.13748237$ |
1.877188842 |
\( \frac{70040772272117338}{375} a^{3} - \frac{441815725662222436}{1125} a^{2} - \frac{13115783656568171}{15} a + \frac{190559503392886078}{125} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 4\) , \( a^{2} - 3\) , \( -\frac{802}{3} a^{3} + \frac{1705}{3} a^{2} + \frac{3739}{3} a - 2224\) , \( \frac{15641}{3} a^{3} - \frac{32924}{3} a^{2} - \frac{73202}{3} a + 42606\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{10}{3}a-4\right){x}^{2}+\left(-\frac{802}{3}a^{3}+\frac{1705}{3}a^{2}+\frac{3739}{3}a-2224\right){x}+\frac{15641}{3}a^{3}-\frac{32924}{3}a^{2}-\frac{73202}{3}a+42606$ |
| 45.2-d2 |
45.2-d |
$4$ |
$10$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{10} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$252.5499295$ |
1.877188842 |
\( -\frac{41814670676}{9375} a^{3} + \frac{87673588187}{9375} a^{2} + \frac{65324061508}{3125} a - \frac{22663004736}{625} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 4\) , \( a^{2} - 3\) , \( -\frac{47}{3} a^{3} + \frac{110}{3} a^{2} + \frac{209}{3} a - 149\) , \( \frac{217}{3} a^{3} - \frac{514}{3} a^{2} - \frac{979}{3} a + 698\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{10}{3}a-4\right){x}^{2}+\left(-\frac{47}{3}a^{3}+\frac{110}{3}a^{2}+\frac{209}{3}a-149\right){x}+\frac{217}{3}a^{3}-\frac{514}{3}a^{2}-\frac{979}{3}a+698$ |
| 45.2-d3 |
45.2-d |
$4$ |
$10$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{10} \cdot 5^{2} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$252.5499295$ |
1.877188842 |
\( \frac{99371573429}{1215} a^{3} + \frac{173840005372}{1215} a^{2} - \frac{73783101712}{405} a - \frac{7160239820}{27} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{7}{3} a - 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( -\frac{4}{3} a^{3} + \frac{13}{3} a^{2} - \frac{11}{3} a - 4\) , \( -\frac{148}{3} a^{3} + \frac{463}{3} a^{2} + \frac{79}{3} a - 219\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{7}{3}a-1\right){x}^{2}+\left(-\frac{4}{3}a^{3}+\frac{13}{3}a^{2}-\frac{11}{3}a-4\right){x}-\frac{148}{3}a^{3}+\frac{463}{3}a^{2}+\frac{79}{3}a-219$ |
| 45.2-d4 |
45.2-d |
$4$ |
$10$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{20} \cdot 5 \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$4$ |
\( 2 \) |
$1$ |
$63.13748237$ |
1.877188842 |
\( -\frac{3836363817967386527}{98415} a^{3} - \frac{5183509478246153161}{295245} a^{2} + \frac{4869704099184510329}{19683} a + \frac{7935203543902661383}{32805} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{7}{3} a - 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( 67 a^{3} - 209 a^{2} - 32 a + 276\) , \( -893 a^{3} + 2744 a^{2} + 573 a - 3885\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{7}{3}a-1\right){x}^{2}+\left(67a^{3}-209a^{2}-32a+276\right){x}-893a^{3}+2744a^{2}+573a-3885$ |
| 45.2-e1 |
45.2-e |
$4$ |
$6$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{2} \cdot 5^{6} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.036791216$ |
$713.6884716$ |
2.342042562 |
\( \frac{1931183}{375} a^{3} + \frac{817669}{75} a^{2} - \frac{2329624}{375} a - \frac{1645203}{125} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{4}{3} a + 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -\frac{5}{3} a^{3} + \frac{11}{3} a^{2} + \frac{8}{3} a - 3\) , \( -\frac{10}{3} a^{3} + \frac{28}{3} a^{2} + \frac{10}{3} a - 12\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{4}{3}a-4\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+\frac{4}{3}a+1\right){x}^{2}+\left(-\frac{5}{3}a^{3}+\frac{11}{3}a^{2}+\frac{8}{3}a-3\right){x}-\frac{10}{3}a^{3}+\frac{28}{3}a^{2}+\frac{10}{3}a-12$ |
| 45.2-e2 |
45.2-e |
$4$ |
$6$ |
4.4.4525.1 |
$4$ |
$[4, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$9.67385$ |
$(-1/3a^3-2/3a^2+4/3a+1), (1/3a^3-1/3a^2-7/3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.110373648$ |
$713.6884716$ |
2.342042562 |
\( -\frac{233671}{27} a^{3} - \frac{4623217}{135} a^{2} + \frac{4929508}{45} a + \frac{2261782}{15} \) |
\( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{1}{3} a - 3\) , \( \frac{1}{3} a^{3} - \frac{10}{3} a^{2} - \frac{7}{3} a + 9\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{1}{3}a^{2}-\frac{1}{3}a\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{7}{3}a-4\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{1}{3}a^{2}+\frac{1}{3}a-3\right){x}+\frac{1}{3}a^{3}-\frac{10}{3}a^{2}-\frac{7}{3}a+9$ |
*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.
