| 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 |
| 7.1-a1 |
7.1-a |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$11.56854$ |
$(1/2a^3-5/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.060619827$ |
$869.2993445$ |
1.038271940 |
\( \frac{2548864}{7} a^{3} - \frac{6864896}{7} a^{2} - \frac{13090688}{7} a + 4211008 \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 1\) , \( 1\) , \( \frac{11}{2} a^{3} - a^{2} - \frac{83}{2} a - 25\) , \( \frac{25}{2} a^{3} - \frac{7}{2} a^{2} - 96 a - 61\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-1\right){x}^{2}+\left(\frac{11}{2}a^{3}-a^{2}-\frac{83}{2}a-25\right){x}+\frac{25}{2}a^{3}-\frac{7}{2}a^{2}-96a-61$ |
| 7.1-a2 |
7.1-a |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$11.56854$ |
$(1/2a^3-5/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.121239654$ |
$869.2993445$ |
1.038271940 |
\( -\frac{1076352}{7} a^{3} + \frac{461824}{7} a^{2} + \frac{8449920}{7} a + \frac{5260480}{7} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{53}{2} a^{3} + \frac{139}{2} a^{2} + 136 a - 292\) , \( \frac{575}{2} a^{3} - \frac{1553}{2} a^{2} - 1476 a + 3333\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{9}{2}a\right){x}^{2}+\left(-\frac{53}{2}a^{3}+\frac{139}{2}a^{2}+136a-292\right){x}+\frac{575}{2}a^{3}-\frac{1553}{2}a^{2}-1476a+3333$ |
| 7.1-b1 |
7.1-b |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$11.56854$ |
$(1/2a^3-5/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$824.9059406$ |
2.031615487 |
\( \frac{1076352}{7} a^{3} - \frac{2767232}{7} a^{2} - \frac{6144512}{7} a + \frac{13095872}{7} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -a - 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} + 2 a + 4\) , \( 4 a^{3} - 17 a^{2} + 8 a + 15\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(\frac{3}{2}a^{3}-\frac{11}{2}a^{2}+2a+4\right){x}+4a^{3}-17a^{2}+8a+15$ |
| 7.1-b2 |
7.1-b |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$11.56854$ |
$(1/2a^3-5/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$412.4529703$ |
2.031615487 |
\( -\frac{2548864}{7} a^{3} + \frac{781696}{7} a^{2} + \frac{19173888}{7} a + \frac{12070336}{7} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( a^{3} - a^{2} - 6 a - 3\) , \( 2 a^{3} - \frac{7}{2} a^{2} - \frac{21}{2} a - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+a{x}^{2}+\left(a^{3}-a^{2}-6a-3\right){x}+2a^{3}-\frac{7}{2}a^{2}-\frac{21}{2}a-5$ |
| 7.1-c1 |
7.1-c |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$11.56854$ |
$(1/2a^3-5/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.121239654$ |
$869.2993445$ |
1.038271940 |
\( \frac{1076352}{7} a^{3} - \frac{2767232}{7} a^{2} - \frac{6144512}{7} a + \frac{13095872}{7} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} - 2 a^{2} - \frac{9}{2} a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 6 a + 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{5}{2}a-3\right){x}^{2}+\left(\frac{1}{2}a^{3}-2a^{2}-\frac{9}{2}a+2\right){x}-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+6a+2$ |
| 7.1-c2 |
7.1-c |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$11.56854$ |
$(1/2a^3-5/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.060619827$ |
$869.2993445$ |
1.038271940 |
\( -\frac{2548864}{7} a^{3} + \frac{781696}{7} a^{2} + \frac{19173888}{7} a + \frac{12070336}{7} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{9}{2} a^{3} + \frac{27}{2} a^{2} + 24 a - 57\) , \( -\frac{35}{2} a^{3} + \frac{97}{2} a^{2} + 91 a - 208\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+4\right){x}^{2}+\left(-\frac{9}{2}a^{3}+\frac{27}{2}a^{2}+24a-57\right){x}-\frac{35}{2}a^{3}+\frac{97}{2}a^{2}+91a-208$ |
| 7.1-d1 |
7.1-d |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$11.56854$ |
$(1/2a^3-5/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$412.4529703$ |
2.031615487 |
\( \frac{2548864}{7} a^{3} - \frac{6864896}{7} a^{2} - \frac{13090688}{7} a + 4211008 \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 7\) , \( -\frac{5}{2} a^{3} + \frac{7}{2} a^{2} + 11 a - 17\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a^{3}+2a^{2}+3a-7\right){x}-\frac{5}{2}a^{3}+\frac{7}{2}a^{2}+11a-17$ |
| 7.1-d2 |
7.1-d |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$11.56854$ |
$(1/2a^3-5/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$824.9059406$ |
2.031615487 |
\( -\frac{1076352}{7} a^{3} + \frac{461824}{7} a^{2} + \frac{8449920}{7} a + \frac{5260480}{7} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( a + 1\) , \( 1\) , \( -\frac{3}{2} a^{3} - a^{2} + \frac{13}{2} a + 3\) , \( -\frac{11}{2} a^{3} - \frac{11}{2} a^{2} + 19 a + 11\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-\frac{3}{2}a^{3}-a^{2}+\frac{13}{2}a+3\right){x}-\frac{11}{2}a^{3}-\frac{11}{2}a^{2}+19a+11$ |
| 8.1-a1 |
8.1-a |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{16} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$439.9595193$ |
2.167104221 |
\( 40 a^{3} + \frac{3281}{16} a^{2} - \frac{737}{2} a - \frac{679}{2} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{1}{2} a - 1\) , \( -a + 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{3}{2}a-2\right){x}^{2}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{1}{2}a-1\right){x}-a+1$ |
| 8.1-a2 |
8.1-a |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$879.9190386$ |
2.167104221 |
\( -\frac{106555}{4} a^{3} + \frac{17049}{2} a^{2} + 226838 a + 184484 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( 0\) , \( 6 a^{3} - \frac{43}{2} a^{2} + \frac{21}{2} a + 15\) , \( -26 a^{3} + 112 a^{2} - 56 a - 100\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}^{2}+\left(6a^{3}-\frac{43}{2}a^{2}+\frac{21}{2}a+15\right){x}-26a^{3}+112a^{2}-56a-100$ |
| 8.1-a3 |
8.1-a |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$439.9595193$ |
2.167104221 |
\( \frac{3252059965}{4} a^{3} + \frac{1983512637}{4} a^{2} - 2919685778 a - 419445786 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( 509 a^{3} - \frac{463}{2} a^{2} - \frac{7289}{2} a - 2245\) , \( 3668 a^{3} - 405 a^{2} - 29374 a - 18925\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{9}{2}a+2\right){x}^{2}+\left(509a^{3}-\frac{463}{2}a^{2}-\frac{7289}{2}a-2245\right){x}+3668a^{3}-405a^{2}-29374a-18925$ |
| 8.1-a4 |
8.1-a |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$109.9898798$ |
2.167104221 |
\( -\frac{63546444805}{4} a^{3} + \frac{19553427267}{4} a^{2} + 119478814952 a + 75100798390 \) |
\( \bigl[a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( a\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + 2 a - 7\) , \( -\frac{3}{2} a^{3} - a^{2} + \frac{11}{2} a\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){x}^{2}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+2a-7\right){x}-\frac{3}{2}a^{3}-a^{2}+\frac{11}{2}a$ |
| 8.1-b1 |
8.1-b |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.227197469$ |
$135.5285667$ |
1.820047240 |
\( \frac{3252059965}{4} a^{3} + \frac{1983512637}{4} a^{2} - 2919685778 a - 419445786 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -2 a^{3} + 5 a^{2} + 9 a - 26\) , \( -8 a^{3} + 14 a^{2} + 38 a - 64\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){x}^{2}+\left(-2a^{3}+5a^{2}+9a-26\right){x}-8a^{3}+14a^{2}+38a-64$ |
| 8.1-b2 |
8.1-b |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.113598734$ |
$1084.228533$ |
1.820047240 |
\( -\frac{106555}{4} a^{3} + \frac{17049}{2} a^{2} + 226838 a + 184484 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-1\right){x}-\frac{1}{2}a^{3}+a^{2}+\frac{7}{2}a-2$ |
| 8.1-b3 |
8.1-b |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{16} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.056799367$ |
$542.1142668$ |
1.820047240 |
\( 40 a^{3} + \frac{3281}{16} a^{2} - \frac{737}{2} a - \frac{679}{2} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( \frac{3}{2} a^{3} + \frac{3}{2} a^{2} - 9 a + 4\) , \( 8 a^{2} - 24\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){x}^{2}+\left(\frac{3}{2}a^{3}+\frac{3}{2}a^{2}-9a+4\right){x}+8a^{2}-24$ |
| 8.1-b4 |
8.1-b |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.056799367$ |
$542.1142668$ |
1.820047240 |
\( -\frac{63546444805}{4} a^{3} + \frac{19553427267}{4} a^{2} + 119478814952 a + 75100798390 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( 34 a^{3} - 36 a^{2} - 194 a - 96\) , \( -160 a^{3} - 54 a^{2} + 1456 a + 990\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+3\right){x}^{2}+\left(34a^{3}-36a^{2}-194a-96\right){x}-160a^{3}-54a^{2}+1456a+990$ |
| 8.2-a1 |
8.2-a |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$879.9190386$ |
2.167104221 |
\( \frac{106555}{4} a^{3} - \frac{285567}{4} a^{2} - \frac{655883}{4} a + \frac{1572831}{4} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a\) , \( 0\) , \( -\frac{9}{2} a^{3} - 6 a^{2} + \frac{27}{2} a + 12\) , \( \frac{1}{2} a^{3} + \frac{5}{2} a^{2} + 4 a + 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a\right){x}^{2}+\left(-\frac{9}{2}a^{3}-6a^{2}+\frac{27}{2}a+12\right){x}+\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+4a+2$ |
| 8.2-a2 |
8.2-a |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{16} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$439.9595193$ |
2.167104221 |
\( -40 a^{3} + \frac{5201}{16} a^{2} - \frac{1293}{8} a - \frac{7407}{16} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( a\) , \( a\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}-a{x}^{2}+a{x}+a$ |
| 8.2-a3 |
8.2-a |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$439.9595193$ |
2.167104221 |
\( -\frac{3252059965}{4} a^{3} + 2934923133 a^{2} - \frac{2044462057}{4} a - \frac{4060476827}{2} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -511 a^{3} + \frac{2605}{2} a^{2} + \frac{5177}{2} a - 5637\) , \( -\frac{5759}{2} a^{3} + \frac{16631}{2} a^{2} + 15053 a - 35335\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+3\right){x}^{2}+\left(-511a^{3}+\frac{2605}{2}a^{2}+\frac{5177}{2}a-5637\right){x}-\frac{5759}{2}a^{3}+\frac{16631}{2}a^{2}+15053a-35335$ |
| 8.2-a4 |
8.2-a |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$109.9898798$ |
2.167104221 |
\( \frac{63546444805}{4} a^{3} - 42771476787 a^{2} - \frac{326382779927}{4} a + \frac{367162717915}{2} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 1\) , \( a + 1\) , \( \frac{1}{2} a^{3} - \frac{11}{2} a - 4\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-1\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{11}{2}a-4\right){x}+\frac{3}{2}a^{3}-\frac{11}{2}a^{2}+3$ |
| 8.2-b1 |
8.2-b |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.227197469$ |
$135.5285667$ |
1.820047240 |
\( -\frac{3252059965}{4} a^{3} + 2934923133 a^{2} - \frac{2044462057}{4} a - \frac{4060476827}{2} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 4\) , \( a + 1\) , \( \frac{7}{2} a^{3} - 3 a^{2} - \frac{39}{2} a - 7\) , \( 9 a^{3} - 5 a^{2} - 60 a - 30\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{7}{2}a-4\right){x}^{2}+\left(\frac{7}{2}a^{3}-3a^{2}-\frac{39}{2}a-7\right){x}+9a^{3}-5a^{2}-60a-30$ |
| 8.2-b2 |
8.2-b |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.113598734$ |
$1084.228533$ |
1.820047240 |
\( \frac{106555}{4} a^{3} - \frac{285567}{4} a^{2} - \frac{655883}{4} a + \frac{1572831}{4} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 4\) , \( a + 1\) , \( a^{3} - \frac{1}{2} a^{2} - \frac{9}{2} a + 3\) , \( \frac{3}{2} a^{3} - \frac{1}{2} a^{2} - 7 a + 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{7}{2}a-4\right){x}^{2}+\left(a^{3}-\frac{1}{2}a^{2}-\frac{9}{2}a+3\right){x}+\frac{3}{2}a^{3}-\frac{1}{2}a^{2}-7a+2$ |
| 8.2-b3 |
8.2-b |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{16} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.056799367$ |
$542.1142668$ |
1.820047240 |
\( -40 a^{3} + \frac{5201}{16} a^{2} - \frac{1293}{8} a - \frac{7407}{16} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( \frac{3}{2} a^{3} + 2 a^{2} - \frac{7}{2} a\) , \( 7 a^{3} + 5 a^{2} - 32 a - 22\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}^{2}+\left(\frac{3}{2}a^{3}+2a^{2}-\frac{7}{2}a\right){x}+7a^{3}+5a^{2}-32a-22$ |
| 8.2-b4 |
8.2-b |
$4$ |
$4$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$11.76326$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.056799367$ |
$542.1142668$ |
1.820047240 |
\( \frac{63546444805}{4} a^{3} - 42771476787 a^{2} - \frac{326382779927}{4} a + \frac{367162717915}{2} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -913 a^{3} + 2459 a^{2} + 4690 a - 10552\) , \( 38402 a^{3} - 103390 a^{2} - 197238 a + 443764\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+1\right){x}^{2}+\left(-913a^{3}+2459a^{2}+4690a-10552\right){x}+38402a^{3}-103390a^{2}-197238a+443764$ |
| 14.1-a1 |
14.1-a |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7 \) |
$12.61559$ |
$(1/2a^3+1/2a^2-2a-1), (1/2a^3-5/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.134360114$ |
$1862.055830$ |
2.464677714 |
\( -\frac{102699803}{56} a^{3} + \frac{427167035}{56} a^{2} - \frac{25500177}{7} a - \frac{47490668}{7} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( a^{3} - 5 a^{2} + 2 a + 10\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} - 3 a - 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+2\right){x}^{2}+\left(a^{3}-5a^{2}+2a+10\right){x}-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}-3a-1$ |
| 14.1-a2 |
14.1-a |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{6} \cdot 7^{2} \) |
$12.61559$ |
$(1/2a^3+1/2a^2-2a-1), (1/2a^3-5/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.067180057$ |
$931.0279154$ |
2.464677714 |
\( \frac{110853}{56} a^{3} + 706 a^{2} - \frac{77575}{14} a - \frac{14101}{7} \) |
\( \bigl[1\) , \( a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{3}{2} a^{3} - 17 a^{2} + \frac{109}{2} a + 46\) , \( \frac{49}{2} a^{3} + 92 a^{2} - \frac{863}{2} a - 335\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){y}={x}^{3}+a{x}^{2}+\left(-\frac{3}{2}a^{3}-17a^{2}+\frac{109}{2}a+46\right){x}+\frac{49}{2}a^{3}+92a^{2}-\frac{863}{2}a-335$ |
| 14.1-b1 |
14.1-b |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7 \) |
$12.61559$ |
$(1/2a^3+1/2a^2-2a-1), (1/2a^3-5/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.036081162$ |
$2393.915606$ |
2.552746472 |
\( -\frac{102699803}{56} a^{3} + \frac{427167035}{56} a^{2} - \frac{25500177}{7} a - \frac{47490668}{7} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 2\) , \( 7 a^{3} + \frac{17}{2} a^{2} - \frac{45}{2} a - 18\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-1\right){x}^{2}+\left(a^{3}+\frac{3}{2}a^{2}-\frac{7}{2}a-2\right){x}+7a^{3}+\frac{17}{2}a^{2}-\frac{45}{2}a-18$ |
| 14.1-b2 |
14.1-b |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{6} \cdot 7^{2} \) |
$12.61559$ |
$(1/2a^3+1/2a^2-2a-1), (1/2a^3-5/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.018040581$ |
$1196.957803$ |
2.552746472 |
\( \frac{110853}{56} a^{3} + 706 a^{2} - \frac{77575}{14} a - \frac{14101}{7} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -a^{2} + a + 5\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{5}{2} a - 4\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a\right){x}^{2}+\left(-a^{2}+a+5\right){x}-\frac{1}{2}a^{3}+a^{2}+\frac{5}{2}a-4$ |
| 14.2-a1 |
14.2-a |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7 \) |
$12.61559$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3-5/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.134360114$ |
$1862.055830$ |
2.464677714 |
\( \frac{102699803}{56} a^{3} + \frac{59533813}{28} a^{2} - \frac{342233245}{56} a - \frac{32432441}{7} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -a^{3} - 2 a^{2} + 5 a + 8\) , \( \frac{1}{2} a^{3} + a^{2} - \frac{1}{2} a - 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{7}{2}a-2\right){x}^{2}+\left(-a^{3}-2a^{2}+5a+8\right){x}+\frac{1}{2}a^{3}+a^{2}-\frac{1}{2}a-2$ |
| 14.2-a2 |
14.2-a |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{6} \cdot 7^{2} \) |
$12.61559$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3-5/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.067180057$ |
$931.0279154$ |
2.464677714 |
\( -\frac{110853}{56} a^{3} + \frac{372095}{56} a^{2} - \frac{101331}{56} a - \frac{272719}{56} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( 205 a^{3} - 553 a^{2} - 1055 a + 2377\) , \( -\frac{21727}{2} a^{3} + \frac{58495}{2} a^{2} + 55795 a - 125534\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a\right){x}^{2}+\left(205a^{3}-553a^{2}-1055a+2377\right){x}-\frac{21727}{2}a^{3}+\frac{58495}{2}a^{2}+55795a-125534$ |
| 14.2-b1 |
14.2-b |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7 \) |
$12.61559$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3-5/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.036081162$ |
$2393.915606$ |
2.552746472 |
\( \frac{102699803}{56} a^{3} + \frac{59533813}{28} a^{2} - \frac{342233245}{56} a - \frac{32432441}{7} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( 0\) , \( -5 a^{3} + 21 a^{2} + 29 a - 85\) , \( 29 a^{3} - 67 a^{2} - 144 a + 295\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}^{2}+\left(-5a^{3}+21a^{2}+29a-85\right){x}+29a^{3}-67a^{2}-144a+295$ |
| 14.2-b2 |
14.2-b |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{6} \cdot 7^{2} \) |
$12.61559$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3-5/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.018040581$ |
$1196.957803$ |
2.552746472 |
\( -\frac{110853}{56} a^{3} + \frac{372095}{56} a^{2} - \frac{101331}{56} a - \frac{272719}{56} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( a + 3\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}^{2}+\left(a+3\right){x}+\frac{1}{2}a^{3}-\frac{7}{2}a-3$ |
| 16.2-a1 |
16.2-a |
$1$ |
$1$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$299.0804076$ |
2.946354769 |
\( \frac{1149711}{4} a^{3} - \frac{4783537}{4} a^{2} + \frac{1143783}{2} a + 1064020 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( a^{3} - 6 a + 3\) , \( \frac{5}{2} a^{3} + \frac{3}{2} a^{2} - 10 a\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+2\right){x}^{2}+\left(a^{3}-6a+3\right){x}+\frac{5}{2}a^{3}+\frac{3}{2}a^{2}-10a$ |
| 16.2-b1 |
16.2-b |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{17} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$219.8077559$ |
1.082704873 |
\( \frac{9303850896879}{32} a^{3} + \frac{10797411001713}{32} a^{2} - \frac{1937587510291}{2} a - \frac{2943761556959}{4} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -2 a^{3} - \frac{23}{2} a^{2} - \frac{35}{2} a - 3\) , \( -\frac{141}{2} a^{3} - \frac{117}{2} a^{2} + 302 a + 213\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+2\right){x}^{2}+\left(-2a^{3}-\frac{23}{2}a^{2}-\frac{35}{2}a-3\right){x}-\frac{141}{2}a^{3}-\frac{117}{2}a^{2}+302a+213$ |
| 16.2-b2 |
16.2-b |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{25} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$219.8077559$ |
1.082704873 |
\( -\frac{133698893}{128} a^{3} + \frac{123708829}{32} a^{2} - \frac{28210561}{16} a - \frac{12101397}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( a\) , \( -49 a^{3} + \frac{267}{2} a^{2} + \frac{505}{2} a - 568\) , \( \frac{863}{2} a^{3} - \frac{2319}{2} a^{2} - 2215 a + 4979\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}^{2}+\left(-49a^{3}+\frac{267}{2}a^{2}+\frac{505}{2}a-568\right){x}+\frac{863}{2}a^{3}-\frac{2319}{2}a^{2}-2215a+4979$ |
| 16.2-c1 |
16.2-c |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{25} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$59.68458879$ |
2.057914491 |
\( -\frac{133698893}{128} a^{3} + \frac{123708829}{32} a^{2} - \frac{28210561}{16} a - \frac{12101397}{4} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 3\) , \( 0\) , \( -17 a^{3} - 20 a^{2} + 56 a + 44\) , \( -159 a^{3} - 184 a^{2} + 526 a + 392\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+3\right){x}^{2}+\left(-17a^{3}-20a^{2}+56a+44\right){x}-159a^{3}-184a^{2}+526a+392$ |
| 16.2-c2 |
16.2-c |
$2$ |
$2$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{17} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$59.68458879$ |
2.057914491 |
\( \frac{9303850896879}{32} a^{3} + \frac{10797411001713}{32} a^{2} - \frac{1937587510291}{2} a - \frac{2943761556959}{4} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a\) , \( 0\) , \( -2 a^{3} + 7 a^{2} + 8 a - 32\) , \( -16 a^{3} + 53 a^{2} + 72 a - 252\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a\right){x}^{2}+\left(-2a^{3}+7a^{2}+8a-32\right){x}-16a^{3}+53a^{2}+72a-252$ |
| 16.2-d1 |
16.2-d |
$1$ |
$1$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2), (1/2a^3+1/2a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$75.23853844$ |
0.741203438 |
\( \frac{1149711}{4} a^{3} - \frac{4783537}{4} a^{2} + \frac{1143783}{2} a + 1064020 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( 2 a^{3} - 3 a^{2} - 2 a + 3\) , \( 9 a^{3} - \frac{25}{2} a^{2} - \frac{69}{2} a - 14\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}^{2}+\left(2a^{3}-3a^{2}-2a+3\right){x}+9a^{3}-\frac{25}{2}a^{2}-\frac{69}{2}a-14$ |
| 16.3-a1 |
16.3-a |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$153.0558732$ |
1.507811580 |
\( -\frac{2142331909}{2} a^{3} + \frac{8913266161}{2} a^{2} - 2130537580 a - 3966334907 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( \frac{51}{2} a^{3} - 68 a^{2} - \frac{261}{2} a + 294\) , \( -\frac{68581}{2} a^{3} + \frac{184643}{2} a^{2} + 176121 a - 396257\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{7}{2}a-4\right){x}^{2}+\left(\frac{51}{2}a^{3}-68a^{2}-\frac{261}{2}a+294\right){x}-\frac{68581}{2}a^{3}+\frac{184643}{2}a^{2}+176121a-396257$ |
| 16.3-a2 |
16.3-a |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$153.0558732$ |
1.507811580 |
\( -\frac{728135853331382213}{2} a^{3} + \frac{224049360810344247}{2} a^{2} + 2738054551954718675 a + 1721058939374601181 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( 0\) , \( 9 a^{3} - 2 a^{2} - 66 a - 42\) , \( -\frac{99}{2} a^{3} + \frac{23}{2} a^{2} + 366 a + 230\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}^{2}+\left(9a^{3}-2a^{2}-66a-42\right){x}-\frac{99}{2}a^{3}+\frac{23}{2}a^{2}+366a+230$ |
| 16.3-a3 |
16.3-a |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$612.2234929$ |
1.507811580 |
\( -164286883 a^{3} + 50566227 a^{2} + 1235508110 a + 776641025 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( 0\) , \( \frac{3}{2} a^{3} + \frac{1}{2} a^{2} - 6 a - 2\) , \( a^{2} + 6 a + 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}^{2}+\left(\frac{3}{2}a^{3}+\frac{1}{2}a^{2}-6a-2\right){x}+a^{2}+6a+2$ |
| 16.3-a4 |
16.3-a |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$306.1117464$ |
1.507811580 |
\( \frac{2142331909}{2} a^{3} + 1243135217 a^{2} - \frac{7138461435}{2} a - 2711405361 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -\frac{7}{2} a^{3} + \frac{17}{2} a^{2} + 4 a - 3\) , \( -\frac{11}{2} a^{3} + 4 a^{2} + \frac{65}{2} a + 16\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a+2\right){x}^{2}+\left(-\frac{7}{2}a^{3}+\frac{17}{2}a^{2}+4a-3\right){x}-\frac{11}{2}a^{3}+4a^{2}+\frac{65}{2}a+16$ |
| 16.3-a5 |
16.3-a |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$76.52793662$ |
1.507811580 |
\( \frac{728135853331382213}{2} a^{3} - 980179099591901196 a^{2} - \frac{3739800265535979205}{2} a + 4207070245068800873 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( 113 a^{3} - 78 a^{2} - 746 a - 444\) , \( \frac{1527}{2} a^{3} + \frac{43}{2} a^{2} - 6377 a - 4174\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}-a{x}^{2}+\left(113a^{3}-78a^{2}-746a-444\right){x}+\frac{1527}{2}a^{3}+\frac{43}{2}a^{2}-6377a-4174$ |
| 16.3-a6 |
16.3-a |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$612.2234929$ |
1.507811580 |
\( 164286883 a^{3} - 442294422 a^{2} - 843779915 a + 1898428479 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( 48 a^{3} - 18 a^{2} - 356 a - 224\) , \( -437 a^{3} + 131 a^{2} + 3293 a + 2070\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}-a{x}^{2}+\left(48a^{3}-18a^{2}-356a-224\right){x}-437a^{3}+131a^{2}+3293a+2070$ |
| 16.3-b1 |
16.3-b |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$19.13198415$ |
0.753905790 |
\( -\frac{728135853331382213}{2} a^{3} + \frac{224049360810344247}{2} a^{2} + 2738054551954718675 a + 1721058939374601181 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( 41 a^{3} - 170 a^{2} + 86 a + 142\) , \( 3971 a^{3} - 16520 a^{2} + 7899 a + 14698\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}^{2}+\left(41a^{3}-170a^{2}+86a+142\right){x}+3971a^{3}-16520a^{2}+7899a+14698$ |
| 16.3-b2 |
16.3-b |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$612.2234929$ |
0.753905790 |
\( \frac{728135853331382213}{2} a^{3} - 980179099591901196 a^{2} - \frac{3739800265535979205}{2} a + 4207070245068800873 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{7}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -28 a^{3} + \frac{141}{2} a^{2} + \frac{287}{2} a - 304\) , \( 165 a^{3} - 423 a^{2} - 838 a + 1829\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{7}{2}a+2\right){x}^{2}+\left(-28a^{3}+\frac{141}{2}a^{2}+\frac{287}{2}a-304\right){x}+165a^{3}-423a^{2}-838a+1829$ |
| 16.3-b3 |
16.3-b |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1224.446985$ |
0.753905790 |
\( 164286883 a^{3} - 442294422 a^{2} - 843779915 a + 1898428479 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{7}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -3 a^{3} + \frac{1}{2} a^{2} + \frac{27}{2} a - 4\) , \( \frac{5}{2} a^{3} + \frac{1}{2} a^{2} - 10 a + 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{7}{2}a+2\right){x}^{2}+\left(-3a^{3}+\frac{1}{2}a^{2}+\frac{27}{2}a-4\right){x}+\frac{5}{2}a^{3}+\frac{1}{2}a^{2}-10a+1$ |
| 16.3-b4 |
16.3-b |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$76.52793662$ |
0.753905790 |
\( -\frac{2142331909}{2} a^{3} + \frac{8913266161}{2} a^{2} - 2130537580 a - 3966334907 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 4\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( 7 a^{3} - \frac{45}{2} a^{2} - \frac{1}{2} a + 26\) , \( \frac{43}{2} a^{3} - \frac{163}{2} a^{2} + 30 a + 71\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+4\right){x}^{2}+\left(7a^{3}-\frac{45}{2}a^{2}-\frac{1}{2}a+26\right){x}+\frac{43}{2}a^{3}-\frac{163}{2}a^{2}+30a+71$ |
| 16.3-b5 |
16.3-b |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$612.2234929$ |
0.753905790 |
\( \frac{2142331909}{2} a^{3} + 1243135217 a^{2} - \frac{7138461435}{2} a - 2711405361 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -a^{3} + \frac{3}{2} a^{2} + \frac{7}{2} a - 2\) , \( 31 a^{3} - 9 a^{2} - 236 a - 151\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}^{2}+\left(-a^{3}+\frac{3}{2}a^{2}+\frac{7}{2}a-2\right){x}+31a^{3}-9a^{2}-236a-151$ |
| 16.3-b6 |
16.3-b |
$6$ |
$8$ |
4.4.10304.1 |
$4$ |
$[4, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{12} \) |
$12.82793$ |
$(-1/2a^3+a^2+5/2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$306.1117464$ |
0.753905790 |
\( -164286883 a^{3} + 50566227 a^{2} + 1235508110 a + 776641025 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 2\) , \( 0\) , \( -156 a^{3} + \frac{777}{2} a^{2} + \frac{1569}{2} a - 1684\) , \( 2203 a^{3} - 6023 a^{2} - 11359 a + 25795\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+2\right){x}^{2}+\left(-156a^{3}+\frac{777}{2}a^{2}+\frac{1569}{2}a-1684\right){x}+2203a^{3}-6023a^{2}-11359a+25795$ |
*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.
