| 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 |
| 2.2-a1 |
2.2-a |
$1$ |
$1$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{7} \) |
$8.96722$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$145.6108409$ |
1.582352674 |
\( -\frac{205591959}{8} a^{3} - \frac{131630593}{4} a^{2} + \frac{429384417}{8} a + \frac{90334967}{2} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 4\) , \( a^{3} - 4 a\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 4 a^{3} - 3 a^{2} - 10 a + 19\) , \( 3 a^{3} + 23 a^{2} - 9 a - 79\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-4\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(4a^{3}-3a^{2}-10a+19\right){x}+3a^{3}+23a^{2}-9a-79$ |
| 4.1-a1 |
4.1-a |
$8$ |
$12$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{27} \) |
$9.77882$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$11.10764894$ |
0.543180580 |
\( -\frac{2017122818183715}{32768} a^{3} - \frac{640304695034345}{32768} a^{2} + \frac{9242080729780363}{32768} a + \frac{6124427747500867}{32768} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( 0\) , \( a^{2} + a - 3\) , \( 62 a^{3} + 71 a^{2} - 151 a - 120\) , \( -155 a^{3} - 239 a^{2} + 216 a + 214\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(62a^{3}+71a^{2}-151a-120\right){x}-155a^{3}-239a^{2}+216a+214$ |
| 4.1-a2 |
4.1-a |
$8$ |
$12$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{9} \) |
$9.77882$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$899.7195644$ |
0.543180580 |
\( -\frac{49083}{32} a^{3} - \frac{22249}{32} a^{2} + \frac{204851}{32} a + \frac{138211}{32} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( 0\) , \( a^{2} + a - 3\) , \( -8 a^{3} - 9 a^{2} + 19 a + 15\) , \( 17 a^{3} + 23 a^{2} - 34 a - 32\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-8a^{3}-9a^{2}+19a+15\right){x}+17a^{3}+23a^{2}-34a-32$ |
| 4.1-a3 |
4.1-a |
$8$ |
$12$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{36} \) |
$9.77882$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$22.21529788$ |
0.543180580 |
\( -\frac{103197418014935772861}{1073741824} a^{3} + \frac{298366089222762532681}{1073741824} a^{2} - \frac{48288901045778826923}{1073741824} a - \frac{218265786975685158499}{1073741824} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{3} + 4 a\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -56 a^{3} + 71 a^{2} + 277 a - 352\) , \( -433 a^{3} + 628 a^{2} + 2029 a - 2774\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-56a^{3}+71a^{2}+277a-352\right){x}-433a^{3}+628a^{2}+2029a-2774$ |
| 4.1-a4 |
4.1-a |
$8$ |
$12$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$9.77882$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$449.8597822$ |
0.543180580 |
\( \frac{418772189971475}{32} a^{3} + \frac{535365435783433}{32} a^{2} - \frac{874080194531195}{32} a - \frac{735200287885507}{32} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{3} + 4 a\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -16 a^{3} + 16 a^{2} + 72 a - 77\) , \( -11 a^{3} + 4 a^{2} + 74 a - 72\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-16a^{3}+16a^{2}+72a-77\right){x}-11a^{3}+4a^{2}+74a-72$ |
| 4.1-a5 |
4.1-a |
$8$ |
$12$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{12} \) |
$9.77882$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1799.439128$ |
0.543180580 |
\( \frac{1078990275}{1024} a^{3} + \frac{1355433161}{1024} a^{2} - \frac{2267242795}{1024} a - \frac{1824613603}{1024} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{3} + 4 a\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -11 a^{3} + 11 a^{2} + 42 a - 37\) , \( 28 a^{3} - 55 a^{2} - 106 a + 184\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-11a^{3}+11a^{2}+42a-37\right){x}+28a^{3}-55a^{2}-106a+184$ |
| 4.1-a6 |
4.1-a |
$8$ |
$12$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{18} \) |
$9.77882$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$5.553824472$ |
0.543180580 |
\( -\frac{4805183673340933833555207645}{32768} a^{3} + \frac{13892842413061957269593102825}{32768} a^{2} - \frac{2248500959882331965050402955}{32768} a - \frac{10163141374849226219320738627}{32768} \) |
\( \bigl[a^{2} + a - 3\) , \( a + 1\) , \( a\) , \( 2597 a^{3} + 802 a^{2} - 11931 a - 7902\) , \( 30604 a^{3} + 9757 a^{2} - 140059 a - 92840\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2597a^{3}+802a^{2}-11931a-7902\right){x}+30604a^{3}+9757a^{2}-140059a-92840$ |
| 4.1-a7 |
4.1-a |
$8$ |
$12$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{21} \) |
$9.77882$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$899.7195644$ |
0.543180580 |
\( \frac{639705026617475}{1048576} a^{3} - \frac{1090455296107255}{1048576} a^{2} - \frac{2430163563461611}{1048576} a + \frac{3631465742455389}{1048576} \) |
\( \bigl[1\) , \( a^{2} + a - 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -7 a^{3} - 3 a^{2} + 19 a\) , \( 12 a^{3} - 6 a^{2} - 38 a + 30\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-7a^{3}-3a^{2}+19a\right){x}+12a^{3}-6a^{2}-38a+30$ |
| 4.1-a8 |
4.1-a |
$8$ |
$12$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{63} \) |
$9.77882$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$11.10764894$ |
0.543180580 |
\( \frac{101013845860548296655747}{1152921504606846976} a^{3} + \frac{502153865167741533013513}{1152921504606846976} a^{2} - \frac{441005339831160151508715}{1152921504606846976} a - \frac{521830695447667986870435}{1152921504606846976} \) |
\( \bigl[1\) , \( a^{2} + a - 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -127 a^{3} - 158 a^{2} + 264 a + 205\) , \( -2046 a^{3} - 2643 a^{2} + 4237 a + 3626\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-127a^{3}-158a^{2}+264a+205\right){x}-2046a^{3}-2643a^{2}+4237a+3626$ |
| 4.1-b1 |
4.1-b |
$4$ |
$14$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{21} \) |
$9.77882$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7^{2} \) |
$1$ |
$500.1076211$ |
2.717334185 |
\( -\frac{1412812356381}{16384} a^{3} + \frac{4086128005673}{16384} a^{2} - \frac{662008212811}{16384} a - \frac{2989342322179}{16384} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{3} - 4 a - 1\) , \( -60 a^{3} - 77 a^{2} + 126 a + 109\) , \( 567 a^{3} + 723 a^{2} - 1189 a - 999\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-60a^{3}-77a^{2}+126a+109\right){x}+567a^{3}+723a^{2}-1189a-999$ |
| 4.1-b2 |
4.1-b |
$4$ |
$14$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{3} \) |
$9.77882$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$2401$ |
\( 2 \) |
$1$ |
$0.208291387$ |
2.717334185 |
\( \frac{581980280458447849610157957}{4} a^{3} - \frac{992057768211267295218506099}{4} a^{2} - \frac{2210873323585808821780844309}{4} a + \frac{3303776061430478937512484869}{4} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{3} - 4 a - 1\) , \( -8300 a^{3} - 11532 a^{2} + 14281 a + 12109\) , \( -1192548 a^{3} - 1564446 a^{2} + 2378949 a + 2027873\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-8300a^{3}-11532a^{2}+14281a+12109\right){x}-1192548a^{3}-1564446a^{2}+2378949a+2027873$ |
| 4.1-b3 |
4.1-b |
$4$ |
$14$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{3} \) |
$9.77882$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$2401$ |
\( 2 \) |
$1$ |
$0.208291387$ |
2.717334185 |
\( -1610437667357251763217109230 a^{3} - 511202207864667599279117666 a^{2} + \frac{14757429802555754254733110503}{2} a + \frac{9779263712874017525699755731}{2} \) |
\( \bigl[1\) , \( -a^{2} - a + 3\) , \( a^{3} - 3 a - 1\) , \( -84 a^{3} + 699 a^{2} + 102 a - 2906\) , \( -3014 a^{3} + 14297 a^{2} + 7947 a - 56731\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-84a^{3}+699a^{2}+102a-2906\right){x}-3014a^{3}+14297a^{2}+7947a-56731$ |
| 4.1-b4 |
4.1-b |
$4$ |
$14$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{21} \) |
$9.77882$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2 \cdot 7^{2} \) |
$1$ |
$500.1076211$ |
2.717334185 |
\( \frac{74777}{128} a^{3} - \frac{923525}{128} a^{2} + \frac{1135483}{128} a + \frac{1314515}{128} \) |
\( \bigl[1\) , \( -a^{2} - a + 3\) , \( a^{3} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 4\) , \( -a^{2} - a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(a^{3}-a^{2}-3a+4\right){x}-a^{2}-a+1$ |
| 4.2-a1 |
4.2-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$9.77882$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 3 \) |
$0.043002079$ |
$3275.488583$ |
1.147985451 |
\( -24165 a^{3} + 74001 a^{2} - 15843 a - 49051 \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{3} - 3 a\) , \( 4 a^{3} - 20 a - 10\) , \( -12 a^{3} - 4 a^{2} + 54 a + 35\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(4a^{3}-20a-10\right){x}-12a^{3}-4a^{2}+54a+35$ |
| 4.2-a2 |
4.2-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$9.77882$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.021501039$ |
$1637.744291$ |
1.147985451 |
\( 12925503 a^{3} + 16520573 a^{2} - 26980423 a - 22682783 \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{3} - 4 a - 1\) , \( -4 a^{3} - 2 a^{2} + 21 a + 18\) , \( -17 a^{3} - 5 a^{2} + 76 a + 50\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-4a^{3}-2a^{2}+21a+18\right){x}-17a^{3}-5a^{2}+76a+50$ |
| 4.2-a3 |
4.2-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$9.77882$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.172008317$ |
$204.7180364$ |
1.147985451 |
\( 254479231303701 a^{3} - 433791499010047 a^{2} - 966736095395959 a + 1444623504900787 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} + a^{2} - 3 a - 5\) , \( a^{2} - 3\) , \( 6 a^{2} + 6 a - 8\) , \( 36 a^{3} + 2 a^{2} - 168 a - 82\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-5\right){x}^{2}+\left(6a^{2}+6a-8\right){x}+36a^{3}+2a^{2}-168a-82$ |
| 4.2-a4 |
4.2-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$9.77882$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.172008317$ |
$204.7180364$ |
1.147985451 |
\( -98865789 a^{3} - 29868857 a^{2} + 456908191 a + 302185093 \) |
\( \bigl[a + 1\) , \( a^{3} - 4 a\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -6 a^{3} + 17 a^{2} - 2 a - 10\) , \( -3 a^{3} + 13 a^{2} - 8 a - 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-6a^{3}+17a^{2}-2a-10\right){x}-3a^{3}+13a^{2}-8a-13$ |
| 4.2-a5 |
4.2-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$9.77882$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.021501039$ |
$1637.744291$ |
1.147985451 |
\( -10502479899 a^{3} + 30361935883 a^{2} - 4909662125 a - 22208249153 \) |
\( \bigl[a + 1\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 4 a - 1\) , \( 4 a^{3} - 4 a^{2} - 14 a + 6\) , \( -a^{3} - 4 a^{2} + 4 a + 24\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(4a^{3}-4a^{2}-14a+6\right){x}-a^{3}-4a^{2}+4a+24$ |
| 4.2-a6 |
4.2-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{4} \) |
$9.77882$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 3 \) |
$0.086004158$ |
$1637.744291$ |
1.147985451 |
\( 5959071 a^{3} - 10164927 a^{2} - 22634295 a + 33861581 \) |
\( \bigl[a + 1\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{2} - 3\) , \( -15 a^{3} - 19 a^{2} + 33 a + 28\) , \( -39 a^{3} - 50 a^{2} + 80 a + 66\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-15a^{3}-19a^{2}+33a+28\right){x}-39a^{3}-50a^{2}+80a+66$ |
| 8.1-a1 |
8.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$10.66388$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$415.0784623$ |
2.255328348 |
\( \frac{94658711543}{4} a^{3} - \frac{161357538715}{4} a^{2} - \frac{359597097919}{4} a + \frac{537356989545}{4} \) |
\( \bigl[a^{2} - 3\) , \( -a - 1\) , \( a^{3} - 4 a - 1\) , \( -12 a^{3} - 16 a^{2} + 24 a + 22\) , \( 54 a^{3} + 69 a^{2} - 114 a - 97\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a^{3}-16a^{2}+24a+22\right){x}+54a^{3}+69a^{2}-114a-97$ |
| 8.1-a2 |
8.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$10.66388$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$830.1569247$ |
2.255328348 |
\( -\frac{23217573}{16} a^{3} - \frac{9201007}{16} a^{2} + \frac{107135741}{16} a + \frac{78532997}{16} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a\) , \( a^{3} - 3 a\) , \( a^{3} + 7 a^{2} - 9 a - 33\) , \( -11 a^{3} + 7 a^{2} + 45 a - 15\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(a^{3}+7a^{2}-9a-33\right){x}-11a^{3}+7a^{2}+45a-15$ |
| 8.1-a3 |
8.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{24} \) |
$10.66388$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$51.88480779$ |
2.255328348 |
\( -\frac{1771507905821}{65536} a^{3} + \frac{5121477086249}{65536} a^{2} - \frac{828769502027}{65536} a - \frac{3746398911491}{65536} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{2} - 3\) , \( -274 a^{3} - 348 a^{2} + 580 a + 488\) , \( -5729 a^{3} - 7317 a^{2} + 11975 a + 10065\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-274a^{3}-348a^{2}+580a+488\right){x}-5729a^{3}-7317a^{2}+11975a+10065$ |
| 8.1-a4 |
8.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$10.66388$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$415.0784623$ |
2.255328348 |
\( \frac{5128409971}{256} a^{3} + \frac{6557639129}{256} a^{2} - \frac{10704842587}{256} a - \frac{9004146323}{256} \) |
\( \bigl[a + 1\) , \( a^{3} + a^{2} - 4 a - 5\) , \( a^{2} - 3\) , \( -2 a^{3} - 3 a^{2} + 8 a + 8\) , \( -5 a^{3} - 7 a^{2} + 10 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-5\right){x}^{2}+\left(-2a^{3}-3a^{2}+8a+8\right){x}-5a^{3}-7a^{2}+10a+7$ |
| 8.1-a5 |
8.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{12} \) |
$10.66388$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$51.88480779$ |
2.255328348 |
\( \frac{76762693584552037}{16} a^{3} + \frac{98134472178793935}{16} a^{2} - \frac{160222550947528285}{16} a - \frac{134765159868517637}{16} \) |
\( \bigl[a + 1\) , \( a^{3} + a^{2} - 4 a - 5\) , \( a^{2} - 3\) , \( -27 a^{3} - 33 a^{2} + 58 a + 48\) , \( -230 a^{3} - 298 a^{2} + 482 a + 407\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-5\right){x}^{2}+\left(-27a^{3}-33a^{2}+58a+48\right){x}-230a^{3}-298a^{2}+482a+407$ |
| 8.1-a6 |
8.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$10.66388$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$415.0784623$ |
2.255328348 |
\( -\frac{56843346346407}{4} a^{3} - \frac{18043811560901}{4} a^{2} + \frac{260445243508207}{4} a + \frac{172588499469335}{4} \) |
\( \bigl[a + 1\) , \( -a^{3} + 3 a + 2\) , \( a^{2} + a - 2\) , \( 11 a^{3} - 3 a^{2} - 9 a - 1\) , \( -202 a^{3} - 215 a^{2} + 398 a + 315\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+3a+2\right){x}^{2}+\left(11a^{3}-3a^{2}-9a-1\right){x}-202a^{3}-215a^{2}+398a+315$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{11} \) |
$10.66388$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$241.6489716$ |
2.625998819 |
\( 93198 a^{3} - 268937 a^{2} + 43293 a + 196636 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( -a^{3} + a^{2} + 5 a - 3\) , \( a^{3} - 4 a - 1\) , \( -a^{3} - 3 a^{2} + 9 a + 18\) , \( -5 a^{3} + a^{2} + 25 a + 9\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-3\right){x}^{2}+\left(-a^{3}-3a^{2}+9a+18\right){x}-5a^{3}+a^{2}+25a+9$ |
| 8.2-b1 |
8.2-b |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{4} \) |
$10.66388$ |
$(a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2598.547311$ |
0.882450239 |
\( -45500971 a^{3} + 131552831 a^{2} - 21289773 a - 96234869 \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 3\) , \( a + 1\) , \( -a^{2} + a + 2\) , \( -a\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{2}+a+2\right){x}-a$ |
| 8.2-b2 |
8.2-b |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$10.66388$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1299.273655$ |
0.882450239 |
\( 995 a^{3} - 1495 a^{2} - 235 a + 39261 \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{2} - 3\) , \( -5 a^{3} + 7 a^{2} + 19 a - 23\) , \( 5 a^{3} - 9 a^{2} - 19 a + 30\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-5a^{3}+7a^{2}+19a-23\right){x}+5a^{3}-9a^{2}-19a+30$ |
| 8.2-b3 |
8.2-b |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$10.66388$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$10.15057543$ |
0.882450239 |
\( -330313590884355525 a^{3} - 104851643977732475 a^{2} + 1513433189345287375 a + 1002902434125191903 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 46 a^{3} - 125 a^{2} - 9 a + 118\) , \( 350 a^{3} - 1059 a^{2} + 238 a + 722\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(46a^{3}-125a^{2}-9a+118\right){x}+350a^{3}-1059a^{2}+238a+722$ |
| 8.2-b4 |
8.2-b |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{4} \) |
$10.66388$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$649.6368277$ |
0.882450239 |
\( 197387951 a^{3} - 336472311 a^{2} - 749853167 a + 1120528669 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - a^{2} - 5 a + 2\) , \( a^{3} + a^{2} - 4 a - 4\) , \( 3 a^{2} - 2 a - 13\) , \( a^{3} - 7 a\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+2\right){x}^{2}+\left(3a^{2}-2a-13\right){x}+a^{3}-7a$ |
| 8.2-b5 |
8.2-b |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{4} \) |
$10.66388$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$162.4092069$ |
0.882450239 |
\( -82698225 a^{3} + 115466225 a^{2} + 746782625 a + 439944053 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 5 a + 2\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -80 a^{3} - 103 a^{2} + 166 a + 141\) , \( -1002 a^{3} - 1298 a^{2} + 2047 a + 1736\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(-a^{3}+5a+2\right){x}^{2}+\left(-80a^{3}-103a^{2}+166a+141\right){x}-1002a^{3}-1298a^{2}+2047a+1736$ |
| 8.2-b6 |
8.2-b |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$10.66388$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$10.15057543$ |
0.882450239 |
\( 259947873688049605 a^{3} + 332320899481110395 a^{2} - 542574908340088015 a - 456366434264040719 \) |
\( \bigl[a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 3 a\) , \( 186 a^{3} + 67 a^{2} - 866 a - 577\) , \( 2558 a^{3} + 786 a^{2} - 11680 a - 7728\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(186a^{3}+67a^{2}-866a-577\right){x}+2558a^{3}+786a^{2}-11680a-7728$ |
| 8.3-a1 |
8.3-a |
$1$ |
$1$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{9} \) |
$10.66388$ |
$(a^2-2), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$197.0876183$ |
2.141750696 |
\( \frac{721}{2} a^{3} - 564 a^{2} - \frac{1981}{2} a - 294 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -3 a - 1\) , \( 2 a^{3} + 2 a^{2} - 7 a - 5\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-1\right){x}+2a^{3}+2a^{2}-7a-5$ |
| 11.1-a1 |
11.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{2} \) |
$11.09694$ |
$(-a^3+5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$263.1546805$ |
1.429850654 |
\( \frac{52453191882531334063690}{121} a^{3} - \frac{89412989102580946117087}{121} a^{2} - \frac{199263388406668517565355}{121} a + \frac{297765414922041632920059}{121} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{2} - 4\) , \( a + 1\) , \( -63 a^{3} + 105 a^{2} + 249 a - 361\) , \( 569 a^{3} - 911 a^{2} - 2370 a + 3401\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-63a^{3}+105a^{2}+249a-361\right){x}+569a^{3}-911a^{2}-2370a+3401$ |
| 11.1-a2 |
11.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$11.09694$ |
$(-a^3+5a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1052.618722$ |
1.429850654 |
\( \frac{113942645520611}{14641} a^{3} - \frac{194229307373892}{14641} a^{2} - \frac{432854923791669}{14641} a + \frac{646828300879973}{14641} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{2} - 4\) , \( a + 1\) , \( 2 a^{3} - 10 a^{2} + 19 a - 6\) , \( -7 a^{3} + 40 a^{2} - 62 a + 27\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(2a^{3}-10a^{2}+19a-6\right){x}-7a^{3}+40a^{2}-62a+27$ |
| 11.1-a3 |
11.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$11.09694$ |
$(-a^3+5a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1052.618722$ |
1.429850654 |
\( -\frac{1191940424}{121} a^{3} - \frac{385426302}{121} a^{2} + \frac{5466848130}{121} a + \frac{3655092681}{121} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a\) , \( -48 a^{3} - 63 a^{2} + 100 a + 91\) , \( 322 a^{3} + 409 a^{2} - 676 a - 564\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(-48a^{3}-63a^{2}+100a+91\right){x}+322a^{3}+409a^{2}-676a-564$ |
| 11.1-a4 |
11.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$11.09694$ |
$(-a^3+5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$526.3093611$ |
1.429850654 |
\( -\frac{472250}{11} a^{3} + \frac{1408906}{11} a^{2} - \frac{295898}{11} a - \frac{1054151}{11} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -4 a^{3} + 6 a^{2} + 15 a - 19\) , \( 2 a^{3} - 2 a^{2} - 8 a + 5\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-4a^{3}+6a^{2}+15a-19\right){x}+2a^{3}-2a^{2}-8a+5$ |
| 11.1-a5 |
11.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$11.09694$ |
$(-a^3+5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$131.5773402$ |
1.429850654 |
\( -\frac{6711090864784099}{11} a^{3} - \frac{2130296807619402}{11} a^{2} + \frac{30748947414059961}{11} a + \frac{20376313428774907}{11} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + 5 a + 2\) , \( a^{3} - 3 a - 1\) , \( -35 a^{3} + 19 a^{2} + 42 a + 5\) , \( 91 a^{3} + 9 a^{2} - 130 a - 45\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{3}+5a+2\right){x}^{2}+\left(-35a^{3}+19a^{2}+42a+5\right){x}+91a^{3}+9a^{2}-130a-45$ |
| 11.1-a6 |
11.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{8} \) |
$11.09694$ |
$(-a^3+5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$263.1546805$ |
1.429850654 |
\( -\frac{208267603474769842}{214358881} a^{3} + \frac{602139161231955759}{214358881} a^{2} - \frac{97425123052023429}{214358881} a - \frac{440518860090715787}{214358881} \) |
\( \bigl[1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 3\) , \( 12 a^{3} + 15 a^{2} - 24 a - 19\) , \( -15 a^{3} - 19 a^{2} + 30 a + 23\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(12a^{3}+15a^{2}-24a-19\right){x}-15a^{3}-19a^{2}+30a+23$ |
| 16.1-a1 |
16.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{5} \) |
$11.62904$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$188.2502113$ |
1.022857307 |
\( -\frac{37371}{2} a^{3} - \frac{12329}{2} a^{2} + \frac{171955}{2} a + \frac{114211}{2} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} - a + 3\) , \( a^{3} + a^{2} - 4 a - 4\) , \( 2 a^{3} - a^{2} - 8 a + 1\) , \( a^{3} - a^{2} - 5 a - 1\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(2a^{3}-a^{2}-8a+1\right){x}+a^{3}-a^{2}-5a-1$ |
| 16.1-a2 |
16.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{19} \) |
$11.62904$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$188.2502113$ |
1.022857307 |
\( -\frac{23645373655037}{256} a^{3} - \frac{7505912173175}{256} a^{2} + \frac{108338593297301}{256} a + \frac{71793012043229}{256} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{2} - 3\) , \( -140 a^{3} + 229 a^{2} + 533 a - 754\) , \( 1547 a^{3} - 2647 a^{2} - 5873 a + 8822\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+4\right){x}^{2}+\left(-140a^{3}+229a^{2}+533a-754\right){x}+1547a^{3}-2647a^{2}-5873a+8822$ |
| 16.1-a3 |
16.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$11.62904$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$376.5004227$ |
1.022857307 |
\( -\frac{741813}{4} a^{3} + \frac{2332849}{4} a^{2} - \frac{565691}{4} a - \frac{1600003}{4} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a + 1\) , \( -48 a^{3} - 65 a^{2} + 97 a + 91\) , \( -556 a^{3} - 711 a^{2} + 1157 a + 970\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-2\right){x}^{2}+\left(-48a^{3}-65a^{2}+97a+91\right){x}-556a^{3}-711a^{2}+1157a+970$ |
| 16.1-a4 |
16.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{11} \) |
$11.62904$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$47.06255283$ |
1.022857307 |
\( -\frac{1295043592119}{2} a^{3} + \frac{3745199226953}{2} a^{2} - \frac{609385447629}{2} a - \frac{2736233118363}{2} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a + 1\) , \( -93 a^{3} - 115 a^{2} + 212 a + 181\) , \( 137 a^{3} + 193 a^{2} - 242 a - 222\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-2\right){x}^{2}+\left(-93a^{3}-115a^{2}+212a+181\right){x}+137a^{3}+193a^{2}-242a-222$ |
| 16.1-a5 |
16.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{14} \) |
$11.62904$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$376.5004227$ |
1.022857307 |
\( \frac{16524955731}{16} a^{3} + \frac{21127597321}{16} a^{2} - \frac{34486784731}{16} a - \frac{29008811747}{16} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 3\) , \( a^{2} + a - 2\) , \( a^{3} - a^{2} - 6 a - 3\) , \( -2 a^{3} - a^{2} + 8 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(a^{3}-a^{2}-6a-3\right){x}-2a^{3}-a^{2}+8a+3$ |
| 16.1-a6 |
16.1-a |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{13} \) |
$11.62904$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$47.06255283$ |
1.022857307 |
\( \frac{51012343375668314641}{4} a^{3} + \frac{65214874023760232715}{4} a^{2} - \frac{106475260361010186677}{4} a - \frac{89557652154197998525}{4} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 3\) , \( a^{2} + a - 2\) , \( a^{3} - 11 a^{2} - 6 a + 17\) , \( -6 a^{3} - 9 a^{2} + 10 a + 31\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(a^{3}-11a^{2}-6a+17\right){x}-6a^{3}-9a^{2}+10a+31$ |
| 16.1-b1 |
16.1-b |
$2$ |
$2$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{13} \) |
$11.62904$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$420.9402750$ |
2.287178501 |
\( \frac{43903263}{4} a^{3} + \frac{57076013}{4} a^{2} - \frac{92895955}{4} a - \frac{77071555}{4} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - a^{2} - 5 a + 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -5 a^{3} + 8 a^{2} + 16 a - 31\) , \( 6 a^{3} - 10 a^{2} - 24 a + 31\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+3\right){x}^{2}+\left(-5a^{3}+8a^{2}+16a-31\right){x}+6a^{3}-10a^{2}-24a+31$ |
| 16.1-b2 |
16.1-b |
$2$ |
$2$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{11} \) |
$11.62904$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$420.9402750$ |
2.287178501 |
\( -\frac{1310137}{2} a^{3} - \frac{417785}{2} a^{2} + \frac{5998669}{2} a + \frac{3975659}{2} \) |
\( \bigl[a + 1\) , \( -a^{3} + 4 a + 1\) , \( a + 1\) , \( -15 a^{3} + 22 a^{2} + 58 a - 74\) , \( 217 a^{3} - 372 a^{2} - 823 a + 1237\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-15a^{3}+22a^{2}+58a-74\right){x}+217a^{3}-372a^{2}-823a+1237$ |
| 16.1-c1 |
16.1-c |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{13} \) |
$11.62904$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$88.77307244$ |
0.964696774 |
\( -\frac{57697350051}{32} a^{3} - \frac{18314719337}{32} a^{2} + \frac{264358068235}{32} a + \frac{175180662467}{32} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 0\) , \( -16 a^{3} + 40 a^{2} + 10 a - 39\) , \( -267 a^{3} + 755 a^{2} - 61 a - 623\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(-16a^{3}+40a^{2}+10a-39\right){x}-267a^{3}+755a^{2}-61a-623$ |
| 16.1-c2 |
16.1-c |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{28} \) |
$11.62904$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$355.0922897$ |
0.964696774 |
\( -\frac{8099428733565}{1048576} a^{3} + \frac{23430249137161}{1048576} a^{2} - \frac{3808217817323}{1048576} a - \frac{17127172414115}{1048576} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + 2\) , \( a^{2} - 3\) , \( -12 a^{3} - 7 a^{2} + 31 a + 2\) , \( -35 a^{3} - 21 a^{2} + 87 a + 4\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-12a^{3}-7a^{2}+31a+2\right){x}-35a^{3}-21a^{2}+87a+4$ |
| 16.1-c3 |
16.1-c |
$6$ |
$8$ |
4.4.8468.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{20} \) |
$11.62904$ |
$(a^2-2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$88.77307244$ |
0.964696774 |
\( -\frac{971173930893075011}{1024} a^{3} + \frac{2807877612301492663}{1024} a^{2} - \frac{454443877219076181}{1024} a - \frac{2054069067625927837}{1024} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + 2\) , \( a^{2} - 3\) , \( -137 a^{3} - 187 a^{2} + 286 a + 262\) , \( -2121 a^{3} - 2639 a^{2} + 4453 a + 3564\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-137a^{3}-187a^{2}+286a+262\right){x}-2121a^{3}-2639a^{2}+4453a+3564$ |
*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.
