| 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 |
$4$ |
$6$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{3} \) |
$3.62200$ |
$(-1/2a^2+3/2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$108.7031927$ |
2.257692382 |
\( \frac{770908545}{8} a^{2} - \frac{1242553719}{4} a - \frac{473491271}{8} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 4\) , \( 1\) , \( \frac{255813837}{2} a^{2} - \frac{46665869}{2} a - 1402743353\) , \( -1835590565626 a^{2} + 334755643886 a + 20130446177163\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+4\right){x}^{2}+\left(\frac{255813837}{2}a^{2}-\frac{46665869}{2}a-1402743353\right){x}-1835590565626a^{2}+334755643886a+20130446177163$ |
| 2.1-a2 |
2.1-a |
$4$ |
$6$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$3.62200$ |
$(-1/2a^2+3/2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$326.1095781$ |
2.257692382 |
\( \frac{1648641}{2} a^{2} + 2807817 a + \frac{984505}{2} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 4\) , \( 1\) , \( -\frac{5}{2} a^{2} + \frac{11}{2} a + 22\) , \( \frac{1}{2} a^{2} - \frac{5}{2} a + 12\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+4\right){x}^{2}+\left(-\frac{5}{2}a^{2}+\frac{11}{2}a+22\right){x}+\frac{1}{2}a^{2}-\frac{5}{2}a+12$ |
| 2.1-a3 |
2.1-a |
$4$ |
$6$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \) |
$3.62200$ |
$(-1/2a^2+3/2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$54.35159636$ |
2.257692382 |
\( \frac{3470401}{64} a^{2} + \frac{6359881}{32} a + \frac{2186105}{64} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 5\) , \( a\) , \( -\frac{322915991101}{2} a^{2} - \frac{1100796951543}{2} a - 97400643557\) , \( -121907338575688280 a^{2} - 414938810324224411 a - 71497690157315314\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+5\right){x}^{2}+\left(-\frac{322915991101}{2}a^{2}-\frac{1100796951543}{2}a-97400643557\right){x}-121907338575688280a^{2}-414938810324224411a-71497690157315314$ |
| 2.1-a4 |
2.1-a |
$4$ |
$6$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{2} \) |
$3.62200$ |
$(-1/2a^2+3/2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$163.0547890$ |
2.257692382 |
\( \frac{1057}{4} a^{2} + \frac{1065}{2} a + \frac{1369}{4} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 5\) , \( a\) , \( -\frac{7929}{2} a^{2} - \frac{26969}{2} a - 2294\) , \( 377334 a^{2} + 1284474 a + 221731\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+5\right){x}^{2}+\left(-\frac{7929}{2}a^{2}-\frac{26969}{2}a-2294\right){x}+377334a^{2}+1284474a+221731$ |
| 4.1-a1 |
4.1-a |
$2$ |
$2$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{15} \) |
$4.06556$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$105.4225975$ |
1.459704414 |
\( \frac{45367857}{16384} a^{2} - \frac{77471559}{8192} a + \frac{1730025}{16384} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -20560 a^{2} - 70035 a - 12237\) , \( 666138303 a^{2} + 2267565896 a + 391379578\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+3\right){x}^{2}+\left(-20560a^{2}-70035a-12237\right){x}+666138303a^{2}+2267565896a+391379578$ |
| 4.1-a2 |
4.1-a |
$2$ |
$2$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{9} \) |
$4.06556$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$105.4225975$ |
1.459704414 |
\( \frac{327321}{128} a^{2} + \frac{589761}{64} a + \frac{402705}{128} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -198 a^{2} + 37 a + 2171\) , \( \frac{1477}{2} a^{2} - \frac{267}{2} a - 8097\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+3\right){x}^{2}+\left(-198a^{2}+37a+2171\right){x}+\frac{1477}{2}a^{2}-\frac{267}{2}a-8097$ |
| 4.2-a1 |
4.2-a |
$2$ |
$2$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$4.06556$ |
$(1/2a^2-3/2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$150.2949719$ |
1.040508577 |
\( 385 a^{2} + 1650 a + 1289 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{341002745}{2} a^{2} - \frac{1160786317}{2} a - 100170764\) , \( \frac{7692745873353}{2} a^{2} + \frac{26186468554527}{2} a + 2259882505722\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}^{2}+\left(-\frac{341002745}{2}a^{2}-\frac{1160786317}{2}a-100170764\right){x}+\frac{7692745873353}{2}a^{2}+\frac{26186468554527}{2}a+2259882505722$ |
| 4.2-a2 |
4.2-a |
$2$ |
$2$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{8} \) |
$4.06556$ |
$(1/2a^2-3/2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$150.2949719$ |
1.040508577 |
\( 8191 a^{2} - 27154 a - 2361 \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 5\) , \( a + 1\) , \( 60 a^{2} - 4 a - 638\) , \( -244 a^{2} + 116 a + 2905\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+5\right){x}^{2}+\left(60a^{2}-4a-638\right){x}-244a^{2}+116a+2905$ |
| 6.1-a1 |
6.1-a |
$2$ |
$2$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3^{2} \) |
$4.34980$ |
$(-1/2a^2+3/2a+1), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$113.2380680$ |
1.567919133 |
\( \frac{2054225}{288} a^{2} + \frac{3425161}{144} a + \frac{903241}{288} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( 2 a^{2} - 21\) , \( \frac{11}{2} a^{2} - \frac{3}{2} a - 62\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}^{2}+\left(2a^{2}-21\right){x}+\frac{11}{2}a^{2}-\frac{3}{2}a-62$ |
| 6.1-a2 |
6.1-a |
$2$ |
$2$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{10} \cdot 3 \) |
$4.34980$ |
$(-1/2a^2+3/2a+1), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$113.2380680$ |
1.567919133 |
\( -\frac{714452941}{3072} a^{2} + \frac{64478155}{1536} a + \frac{7845236827}{3072} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 5\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{50751}{2} a^{2} - \frac{172763}{2} a - 14908\) , \( -\frac{2612965}{2} a^{2} - \frac{8894669}{2} a - 767631\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+5\right){x}^{2}+\left(-\frac{50751}{2}a^{2}-\frac{172763}{2}a-14908\right){x}-\frac{2612965}{2}a^{2}-\frac{8894669}{2}a-767631$ |
| 6.1-b1 |
6.1-b |
$2$ |
$2$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{6} \cdot 3^{5} \) |
$4.34980$ |
$(-1/2a^2+3/2a+1), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$31.43055320$ |
1.305583005 |
\( -\frac{4438707757}{15552} a^{2} + \frac{270143131}{7776} a + \frac{53091170587}{15552} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -a - 1\) , \( a + 1\) , \( -\frac{49591}{2} a^{2} - \frac{168813}{2} a - 14564\) , \( -\frac{14522661}{2} a^{2} - \frac{49435821}{2} a - 4266292\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-\frac{49591}{2}a^{2}-\frac{168813}{2}a-14564\right){x}-\frac{14522661}{2}a^{2}-\frac{49435821}{2}a-4266292$ |
| 6.1-b2 |
6.1-b |
$2$ |
$2$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{10} \) |
$4.34980$ |
$(-1/2a^2+3/2a+1), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$31.43055320$ |
1.305583005 |
\( \frac{83795801}{472392} a^{2} + \frac{58481317}{236196} a - \frac{548223599}{472392} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 5\) , \( a\) , \( -12 a^{2} + 32 a + 32\) , \( -235 a^{2} + 749 a + 170\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+5\right){x}^{2}+\left(-12a^{2}+32a+32\right){x}-235a^{2}+749a+170$ |
| 6.1-c1 |
6.1-c |
$4$ |
$4$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3 \) |
$4.34980$ |
$(-1/2a^2+3/2a+1), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.307494418$ |
$138.8251303$ |
0.886600137 |
\( -\frac{491455}{24} a^{2} + \frac{48865}{12} a + \frac{5402113}{24} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} + \frac{5}{2} a - 7\) , \( a^{2} - a - 4\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}^{2}+\left(\frac{1}{2}a^{2}+\frac{5}{2}a-7\right){x}+a^{2}-a-4$ |
| 6.1-c2 |
6.1-c |
$4$ |
$4$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{4} \) |
$4.34980$ |
$(-1/2a^2+3/2a+1), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.307494418$ |
$69.41256517$ |
0.886600137 |
\( \frac{57948430405505}{648} a^{2} - \frac{93345525923921}{324} a - \frac{35974054742771}{648} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( a\) , \( 1\) , \( -\frac{3460223}{2} a^{2} - \frac{11778757}{2} a - 1016496\) , \( -4264949166 a^{2} - 14518087398 a - 2505810976\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-\frac{3460223}{2}a^{2}-\frac{11778757}{2}a-1016496\right){x}-4264949166a^{2}-14518087398a-2505810976$ |
| 6.1-c3 |
6.1-c |
$4$ |
$4$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{6} \cdot 3^{2} \) |
$4.34980$ |
$(-1/2a^2+3/2a+1), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.153747209$ |
$277.6502607$ |
0.886600137 |
\( \frac{38356945}{576} a^{2} - \frac{61782727}{288} a - \frac{22809079}{576} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( a\) , \( 1\) , \( -143749 a^{2} - 489326 a - 84451\) , \( -\frac{38259087}{2} a^{2} - \frac{130235729}{2} a - 11239293\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-143749a^{2}-489326a-84451\right){x}-\frac{38259087}{2}a^{2}-\frac{130235729}{2}a-11239293$ |
| 6.1-c4 |
6.1-c |
$4$ |
$4$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{12} \cdot 3 \) |
$4.34980$ |
$(-1/2a^2+3/2a+1), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.076873604$ |
$277.6502607$ |
0.886600137 |
\( -\frac{336264397}{12288} a^{2} + \frac{174458827}{6144} a + \frac{4639926619}{12288} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 5\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{4217741494253}{2} a^{2} - \frac{14357390265363}{2} a - 1239037386548\) , \( \frac{11428768758626979917}{2} a^{2} + \frac{38904065966090659971}{2} a + 3357406278614053133\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+5\right){x}^{2}+\left(-\frac{4217741494253}{2}a^{2}-\frac{14357390265363}{2}a-1239037386548\right){x}+\frac{11428768758626979917}{2}a^{2}+\frac{38904065966090659971}{2}a+3357406278614053133$ |
| 8.1-a1 |
8.1-a |
$2$ |
$2$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$4.56344$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$76.26815533$ |
1.056025611 |
\( \frac{845949825}{256} a^{2} + \frac{1426029705}{128} a + \frac{408193209}{256} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 4\) , \( 0\) , \( -125766565 a^{2} - 428115455 a - 73892885\) , \( -2646277206988 a^{2} - 9008051977284 a - 1554783000579\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+4\right){x}^{2}+\left(-125766565a^{2}-428115455a-73892885\right){x}-2646277206988a^{2}-9008051977284a-1554783000579$ |
| 8.1-a2 |
8.1-a |
$2$ |
$2$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{12} \) |
$4.56344$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$76.26815533$ |
1.056025611 |
\( -\frac{158004049761}{16} a^{2} + \frac{14407547031}{8} a + \frac{1732789543527}{16} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( 0\) , \( 18 a^{2} - 7 a - 204\) , \( -\frac{265}{2} a^{2} + \frac{17}{2} a + 1405\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}^{2}+\left(18a^{2}-7a-204\right){x}-\frac{265}{2}a^{2}+\frac{17}{2}a+1405$ |
| 8.1-b1 |
8.1-b |
$2$ |
$3$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{7} \) |
$4.56344$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.055515878$ |
$228.5778020$ |
3.162678019 |
\( -\frac{15625}{8} a^{2} + \frac{26031}{4} a + \frac{10239}{8} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{163572165}{2} a^{2} + \frac{526976743}{2} a + 50772365\) , \( 1304663991975 a^{2} - 4203206520392 a - 809928383823\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-4\right){x}^{2}+\left(-\frac{163572165}{2}a^{2}+\frac{526976743}{2}a+50772365\right){x}+1304663991975a^{2}-4203206520392a-809928383823$ |
| 8.1-b2 |
8.1-b |
$2$ |
$3$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{13} \) |
$4.56344$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3^{3} \) |
$0.018505292$ |
$76.19260068$ |
3.162678019 |
\( \frac{124932071}{512} a^{2} - \frac{11492833}{256} a - \frac{1370027665}{512} \) |
\( \bigl[a + 1\) , \( 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( \frac{3373}{2} a^{2} - \frac{615}{2} a - 18494\) , \( -87390 a^{2} + 15937 a + 958383\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+{x}^{2}+\left(\frac{3373}{2}a^{2}-\frac{615}{2}a-18494\right){x}-87390a^{2}+15937a+958383$ |
| 9.1-a1 |
9.1-a |
$2$ |
$2$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$4.65391$ |
$(a^2+a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$1$ |
$102.4173442$ |
3.545232544 |
\( -\frac{26591}{243} a^{2} - \frac{12173}{81} a + \frac{432437}{243} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( 408 a^{2} - 74 a - 4472\) , \( -1646 a^{2} + 302 a + 18057\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+a{x}^{2}+\left(408a^{2}-74a-4472\right){x}-1646a^{2}+302a+18057$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{20} \) |
$4.65391$ |
$(a^2+a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$51.20867211$ |
3.545232544 |
\( \frac{28278821}{13122} a^{2} + \frac{830400835}{118098} a + \frac{169234624}{59049} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{3189}{2} a^{2} + \frac{557}{2} a + 17448\) , \( -18806 a^{2} + 3459 a + 206335\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+a{x}^{2}+\left(-\frac{3189}{2}a^{2}+\frac{557}{2}a+17448\right){x}-18806a^{2}+3459a+206335$ |
| 9.1-b1 |
9.1-b |
$1$ |
$1$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$4.65391$ |
$(a^2+a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$24.25766275$ |
0.671753840 |
\( \frac{7317545}{6} a^{2} - \frac{281649}{2} a - \frac{41170375}{3} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( 6 a^{2} - 6 a - 70\) , \( 17 a^{2} - 170\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-4\right){x}^{2}+\left(6a^{2}-6a-70\right){x}+17a^{2}-170$ |
| 12.1-a1 |
12.1-a |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{7} \cdot 3^{6} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$22.34582697$ |
1.856431336 |
\( \frac{75239643131}{5832} a^{2} + \frac{128059994329}{2916} a + \frac{44208011137}{5832} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -25666923 a^{2} - 87304868 a - 14865839\) , \( -\frac{487388227239}{2} a^{2} - \frac{1659044416615}{2} a - 143101710044\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-4\right){x}^{2}+\left(-25666923a^{2}-87304868a-14865839\right){x}-\frac{487388227239}{2}a^{2}-\frac{1659044416615}{2}a-143101710044$ |
| 12.1-a2 |
12.1-a |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{13} \cdot 3^{6} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$11.17291348$ |
1.856431336 |
\( \frac{5933743236199673}{2985984} a^{2} - \frac{9558307374832703}{1492992} a - \frac{3683607960899471}{2985984} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( 0\) , \( 39147189092125861975 a^{2} + 133258871449076056517 a + 23000381095082182870\) , \( -\frac{6226830853007212981507371741587}{2} a^{2} - \frac{21196424862671235334620488472033}{2} a - 1829243503240300485234944290049\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(39147189092125861975a^{2}+133258871449076056517a+23000381095082182870\right){x}-\frac{6226830853007212981507371741587}{2}a^{2}-\frac{21196424862671235334620488472033}{2}a-1829243503240300485234944290049$ |
| 12.1-a3 |
12.1-a |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{24} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$44.69165394$ |
1.856431336 |
\( -\frac{6946499400744825811}{2259436291848} a^{2} + \frac{158451423841350220}{282429536481} a + \frac{76186930920955673683}{2259436291848} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\) , \( a + 1\) , \( -\frac{223783323974319}{2} a^{2} - \frac{761768952159271}{2} a - 65740374910357\) , \( \frac{3359887203898694744041}{2} a^{2} + \frac{11437213944890704278567}{2} a + 987027267070307699614\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+4\right){x}^{2}+\left(-\frac{223783323974319}{2}a^{2}-\frac{761768952159271}{2}a-65740374910357\right){x}+\frac{3359887203898694744041}{2}a^{2}+\frac{11437213944890704278567}{2}a+987027267070307699614$ |
| 12.1-a4 |
12.1-a |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{12} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$44.69165394$ |
1.856431336 |
\( \frac{344778614497}{34012224} a^{2} - \frac{499919976871}{17006112} a + \frac{29578016921}{34012224} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\) , \( a + 1\) , \( -38579204063692 a^{2} - 131325423729593 a - 22666669503592\) , \( -427801938618094180192 a^{2} - 1456257904234582470158 a - 251349020188277168101\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+4\right){x}^{2}+\left(-38579204063692a^{2}-131325423729593a-22666669503592\right){x}-427801938618094180192a^{2}-1456257904234582470158a-251349020188277168101$ |
| 12.1-a5 |
12.1-a |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{7} \cdot 3^{2} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$33.51874045$ |
1.856431336 |
\( -\frac{9879454030429}{144} a^{2} + \frac{112606986197}{9} a + \frac{108345417209149}{144} \) |
\( \bigl[1\) , \( -a - 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{5155389375385}{2} a^{2} - \frac{17549187718883}{2} a - 1514488307809\) , \( 53334987550264452674 a^{2} + 181554804176945369179 a + 31336222799309286317\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-\frac{5155389375385}{2}a^{2}-\frac{17549187718883}{2}a-1514488307809\right){x}+53334987550264452674a^{2}+181554804176945369179a+31336222799309286317$ |
| 12.1-a6 |
12.1-a |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{8} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$134.0749618$ |
1.856431336 |
\( \frac{75340757429447}{52488} a^{2} + \frac{251839325150489}{52488} a + \frac{21711099570335}{26244} \) |
\( \bigl[1\) , \( a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -61507823 a^{2} - 209375520 a - 36138056\) , \( \frac{1810025668855}{2} a^{2} + \frac{6161412441591}{2} a + 531727579181\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+a{x}^{2}+\left(-61507823a^{2}-209375520a-36138056\right){x}+\frac{1810025668855}{2}a^{2}+\frac{6161412441591}{2}a+531727579181$ |
| 12.1-a7 |
12.1-a |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$134.0749618$ |
1.856431336 |
\( -\frac{22934753}{324} a^{2} + \frac{24742241}{648} a + \frac{70861751}{81} \) |
\( \bigl[1\) , \( a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -3849258 a^{2} - 13103055 a - 2261576\) , \( \frac{28197055709}{2} a^{2} + \frac{95984102797}{2} a + 8283392013\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+a{x}^{2}+\left(-3849258a^{2}-13103055a-2261576\right){x}+\frac{28197055709}{2}a^{2}+\frac{95984102797}{2}a+8283392013$ |
| 12.1-a8 |
12.1-a |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{13} \cdot 3^{2} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$67.03748091$ |
1.856431336 |
\( \frac{63697}{576} a^{2} + \frac{34393}{144} a - \frac{48091}{144} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\) , \( a + 1\) , \( a^{2} - 7 a + 4\) , \( 21 a^{2} - 70 a - 11\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+4\right){x}^{2}+\left(a^{2}-7a+4\right){x}+21a^{2}-70a-11$ |
| 12.1-b1 |
12.1-b |
$4$ |
$6$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3^{2} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.078727738$ |
$227.2159988$ |
1.486103798 |
\( -\frac{3965}{36} a^{2} + \frac{23903}{18} a + \frac{19201}{72} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 5\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{8523195}{2} a^{2} + \frac{27458989}{2} a + 2645570\) , \( 17553213623 a^{2} - 56550791933 a - 10896940540\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-5\right){x}^{2}+\left(-\frac{8523195}{2}a^{2}+\frac{27458989}{2}a+2645570\right){x}+17553213623a^{2}-56550791933a-10896940540$ |
| 12.1-b2 |
12.1-b |
$4$ |
$6$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{9} \cdot 3 \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.157455477$ |
$227.2159988$ |
1.486103798 |
\( \frac{327677755}{192} a^{2} - \frac{528399289}{96} a - \frac{199435573}{192} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 5\) , \( 1\) , \( -\frac{904475177188095}{2} a^{2} + \frac{2913927253051131}{2} a + 280746660814146\) , \( 16610825170436481186926 a^{2} - 53514720337910090484930 a - 10311910857444710121492\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-5\right){x}^{2}+\left(-\frac{904475177188095}{2}a^{2}+\frac{2913927253051131}{2}a+280746660814146\right){x}+16610825170436481186926a^{2}-53514720337910090484930a-10311910857444710121492$ |
| 12.1-b3 |
12.1-b |
$4$ |
$6$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{3} \cdot 3^{6} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.236183216$ |
$75.73866627$ |
1.486103798 |
\( \frac{304539391}{729} a^{2} + \frac{302784646}{729} a - \frac{4368522527}{1458} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{44409}{2} a^{2} - \frac{8105}{2} a - 243526\) , \( -\frac{8299425}{2} a^{2} + \frac{1513549}{2} a + 45508798\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+4\right){x}^{2}+\left(\frac{44409}{2}a^{2}-\frac{8105}{2}a-243526\right){x}-\frac{8299425}{2}a^{2}+\frac{1513549}{2}a+45508798$ |
| 12.1-b4 |
12.1-b |
$4$ |
$6$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{3} \cdot 3^{3} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.472366432$ |
$75.73866627$ |
1.486103798 |
\( -\frac{46352334499837}{54} a^{2} + \frac{16906511401963}{108} a + \frac{1016668125666029}{108} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\) , \( 0\) , \( -\frac{19}{2} a^{2} + \frac{57}{2} a + 13\) , \( -\frac{23}{2} a^{2} + \frac{73}{2} a + 9\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+4\right){x}^{2}+\left(-\frac{19}{2}a^{2}+\frac{57}{2}a+13\right){x}-\frac{23}{2}a^{2}+\frac{73}{2}a+9$ |
| 12.1-c1 |
12.1-c |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{14} \cdot 3 \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$54.94604926$ |
1.521590105 |
\( \frac{54248581}{192} a^{2} - \frac{87046351}{96} a - \frac{35703151}{192} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 4\) , \( 0\) , \( 216 a^{2} - 42 a - 2356\) , \( 4304 a^{2} - 788 a - 47192\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-4\right){x}^{2}+\left(216a^{2}-42a-2356\right){x}+4304a^{2}-788a-47192$ |
| 12.1-c2 |
12.1-c |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{26} \cdot 3 \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$54.94604926$ |
1.521590105 |
\( \frac{2381639892659}{50331648} a^{2} + \frac{3939433235275}{25165824} a + \frac{1996095840475}{50331648} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{2997358407475}{2} a^{2} - \frac{10203148884299}{2} a - 880527915921\) , \( 3439719303324971887 a^{2} + 11708966163164085212 a + 2020958762847630756\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(-\frac{2997358407475}{2}a^{2}-\frac{10203148884299}{2}a-880527915921\right){x}+3439719303324971887a^{2}+11708966163164085212a+2020958762847630756$ |
| 12.1-c3 |
12.1-c |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{4} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \) |
$1$ |
$6.868256157$ |
1.521590105 |
\( -\frac{9614322687857935043}{5184} a^{2} + \frac{876679990259783405}{2592} a + \frac{105437790045273389381}{5184} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -669923 a^{2} - 2283899 a - 404718\) , \( -\frac{2040757473}{2} a^{2} - \frac{6947124485}{2} a - 599976561\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+4\right){x}^{2}+\left(-669923a^{2}-2283899a-404718\right){x}-\frac{2040757473}{2}a^{2}-\frac{6947124485}{2}a-599976561$ |
| 12.1-c4 |
12.1-c |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$54.94604926$ |
1.521590105 |
\( -\frac{480845710319}{36864} a^{2} + \frac{43842468761}{18432} a + \frac{5273407342793}{36864} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -77488 a^{2} - 263984 a - 46208\) , \( \frac{30280475}{2} a^{2} + \frac{103070807}{2} a + 8886811\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+4\right){x}^{2}+\left(-77488a^{2}-263984a-46208\right){x}+\frac{30280475}{2}a^{2}+\frac{103070807}{2}a+8886811$ |
| 12.1-c5 |
12.1-c |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{14} \cdot 3^{3} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$18.31534975$ |
1.521590105 |
\( \frac{5841236462851931}{6912} a^{2} - \frac{9409290087511781}{3456} a - \frac{3626206167915533}{6912} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -8923205580144747651 a^{2} - 30375011156364885604 a - 5242704112360441364\) , \( -41770287508302525942343713709 a^{2} - 142188021734092747794571810030 a - 24541545725829452672841345040\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8923205580144747651a^{2}-30375011156364885604a-5242704112360441364\right){x}-41770287508302525942343713709a^{2}-142188021734092747794571810030a-24541545725829452672841345040$ |
| 12.1-c6 |
12.1-c |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{12} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.289418719$ |
1.521590105 |
\( \frac{211159711846104331363}{8503056} a^{2} + \frac{718797583652098568095}{8503056} a + \frac{62031962618934403693}{4251528} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -\frac{183409684664571}{2} a^{2} - \frac{624614729582273}{2} a - 54330191331833\) , \( -\frac{3297522855443557976489}{2} a^{2} - \frac{11224992678139195131497}{2} a - 968819226347214173821\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-\frac{183409684664571}{2}a^{2}-\frac{624614729582273}{2}a-54330191331833\right){x}-\frac{3297522855443557976489}{2}a^{2}-\frac{11224992678139195131497}{2}a-968819226347214173821$ |
| 12.1-c7 |
12.1-c |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{16} \cdot 3^{6} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$18.31534975$ |
1.521590105 |
\( \frac{1789034879}{1458} a^{2} + \frac{131567016847}{46656} a + \frac{11085216667}{23328} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -\frac{11460945941211}{2} a^{2} - \frac{39039220742713}{2} a - 3408132031133\) , \( -\frac{51523049068944509433}{2} a^{2} - \frac{175386850265331500313}{2} a - 15135773304060031597\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-\frac{11460945941211}{2}a^{2}-\frac{39039220742713}{2}a-3408132031133\right){x}-\frac{51523049068944509433}{2}a^{2}-\frac{175386850265331500313}{2}a-15135773304060031597$ |
| 12.1-c8 |
12.1-c |
$8$ |
$12$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{26} \cdot 3^{3} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$18.31534975$ |
1.521590105 |
\( -\frac{21383621}{110592} a^{2} - \frac{28656737}{27648} a + \frac{42715943}{27648} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -52019561241 a^{2} + 9485961380 a + 570482417593\) , \( -233828025440192 a^{2} + 42642238654450 a + 2564328637541965\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+4\right){x}^{2}+\left(-52019561241a^{2}+9485961380a+570482417593\right){x}-233828025440192a^{2}+42642238654450a+2564328637541965$ |
| 12.1-d1 |
12.1-d |
$6$ |
$8$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{7} \cdot 3^{2} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.093605638$ |
$94.26322366$ |
3.665192259 |
\( \frac{211711655128592839}{288} a^{2} - \frac{341033420593305649}{144} a - \frac{131428833583474753}{288} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 5\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{242347195549}{2} a^{2} - \frac{44196756061}{2} a - 1328879503696\) , \( -\frac{107203252560798423}{2} a^{2} + \frac{19550612031369799}{2} a + 587835170642240838\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-5\right){x}^{2}+\left(\frac{242347195549}{2}a^{2}-\frac{44196756061}{2}a-1328879503696\right){x}-\frac{107203252560798423}{2}a^{2}+\frac{19550612031369799}{2}a+587835170642240838$ |
| 12.1-d2 |
12.1-d |
$6$ |
$8$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{14} \cdot 3^{4} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.046802819$ |
$188.5264473$ |
3.665192259 |
\( \frac{501039024145}{82944} a^{2} - \frac{806769082471}{41472} a - \frac{306904370743}{82944} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 5\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{15222896969}{2} a^{2} - \frac{2776193621}{2} a - 83472787216\) , \( -\frac{1657349691891137}{2} a^{2} + \frac{302250165483845}{2} a + 9087862687700300\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-5\right){x}^{2}+\left(\frac{15222896969}{2}a^{2}-\frac{2776193621}{2}a-83472787216\right){x}-\frac{1657349691891137}{2}a^{2}+\frac{302250165483845}{2}a+9087862687700300$ |
| 12.1-d3 |
12.1-d |
$6$ |
$8$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{41} \cdot 3 \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.187211276$ |
$23.56580591$ |
3.665192259 |
\( -\frac{10760883583708477}{3298534883328} a^{2} - \frac{17713193080059941}{1649267441664} a - \frac{2079878040278933}{3298534883328} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 5\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{41}{2} a^{2} - \frac{129}{2} a - 12\) , \( 628 a^{2} - 2022 a - 397\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-5\right){x}^{2}+\left(\frac{41}{2}a^{2}-\frac{129}{2}a-12\right){x}+628a^{2}-2022a-397$ |
| 12.1-d4 |
12.1-d |
$6$ |
$8$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{11} \cdot 3 \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 5 \) |
$0.187211276$ |
$23.56580591$ |
3.665192259 |
\( \frac{4252912734935709658813}{3072} a^{2} + \frac{7238557410792780574757}{1536} a + \frac{2498739141595766194709}{3072} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 5\) , \( 0\) , \( \frac{1409991}{2} a^{2} - \frac{257389}{2} a - 7731889\) , \( \frac{1503555951}{2} a^{2} - \frac{274199805}{2} a - 8244549657\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-5\right){x}^{2}+\left(\frac{1409991}{2}a^{2}-\frac{257389}{2}a-7731889\right){x}+\frac{1503555951}{2}a^{2}-\frac{274199805}{2}a-8244549657$ |
| 12.1-d5 |
12.1-d |
$6$ |
$8$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{22} \cdot 3^{2} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.093605638$ |
$94.26322366$ |
3.665192259 |
\( \frac{2277868846225225}{9437184} a^{2} + \frac{3876971730726545}{4718592} a + \frac{1338347244036161}{9437184} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 5\) , \( 0\) , \( 51038 a^{2} - 9317 a - 559734\) , \( 7765708 a^{2} - 1416199 a - 85164402\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-5\right){x}^{2}+\left(51038a^{2}-9317a-559734\right){x}+7765708a^{2}-1416199a-85164402$ |
| 12.1-d6 |
12.1-d |
$6$ |
$8$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{13} \cdot 3^{8} \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.023401409$ |
$94.26322366$ |
3.665192259 |
\( -\frac{89195953}{209952} a^{2} + \frac{204083407}{104976} a + \frac{77410249}{209952} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 5\) , \( 0\) , \( -\frac{16289312128311}{2} a^{2} + \frac{2970674982485}{2} a + 89320336312929\) , \( -6977805862893237218303 a^{2} + 1272539517196133736584 a + 76523791995879966592524\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-5\right){x}^{2}+\left(-\frac{16289312128311}{2}a^{2}+\frac{2970674982485}{2}a+89320336312929\right){x}-6977805862893237218303a^{2}+1272539517196133736584a+76523791995879966592524$ |
| 12.1-e1 |
12.1-e |
$4$ |
$6$ |
3.3.1304.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{12} \cdot 3 \) |
$4.88248$ |
$(-1/2a^2+3/2a+1), (1/2a^2-3/2a), (a^2-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.122347496$ |
$98.52385156$ |
5.007130762 |
\( \frac{785746681187}{3072} a^{2} - \frac{1267450114565}{1536} a - \frac{475649613557}{3072} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -54 a^{2} + 166 a + 44\) , \( \frac{1325}{2} a^{2} - \frac{4261}{2} a - 398\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+4\right){x}^{2}+\left(-54a^{2}+166a+44\right){x}+\frac{1325}{2}a^{2}-\frac{4261}{2}a-398$ |
*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.
