| 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 |
| 2.1-a1 |
2.1-a |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{10} \) |
$12.00930$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$283.5900128$ |
1.150563631 |
\( -\frac{166049416087}{1024} a^{3} + \frac{66560725625}{1024} a^{2} + \frac{1202221601571}{1024} a + \frac{554274486111}{1024} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 2\) , \( a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - a^{2} - 6 a\) , \( \frac{29}{2} a^{3} + 5 a^{2} - \frac{231}{2} a - 120\) , \( \frac{205}{2} a^{3} - 29 a^{2} - \frac{1505}{2} a - 426\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-2\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a-1\right){x}^{2}+\left(\frac{29}{2}a^{3}+5a^{2}-\frac{231}{2}a-120\right){x}+\frac{205}{2}a^{3}-29a^{2}-\frac{1505}{2}a-426$ |
| 2.1-a2 |
2.1-a |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$12.00930$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$567.1800256$ |
1.150563631 |
\( \frac{98697}{32} a^{3} + \frac{554553}{32} a^{2} + \frac{913955}{32} a + \frac{379807}{32} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 2\) , \( a^{2} - a - 3\) , \( a^{3} - a^{2} - 6 a\) , \( -a^{3} + 2 a^{2} + 5 a - 1\) , \( a^{2} - 2 a - 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{5}{2}a+2\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-a^{3}+2a^{2}+5a-1\right){x}+a^{2}-2a-3$ |
| 2.1-b1 |
2.1-b |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{10} \) |
$12.00930$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.022413034$ |
$995.0078592$ |
1.809576182 |
\( -\frac{166049416087}{1024} a^{3} + \frac{66560725625}{1024} a^{2} + \frac{1202221601571}{1024} a + \frac{554274486111}{1024} \) |
\( \bigl[a^{3} - a^{2} - 6 a + 1\) , \( a^{2} - 4\) , \( a\) , \( -15 a^{3} + 23 a^{2} + 96 a - 61\) , \( \frac{29}{2} a^{3} - 21 a^{2} - \frac{179}{2} a + 58\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-15a^{3}+23a^{2}+96a-61\right){x}+\frac{29}{2}a^{3}-21a^{2}-\frac{179}{2}a+58$ |
| 2.1-b2 |
2.1-b |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$12.00930$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.044826068$ |
$995.0078592$ |
1.809576182 |
\( \frac{98697}{32} a^{3} + \frac{554553}{32} a^{2} + \frac{913955}{32} a + \frac{379807}{32} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( 0\) , \( -\frac{3}{2} a^{3} - 3 a^{2} + \frac{3}{2} a + 3\) , \( -6 a^{3} - 13 a^{2} + 2 a + 4\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-1\right){x}^{2}+\left(-\frac{3}{2}a^{3}-3a^{2}+\frac{3}{2}a+3\right){x}-6a^{3}-13a^{2}+2a+4$ |
| 4.3-a1 |
4.3-a |
$1$ |
$1$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{4} \) |
$13.09623$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.019162982$ |
$1428.446661$ |
2.665373564 |
\( \frac{121311}{2} a^{3} - 194138 a^{2} + \frac{5077}{2} a + 55183 \) |
\( \bigl[a\) , \( -a^{2} + a + 4\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( -2 a^{2} + 2 a + 6\) , \( -a^{3} + a^{2} + 6 a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+3\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-2a^{2}+2a+6\right){x}-a^{3}+a^{2}+6a+1$ |
| 4.3-b1 |
4.3-b |
$1$ |
$1$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{4} \) |
$13.09623$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.031802956$ |
$1467.488140$ |
1.514787770 |
\( \frac{121311}{2} a^{3} - 194138 a^{2} + \frac{5077}{2} a + 55183 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 3\) , \( a^{3} - a^{2} - 5 a\) , \( -\frac{9}{2} a^{3} - 10 a^{2} + \frac{17}{2} a + 7\) , \( \frac{167}{2} a^{3} + 177 a^{2} - \frac{79}{2} a - 53\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+3\right){x}^{2}+\left(-\frac{9}{2}a^{3}-10a^{2}+\frac{17}{2}a+7\right){x}+\frac{167}{2}a^{3}+177a^{2}-\frac{79}{2}a-53$ |
| 8.1-a1 |
8.1-a |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{20} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1.266020615$ |
$11.93280443$ |
2.206508026 |
\( -\frac{260222205249499226295}{4096} a^{3} + \frac{832776833742061973849}{4096} a^{2} - \frac{10764100324864212285}{4096} a - \frac{236538463696945658497}{4096} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( a^{2} - 2 a - 5\) , \( a^{3} - a^{2} - 6 a\) , \( -\frac{1151}{2} a^{3} + 915 a^{2} + \frac{7115}{2} a - 2733\) , \( -14743 a^{3} + 22162 a^{2} + 92256 a - 61356\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-\frac{1151}{2}a^{3}+915a^{2}+\frac{7115}{2}a-2733\right){x}-14743a^{3}+22162a^{2}+92256a-61356$ |
| 8.1-a2 |
8.1-a |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{12} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.422006871$ |
$966.5571593$ |
2.206508026 |
\( -\frac{19362215}{16} a^{3} + \frac{9826489}{16} a^{2} + \frac{134799283}{16} a + \frac{61542111}{16} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( a^{2} - 2 a - 5\) , \( a^{3} - a^{2} - 6 a\) , \( \frac{9}{2} a^{3} + 20 a^{2} - \frac{105}{2} a - 158\) , \( -59 a^{3} - 67 a^{2} + 508 a + 817\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(\frac{9}{2}a^{3}+20a^{2}-\frac{105}{2}a-158\right){x}-59a^{3}-67a^{2}+508a+817$ |
| 8.1-a3 |
8.1-a |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{11} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$5.064082460$ |
$5.966402217$ |
2.206508026 |
\( \frac{365930205158442747799919367}{8} a^{3} - \frac{545488134721715549646714369}{8} a^{2} - \frac{2293846404113302980827034483}{8} a + \frac{1491495422931065288500173097}{8} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 3\) , \( a + 1\) , \( -577 a^{3} + 865 a^{2} + 3617 a - 2387\) , \( -13151 a^{3} + 19629 a^{2} + 82420 a - 53776\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{7}{2}a-3\right){x}^{2}+\left(-577a^{3}+865a^{2}+3617a-2387\right){x}-13151a^{3}+19629a^{2}+82420a-53776$ |
| 8.1-a4 |
8.1-a |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2 \) |
$2.532041230$ |
$23.86560887$ |
2.206508026 |
\( \frac{167536225444761}{64} a^{3} - \frac{249738954540631}{64} a^{2} - \frac{1050226944880333}{64} a + \frac{682871449539503}{64} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 3\) , \( a + 1\) , \( -\frac{59}{2} a^{3} + 50 a^{2} + \frac{369}{2} a - 162\) , \( -\frac{295}{2} a^{3} + 241 a^{2} + \frac{1823}{2} a - 747\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{7}{2}a-3\right){x}^{2}+\left(-\frac{59}{2}a^{3}+50a^{2}+\frac{369}{2}a-162\right){x}-\frac{295}{2}a^{3}+241a^{2}+\frac{1823}{2}a-747$ |
| 8.1-a5 |
8.1-a |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1.688027486$ |
$483.2785796$ |
2.206508026 |
\( \frac{686358549}{2} a^{3} + \frac{712933371}{2} a^{2} - \frac{1522892961}{2} a + \frac{508888501}{2} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 3\) , \( a + 1\) , \( -7 a^{3} + 10 a^{2} + 47 a - 22\) , \( -10 a^{3} + 15 a^{2} + 65 a - 36\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{7}{2}a-3\right){x}^{2}+\left(-7a^{3}+10a^{2}+47a-22\right){x}-10a^{3}+15a^{2}+65a-36$ |
| 8.1-a6 |
8.1-a |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.844013743$ |
$1933.114318$ |
2.206508026 |
\( \frac{22809}{4} a^{3} - \frac{2951}{4} a^{2} - \frac{90749}{4} a + \frac{65679}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 3\) , \( a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a + 3\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{1}{2} a - 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{7}{2}a-3\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a+3\right){x}+\frac{1}{2}a^{3}+a^{2}-\frac{1}{2}a-1$ |
| 8.1-a7 |
8.1-a |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{11} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$5.064082460$ |
$5.966402217$ |
2.206508026 |
\( -\frac{7653745985823}{8} a^{3} + \frac{3068262626545}{8} a^{2} + \frac{55415265489995}{8} a + \frac{25548605750567}{8} \) |
\( \bigl[a + 1\) , \( a^{3} - a^{2} - 7 a + 1\) , \( a^{3} - a^{2} - 6 a\) , \( -527 a^{3} + 800 a^{2} + 3292 a - 2249\) , \( -13236 a^{3} + 19779 a^{2} + 82929 a - 54281\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a+1\right){x}^{2}+\left(-527a^{3}+800a^{2}+3292a-2249\right){x}-13236a^{3}+19779a^{2}+82929a-54281$ |
| 8.1-a8 |
8.1-a |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1.688027486$ |
$483.2785796$ |
2.206508026 |
\( -\frac{5327}{2} a^{3} + \frac{2657}{2} a^{2} + \frac{38267}{2} a + \frac{17527}{2} \) |
\( \bigl[a + 1\) , \( a^{3} - a^{2} - 7 a + 1\) , \( a^{3} - a^{2} - 6 a\) , \( 3 a^{3} - 5 a^{2} - 18 a + 16\) , \( -56 a^{3} + 84 a^{2} + 351 a - 232\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a+1\right){x}^{2}+\left(3a^{3}-5a^{2}-18a+16\right){x}-56a^{3}+84a^{2}+351a-232$ |
| 8.1-b1 |
8.1-b |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{20} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$34.11885164$ |
2.491647610 |
\( -\frac{260222205249499226295}{4096} a^{3} + \frac{832776833742061973849}{4096} a^{2} - \frac{10764100324864212285}{4096} a - \frac{236538463696945658497}{4096} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( a\) , \( 0\) , \( 10 a^{3} + 13 a^{2} - 79 a - 130\) , \( 5 a^{3} - 72 a^{2} - 29 a + 338\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}={x}^{3}+a{x}^{2}+\left(10a^{3}+13a^{2}-79a-130\right){x}+5a^{3}-72a^{2}-29a+338$ |
| 8.1-b2 |
8.1-b |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$272.9508131$ |
2.491647610 |
\( \frac{167536225444761}{64} a^{3} - \frac{249738954540631}{64} a^{2} - \frac{1050226944880333}{64} a + \frac{682871449539503}{64} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -a^{2} + 5\) , \( a + 1\) , \( -\frac{167}{2} a^{3} - 176 a^{2} + \frac{87}{2} a + 57\) , \( -\frac{4019}{2} a^{3} - 4204 a^{2} + \frac{2139}{2} a + 1300\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-\frac{167}{2}a^{3}-176a^{2}+\frac{87}{2}a+57\right){x}-\frac{4019}{2}a^{3}-4204a^{2}+\frac{2139}{2}a+1300$ |
| 8.1-b3 |
8.1-b |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{11} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3^{2} \) |
$1$ |
$136.4754065$ |
2.491647610 |
\( \frac{365930205158442747799919367}{8} a^{3} - \frac{545488134721715549646714369}{8} a^{2} - \frac{2293846404113302980827034483}{8} a + \frac{1491495422931065288500173097}{8} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -a^{2} + 5\) , \( a + 1\) , \( -221 a^{3} - 421 a^{2} + 186 a + 92\) , \( 5205 a^{3} + 10808 a^{2} - 2894 a - 3249\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-221a^{3}-421a^{2}+186a+92\right){x}+5205a^{3}+10808a^{2}-2894a-3249$ |
| 8.1-b4 |
8.1-b |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{11} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3^{2} \) |
$1$ |
$136.4754065$ |
2.491647610 |
\( -\frac{7653745985823}{8} a^{3} + \frac{3068262626545}{8} a^{2} + \frac{55415265489995}{8} a + \frac{25548605750567}{8} \) |
\( \bigl[a + 1\) , \( a^{2} - 5\) , \( a + 1\) , \( -9 a^{3} + 4 a^{2} + 26 a - 59\) , \( -9 a^{3} - 159 a^{2} - 152 a + 339\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-9a^{3}+4a^{2}+26a-59\right){x}-9a^{3}-159a^{2}-152a+339$ |
| 8.1-b5 |
8.1-b |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1228.278659$ |
2.491647610 |
\( -\frac{5327}{2} a^{3} + \frac{2657}{2} a^{2} + \frac{38267}{2} a + \frac{17527}{2} \) |
\( \bigl[a + 1\) , \( a^{2} - 5\) , \( a + 1\) , \( a^{3} - a^{2} - 4 a + 6\) , \( a^{2} + a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(a^{3}-a^{2}-4a+6\right){x}+a^{2}+a-3$ |
| 8.1-b6 |
8.1-b |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1$ |
$2456.557318$ |
2.491647610 |
\( \frac{22809}{4} a^{3} - \frac{2951}{4} a^{2} - \frac{90749}{4} a + \frac{65679}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( a + 1\) , \( a + 1\) , \( -\frac{3}{2} a^{3} + \frac{9}{2} a - 2\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{3}{2} a\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{3}{2}a^{3}+\frac{9}{2}a-2\right){x}+\frac{1}{2}a^{3}+a^{2}-\frac{3}{2}a$ |
| 8.1-b7 |
8.1-b |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{12} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$307.0696648$ |
2.491647610 |
\( -\frac{19362215}{16} a^{3} + \frac{9826489}{16} a^{2} + \frac{134799283}{16} a + \frac{61542111}{16} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( -a^{2} + a + 4\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( -\frac{63}{2} a^{3} + 46 a^{2} + \frac{393}{2} a - 120\) , \( -\frac{333}{2} a^{3} + 248 a^{2} + \frac{2087}{2} a - 678\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-\frac{63}{2}a^{3}+46a^{2}+\frac{393}{2}a-120\right){x}-\frac{333}{2}a^{3}+248a^{2}+\frac{2087}{2}a-678$ |
| 8.1-b8 |
8.1-b |
$8$ |
$12$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1228.278659$ |
2.491647610 |
\( \frac{686358549}{2} a^{3} + \frac{712933371}{2} a^{2} - \frac{1522892961}{2} a + \frac{508888501}{2} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( -a^{2} + 5\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( -296 a^{3} + 122 a^{2} + 2140 a + 965\) , \( 5869 a^{3} - 2354 a^{2} - 42492 a - 19581\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-296a^{3}+122a^{2}+2140a+965\right){x}+5869a^{3}-2354a^{2}-42492a-19581$ |
| 8.3-a1 |
8.3-a |
$2$ |
$3$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{28} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$4.989983237$ |
2.915286818 |
\( \frac{4899241543}{512} a^{3} - \frac{818402245813}{256} a^{2} + \frac{175830205315}{512} a + \frac{240479752573}{256} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( \frac{157}{2} a^{3} - 153 a^{2} - \frac{491}{2} a - 74\) , \( 321 a^{3} - 1478 a^{2} + 1192 a + 977\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(\frac{157}{2}a^{3}-153a^{2}-\frac{491}{2}a-74\right){x}+321a^{3}-1478a^{2}+1192a+977$ |
| 8.3-a2 |
8.3-a |
$2$ |
$3$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{12} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$1$ |
$44.90984913$ |
2.915286818 |
\( -\frac{207330423}{16} a^{3} + \frac{154529819}{8} a^{2} + \frac{1299661367}{16} a - \frac{422526687}{8} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( -\frac{3}{2} a^{3} + 2 a^{2} + \frac{29}{2} a + 6\) , \( -3 a^{3} + 2 a^{2} + 27 a + 11\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-\frac{3}{2}a^{3}+2a^{2}+\frac{29}{2}a+6\right){x}-3a^{3}+2a^{2}+27a+11$ |
| 8.3-b1 |
8.3-b |
$2$ |
$3$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{28} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1.596737402$ |
$2.331103321$ |
2.174589185 |
\( \frac{4899241543}{512} a^{3} - \frac{818402245813}{256} a^{2} + \frac{175830205315}{512} a + \frac{240479752573}{256} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( a^{3} - a^{2} - 5 a\) , \( \frac{229}{2} a^{3} - 388 a^{2} + \frac{29}{2} a + 112\) , \( 2783 a^{3} - 8994 a^{2} + 127 a + 2558\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+2\right){x}^{2}+\left(\frac{229}{2}a^{3}-388a^{2}+\frac{29}{2}a+112\right){x}+2783a^{3}-8994a^{2}+127a+2558$ |
| 8.3-b2 |
8.3-b |
$2$ |
$3$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{12} \) |
$14.28154$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.532245800$ |
$188.8193690$ |
2.174589185 |
\( -\frac{207330423}{16} a^{3} + \frac{154529819}{8} a^{2} + \frac{1299661367}{16} a - \frac{422526687}{8} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( a^{3} - a^{2} - 7 a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 3\) , \( -\frac{1}{2} a^{3} - 2 a^{2} + \frac{1}{2} a + 6\) , \( -5 a^{2} - 11 a\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+3\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{5}{2}a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a\right){x}^{2}+\left(-\frac{1}{2}a^{3}-2a^{2}+\frac{1}{2}a+6\right){x}-5a^{2}-11a$ |
| 8.4-a1 |
8.4-a |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{4} \) |
$14.28154$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$898.4478466$ |
3.645126311 |
\( 179051744 a^{3} - 266958512 a^{2} - 1122348032 a + 730122176 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 3\) , \( a^{3} - a^{2} - 5 a\) , \( \frac{25}{2} a^{3} - 14 a^{2} - \frac{131}{2} a - 27\) , \( -50 a^{3} + 69 a^{2} + 236 a + 92\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-1\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-3\right){x}^{2}+\left(\frac{25}{2}a^{3}-14a^{2}-\frac{131}{2}a-27\right){x}-50a^{3}+69a^{2}+236a+92$ |
| 8.4-a2 |
8.4-a |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$14.28154$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$898.4478466$ |
3.645126311 |
\( -1198320 a^{3} + 3833872 a^{2} - 18512 a - 1107600 \) |
\( \bigl[0\) , \( -a^{2} + a + 3\) , \( a^{3} - a^{2} - 5 a\) , \( -21 a^{3} - 64 a^{2} + 15 a + 22\) , \( \frac{657}{2} a^{3} + 798 a^{2} - \frac{375}{2} a - 246\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-21a^{3}-64a^{2}+15a+22\right){x}+\frac{657}{2}a^{3}+798a^{2}-\frac{375}{2}a-246$ |
| 8.4-b1 |
8.4-b |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{8} \) |
$14.28154$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.029415229$ |
$1476.689635$ |
1.409844350 |
\( -1198320 a^{3} + 3833872 a^{2} - 18512 a - 1107600 \) |
\( \bigl[0\) , \( a^{3} - a^{2} - 6 a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( 2 a^{3} - 6 a^{2} - 4 a + 4\) , \( -\frac{7}{2} a^{3} + 13 a^{2} - \frac{9}{2} a - 7\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a+1\right){x}^{2}+\left(2a^{3}-6a^{2}-4a+4\right){x}-\frac{7}{2}a^{3}+13a^{2}-\frac{9}{2}a-7$ |
| 8.4-b2 |
8.4-b |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{4} \) |
$14.28154$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.058830459$ |
$1476.689635$ |
1.409844350 |
\( 179051744 a^{3} - 266958512 a^{2} - 1122348032 a + 730122176 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 3\) , \( -a + 1\) , \( a\) , \( \frac{21}{2} a^{3} - 33 a^{2} - \frac{19}{2} a + 15\) , \( -\frac{105}{2} a^{3} + 169 a^{2} - \frac{15}{2} a - 45\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{5}{2}a+3\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(\frac{21}{2}a^{3}-33a^{2}-\frac{19}{2}a+15\right){x}-\frac{105}{2}a^{3}+169a^{2}-\frac{15}{2}a-45$ |
| 11.1-a1 |
11.1-a |
$1$ |
$1$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{5} \) |
$14.86151$ |
$(1/2a^3-a^2-5/2a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$424.4434513$ |
3.444050755 |
\( -\frac{62950025343}{322102} a^{3} - \frac{161013341310}{161051} a^{2} + \frac{43788411071}{322102} a + \frac{43604724509}{161051} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( a^{2} - a - 3\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( -2 a^{3} + 8 a^{2} + 20 a - 34\) , \( \frac{39}{2} a^{3} - 36 a^{2} - \frac{177}{2} a + 114\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-2a^{3}+8a^{2}+20a-34\right){x}+\frac{39}{2}a^{3}-36a^{2}-\frac{177}{2}a+114$ |
| 11.1-b1 |
11.1-b |
$1$ |
$1$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{5} \) |
$14.86151$ |
$(1/2a^3-a^2-5/2a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$40.49938616$ |
0.328623144 |
\( -\frac{62950025343}{322102} a^{3} - \frac{161013341310}{161051} a^{2} + \frac{43788411071}{322102} a + \frac{43604724509}{161051} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( -a^{2} - 5 a - 7\) , \( 2 a^{3} + a^{2} - 9 a - 6\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+3\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{5}{2}a-3\right){x}^{2}+\left(-a^{2}-5a-7\right){x}+2a^{3}+a^{2}-9a-6$ |
| 16.1-a1 |
16.1-a |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$15.57413$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.033207772$ |
$1535.098023$ |
4.963714621 |
\( \frac{1143241}{64} a^{3} - \frac{5225831}{64} a^{2} - \frac{4098301}{64} a + \frac{28883711}{64} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( 0\) , \( -\frac{3}{2} a^{3} + 3 a^{2} + \frac{11}{2} a - 1\) , \( -2 a^{3} + 2 a^{2} + 11 a + 6\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-3\right){x}^{2}+\left(-\frac{3}{2}a^{3}+3a^{2}+\frac{11}{2}a-1\right){x}-2a^{3}+2a^{2}+11a+6$ |
| 16.1-a2 |
16.1-a |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{11} \) |
$15.57413$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.066415544$ |
$1535.098023$ |
4.963714621 |
\( -\frac{1519}{8} a^{3} + \frac{2697}{8} a^{2} + \frac{14283}{8} a + \frac{4735}{8} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 3\) , \( -\frac{3}{2} a^{3} + a^{2} + \frac{17}{2} a - 1\) , \( -a^{3} + 2 a^{2} + 5 a - 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{5}{2}a+3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{9}{2}a+1\right){x}^{2}+\left(-\frac{3}{2}a^{3}+a^{2}+\frac{17}{2}a-1\right){x}-a^{3}+2a^{2}+5a-2$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$15.57413$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3^{2} \) |
$1$ |
$23.69923422$ |
1.730718868 |
\( -\frac{3863845489}{512} a^{3} - \frac{3635737601}{512} a^{2} + \frac{9179446149}{512} a - \frac{3363551383}{512} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 3\) , \( 0\) , \( -\frac{9}{2} a^{3} + \frac{51}{2} a + 11\) , \( 10 a^{3} - 17 a^{2} - 108 a - 48\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-3\right){x}^{2}+\left(-\frac{9}{2}a^{3}+\frac{51}{2}a+11\right){x}+10a^{3}-17a^{2}-108a-48$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$15.57413$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$177.9423156$ |
1.443872828 |
\( -\frac{3863845489}{512} a^{3} - \frac{3635737601}{512} a^{2} + \frac{9179446149}{512} a - \frac{3363551383}{512} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( -a^{3} + a^{2} + 5 a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( -\frac{29}{2} a^{3} + 16 a^{2} + \frac{185}{2} a - 11\) , \( -\frac{51}{2} a^{3} - 10 a^{2} + \frac{397}{2} a + 233\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-\frac{29}{2}a^{3}+16a^{2}+\frac{185}{2}a-11\right){x}-\frac{51}{2}a^{3}-10a^{2}+\frac{397}{2}a+233$ |
| 16.1-d1 |
16.1-d |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{11} \) |
$15.57413$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.089729601$ |
$722.5052376$ |
2.104197186 |
\( -\frac{1519}{8} a^{3} + \frac{2697}{8} a^{2} + \frac{14283}{8} a + \frac{4735}{8} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( a^{2} - a - 5\) , \( a^{3} - a^{2} - 6 a\) , \( \frac{15}{2} a^{3} - 3 a^{2} - \frac{103}{2} a - 17\) , \( -3 a^{3} + 3 a^{2} + 23 a + 6\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(\frac{15}{2}a^{3}-3a^{2}-\frac{103}{2}a-17\right){x}-3a^{3}+3a^{2}+23a+6$ |
| 16.1-d2 |
16.1-d |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$15.57413$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.179459202$ |
$361.2526188$ |
2.104197186 |
\( \frac{1143241}{64} a^{3} - \frac{5225831}{64} a^{2} - \frac{4098301}{64} a + \frac{28883711}{64} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 3\) , \( 3 a^{2} + 4 a\) , \( \frac{5}{2} a^{3} + 8 a^{2} + \frac{5}{2} a - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{5}{2}a+3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{3}{2}a-2\right){x}^{2}+\left(3a^{2}+4a\right){x}+\frac{5}{2}a^{3}+8a^{2}+\frac{5}{2}a-5$ |
| 16.4-a1 |
16.4-a |
$1$ |
$1$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{12} \) |
$15.57413$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$387.2323713$ |
3.142109831 |
\( \frac{7139}{2} a^{3} - \frac{4057}{2} a^{2} - 27495 a - 12590 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( a\) , \( -2 a + 1\) , \( -2 a^{3} + a^{2} + 13 a + 7\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+3\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-3\right){x}^{2}+\left(-2a+1\right){x}-2a^{3}+a^{2}+13a+7$ |
| 16.4-b1 |
16.4-b |
$1$ |
$1$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{18} \) |
$15.57413$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 7 \) |
$0.008990953$ |
$604.8271455$ |
4.942023011 |
\( -\frac{12345}{64} a^{3} - \frac{34549}{32} a^{2} - \frac{131247}{64} a - \frac{24641}{32} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - a^{2} - 6 a\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( a^{3} - 8 a\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a\right){x}^{2}+\left(a^{3}-8a\right){x}+\frac{1}{2}a^{3}-\frac{7}{2}a$ |
| 16.4-c1 |
16.4-c |
$1$ |
$1$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{18} \) |
$15.57413$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.042764895$ |
$422.2824574$ |
2.344553474 |
\( -\frac{12345}{64} a^{3} - \frac{34549}{32} a^{2} - \frac{131247}{64} a - \frac{24641}{32} \) |
\( \bigl[a\) , \( a^{2} - 3\) , \( a\) , \( -\frac{1}{2} a^{3} + 4 a^{2} - \frac{1}{2} a\) , \( -\frac{1}{2} a^{3} + 9 a^{2} - \frac{35}{2} a + 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-\frac{1}{2}a^{3}+4a^{2}-\frac{1}{2}a\right){x}-\frac{1}{2}a^{3}+9a^{2}-\frac{35}{2}a+7$ |
| 16.4-d1 |
16.4-d |
$1$ |
$1$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.4 |
\( 2^{4} \) |
\( 2^{12} \) |
$15.57413$ |
$(-a), (-1/2a^3+a^2+7/2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$63.81388331$ |
0.517803378 |
\( \frac{7139}{2} a^{3} - \frac{4057}{2} a^{2} - 27495 a - 12590 \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a + 2\) , \( a - 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a+2\right){x}+a-1$ |
| 16.5-a1 |
16.5-a |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{4} \) |
$15.57413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1302.094838$ |
2.641388798 |
\( -2048 a^{3} + 6144 a^{2} + 2048 a - 2048 \) |
\( \bigl[0\) , \( a^{2} - a - 5\) , \( a\) , \( -2 a^{3} - 5 a^{2} + 4 a + 9\) , \( -4 a^{3} - 10 a^{2} - 1\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-2a^{3}-5a^{2}+4a+9\right){x}-4a^{3}-10a^{2}-1$ |
| 16.5-a2 |
16.5-a |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.5 |
\( 2^{4} \) |
\( - 2^{8} \) |
$15.57413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$651.0474192$ |
2.641388798 |
\( 643088 a^{3} - 761888 a^{2} - 3715120 a + 2364144 \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( 2 a^{3} + 8 a^{2} - 24 a - 62\) , \( -\frac{19}{2} a^{3} - 9 a^{2} + \frac{159}{2} a + 112\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{5}{2}a+3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+1\right){x}^{2}+\left(2a^{3}+8a^{2}-24a-62\right){x}-\frac{19}{2}a^{3}-9a^{2}+\frac{159}{2}a+112$ |
| 16.5-b1 |
16.5-b |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.5 |
\( 2^{4} \) |
\( - 2^{8} \) |
$15.57413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$220.3550400$ |
0.894010662 |
\( 643088 a^{3} - 761888 a^{2} - 3715120 a + 2364144 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( a^{2} - 2 a - 5\) , \( a\) , \( -14 a^{3} + 20 a^{2} + 85 a - 50\) , \( -33 a^{3} + 49 a^{2} + 205 a - 135\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-14a^{3}+20a^{2}+85a-50\right){x}-33a^{3}+49a^{2}+205a-135$ |
| 16.5-b2 |
16.5-b |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
16.5 |
\( 2^{4} \) |
\( 2^{4} \) |
$15.57413$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$440.7100800$ |
0.894010662 |
\( -2048 a^{3} + 6144 a^{2} + 2048 a - 2048 \) |
\( \bigl[0\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -2 a^{3} + a^{2} + 15 a + 8\) , \( 4 a^{3} - 2 a^{2} - 30 a - 14\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-3\right){x}^{2}+\left(-2a^{3}+a^{2}+15a+8\right){x}+4a^{3}-2a^{2}-30a-14$ |
| 22.4-a1 |
22.4-a |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
22.4 |
\( 2 \cdot 11 \) |
\( - 2^{2} \cdot 11^{3} \) |
$16.20659$ |
$(-a), (a^3-a^2-6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$149.5348082$ |
0.606683254 |
\( \frac{189111891}{5324} a^{3} - \frac{281935869}{5324} a^{2} - \frac{1185222543}{5324} a + \frac{770863045}{5324} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( a^{2} - 2 a - 3\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -103 a^{3} + 154 a^{2} + 641 a - 405\) , \( -\frac{2003}{2} a^{3} + 1514 a^{2} + \frac{12511}{2} a - 4204\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-103a^{3}+154a^{2}+641a-405\right){x}-\frac{2003}{2}a^{3}+1514a^{2}+\frac{12511}{2}a-4204$ |
| 22.4-a2 |
22.4-a |
$2$ |
$2$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
22.4 |
\( 2 \cdot 11 \) |
\( - 2 \cdot 11^{6} \) |
$16.20659$ |
$(-a), (a^3-a^2-6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$149.5348082$ |
0.606683254 |
\( -\frac{53454532491}{3543122} a^{3} + \frac{151958055781}{3543122} a^{2} + \frac{60060076519}{3543122} a - \frac{13656922445}{3543122} \) |
\( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a\) , \( \frac{13}{2} a^{3} - 3 a^{2} - \frac{93}{2} a - 21\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{9}{2}a+3\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a\right){x}+\frac{13}{2}a^{3}-3a^{2}-\frac{93}{2}a-21$ |
| 22.4-b1 |
22.4-b |
$4$ |
$10$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
22.4 |
\( 2 \cdot 11 \) |
\( 2 \cdot 11^{10} \) |
$16.20659$ |
$(-a), (a^3-a^2-6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2 \cdot 5 \) |
$1$ |
$1.651155725$ |
0.837370694 |
\( \frac{187499602602273530053}{51874849202} a^{3} + \frac{355276479057317508245}{51874849202} a^{2} - \frac{198948540284330300265}{51874849202} a - \frac{160488796817973451293}{51874849202} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( -a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( -11 a^{3} - 39 a^{2} + 15 a - 11\) , \( -\frac{273}{2} a^{3} - 409 a^{2} + \frac{227}{2} a + 68\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+3\right){y}={x}^{3}-a{x}^{2}+\left(-11a^{3}-39a^{2}+15a-11\right){x}-\frac{273}{2}a^{3}-409a^{2}+\frac{227}{2}a+68$ |
| 22.4-b2 |
22.4-b |
$4$ |
$10$ |
4.4.15188.1 |
$4$ |
$[4, 0]$ |
22.4 |
\( 2 \cdot 11 \) |
\( 2^{5} \cdot 11^{2} \) |
$16.20659$ |
$(-a), (a^3-a^2-6a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1031.972328$ |
0.837370694 |
\( \frac{120606869}{3872} a^{3} - \frac{179078811}{3872} a^{2} - \frac{754602873}{3872} a + \frac{491846803}{3872} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( -a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+3\right){y}={x}^{3}-a{x}^{2}+\left(-a^{3}+a^{2}+5a-1\right){x}-\frac{1}{2}a^{3}+a^{2}+\frac{3}{2}a-2$ |
*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.
