| 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 |
$6$ |
$8$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2^{2} \) |
$12.06019$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$265.7208275$ |
1.073516550 |
\( -\frac{619120789957}{4} a^{3} + 571684563734 a^{2} - 349041434175 a - \frac{731162132321}{4} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 5\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -108 a^{3} + 247 a^{2} + 349 a - 636\) , \( 1233 a^{3} - 2879 a^{2} - 3981 a + 7506\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-5\right){x}^{2}+\left(-108a^{3}+247a^{2}+349a-636\right){x}+1233a^{3}-2879a^{2}-3981a+7506$ |
| 2.1-a2 |
2.1-a |
$6$ |
$8$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$12.06019$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$531.4416550$ |
1.073516550 |
\( -\frac{7840733}{2} a^{3} + 2638716 a^{2} + 19150527 a + \frac{11768547}{2} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{2} - 2\) , \( 3 a^{3} - 3 a^{2} - 15 a - 2\) , \( 31 a^{3} - 21 a^{2} - 153 a - 48\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(3a^{3}-3a^{2}-15a-2\right){x}+31a^{3}-21a^{2}-153a-48$ |
| 2.1-a3 |
2.1-a |
$6$ |
$8$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2^{2} \) |
$12.06019$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1062.883310$ |
1.073516550 |
\( \frac{6943429}{4} a^{3} - 4041934 a^{2} - 5607967 a + \frac{42114161}{4} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{2} + 2 a + 2\) , \( a^{2} - 3\) , \( -a^{3} - 3 a^{2} + 8 a + 8\) , \( -2 a^{3} + 3 a^{2} + 6 a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-a^{3}-3a^{2}+8a+8\right){x}-2a^{3}+3a^{2}+6a$ |
| 2.1-a4 |
2.1-a |
$6$ |
$8$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$12.06019$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$132.8604137$ |
1.073516550 |
\( \frac{41221585109029}{2} a^{3} - 48017458659352 a^{2} - 66610464161855 a + \frac{250034209424861}{2} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{2} + 2 a + 2\) , \( a^{2} - 3\) , \( -11 a^{3} + 7 a^{2} + 13 a + 8\) , \( 30 a^{3} - 15 a^{2} - 21 a - 6\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-11a^{3}+7a^{2}+13a+8\right){x}+30a^{3}-15a^{2}-21a-6$ |
| 2.1-a5 |
2.1-a |
$6$ |
$8$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2^{4} \) |
$12.06019$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1062.883310$ |
1.073516550 |
\( -\frac{1493163}{16} a^{3} + \frac{1366361}{4} a^{2} - \frac{813155}{4} a - \frac{1652223}{16} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 6 a^{3} - 6 a^{2} - 29 a - 3\) , \( -11 a^{3} + 6 a^{2} + 53 a + 19\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+3\right){x}^{2}+\left(6a^{3}-6a^{2}-29a-3\right){x}-11a^{3}+6a^{2}+53a+19$ |
| 2.1-a6 |
2.1-a |
$6$ |
$8$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2^{8} \) |
$12.06019$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$265.7208275$ |
1.073516550 |
\( -\frac{3790441995}{256} a^{3} + \frac{676732249}{64} a^{2} + \frac{4719205361}{64} a + \frac{5794180513}{256} \) |
\( \bigl[1\) , \( a - 1\) , \( a^{2} - 2\) , \( -127 a^{3} - 90 a^{2} + 267 a + 95\) , \( -2461 a^{3} - 1705 a^{2} + 5250 a + 1827\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-127a^{3}-90a^{2}+267a+95\right){x}-2461a^{3}-1705a^{2}+5250a+1827$ |
| 2.2-a1 |
2.2-a |
$6$ |
$8$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2 \) |
$12.06019$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$531.4416550$ |
1.073516550 |
\( \frac{7840733}{2} a^{3} - \frac{18244767}{2} a^{2} - \frac{25333719}{2} a + 23753150 \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -9 a^{3} + 17 a^{2} + 33 a - 32\) , \( -13 a^{3} + 25 a^{2} + 48 a - 51\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-3\right){x}^{2}+\left(-9a^{3}+17a^{2}+33a-32\right){x}-13a^{3}+25a^{2}+48a-51$ |
| 2.2-a2 |
2.2-a |
$6$ |
$8$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{2} \) |
$12.06019$ |
$(a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1062.883310$ |
1.073516550 |
\( -\frac{6943429}{4} a^{3} + \frac{4662551}{4} a^{2} + \frac{33937053}{4} a + \frac{5228993}{2} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 2 a^{3} - 6 a - 3\) , \( -a^{3} + 2 a - 2\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(2a^{3}-6a-3\right){x}-a^{3}+2a-2$ |
| 2.2-a3 |
2.2-a |
$6$ |
$8$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2 \) |
$12.06019$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$132.8604137$ |
1.073516550 |
\( -\frac{41221585109029}{2} a^{3} + \frac{27629838008383}{2} a^{2} + \frac{201626007634031}{2} a + 30999974445738 \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 12 a^{3} - 20 a^{2} - a + 2\) , \( -8 a^{3} + 73 a^{2} - 61 a - 31\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(12a^{3}-20a^{2}-a+2\right){x}-8a^{3}+73a^{2}-61a-31$ |
| 2.2-a4 |
2.2-a |
$6$ |
$8$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{4} \) |
$12.06019$ |
$(a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1062.883310$ |
1.073516550 |
\( \frac{1493163}{16} a^{3} + \frac{985955}{16} a^{2} - \frac{3198779}{16} a - \frac{466281}{8} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{2} + 3\) , \( a\) , \( -9 a^{3} + 14 a^{2} + 34 a - 23\) , \( 3 a^{3} - 12 a^{2} - 5 a + 40\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-9a^{3}+14a^{2}+34a-23\right){x}+3a^{3}-12a^{2}-5a+40$ |
| 2.2-a5 |
2.2-a |
$6$ |
$8$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{2} \) |
$12.06019$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$265.7208275$ |
1.073516550 |
\( \frac{619120789957}{4} a^{3} + \frac{429375885065}{4} a^{2} - \frac{1319948403301}{4} a - \frac{229855202021}{2} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a\) , \( 105 a^{3} - 71 a^{2} - 513 a - 154\) , \( -840 a^{3} + 561 a^{2} + 4110 a + 1271\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(105a^{3}-71a^{2}-513a-154\right){x}-840a^{3}+561a^{2}+4110a+1271$ |
| 2.2-a6 |
2.2-a |
$6$ |
$8$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
2.2 |
\( 2 \) |
\( 2^{8} \) |
$12.06019$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$265.7208275$ |
1.073516550 |
\( \frac{3790441995}{256} a^{3} - \frac{8664396989}{256} a^{2} - \frac{12919353451}{256} a + \frac{11793744479}{128} \) |
\( \bigl[1\) , \( -a\) , \( a^{2} - 3\) , \( 127 a^{3} - 471 a^{2} + 293 a + 146\) , \( 2460 a^{3} - 9086 a^{2} + 5544 a + 2909\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}-a{x}^{2}+\left(127a^{3}-471a^{2}+293a+146\right){x}+2460a^{3}-9086a^{2}+5544a+2909$ |
| 4.1-a1 |
4.1-a |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{9} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.856387478$ |
$528.7585263$ |
2.439212162 |
\( \frac{55551499}{64} a^{3} + \frac{5153177}{16} a^{2} - \frac{31243571}{16} a - \frac{837273}{64} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - 4 a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 14 a^{2} - 19 a - 9\) , \( 2 a^{3} + 8 a^{2} - 13 a - 5\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-4a-3\right){x}^{2}+\left(14a^{2}-19a-9\right){x}+2a^{3}+8a^{2}-13a-5$ |
| 4.1-a2 |
4.1-a |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{11} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$2.569162434$ |
$6.527883041$ |
2.439212162 |
\( \frac{78090946968383133271389}{512} a^{3} + \frac{54158039788414000050149}{512} a^{2} - \frac{166487742800179523590269}{512} a - \frac{28992098126199977770199}{256} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - 4 a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 40 a^{3} - 171 a^{2} + 111 a + 51\) , \( 485 a^{3} - 2100 a^{2} + 1402 a + 705\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-4a-3\right){x}^{2}+\left(40a^{3}-171a^{2}+111a+51\right){x}+485a^{3}-2100a^{2}+1402a+705$ |
| 4.1-a3 |
4.1-a |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{27} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.712774956$ |
$264.3792631$ |
2.439212162 |
\( -\frac{137939962377536181}{16777216} a^{3} + \frac{509484747527592835}{16777216} a^{2} - \frac{311065423629019051}{16777216} a - \frac{81451387571906785}{8388608} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 5\) , \( 4 a^{3} + 21 a^{2} - 4 a - 41\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a^{3}-5\right){x}+4a^{3}+21a^{2}-4a-41$ |
| 4.1-a4 |
4.1-a |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{22} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$1.284581217$ |
$13.05576608$ |
2.439212162 |
\( \frac{761611006401787}{262144} a^{3} + \frac{528825605871283}{262144} a^{2} - \frac{1631943548046683}{262144} a - \frac{277572643256305}{131072} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 5 a + 2\) , \( a^{3} - 5 a - 2\) , \( -339 a^{3} + 815 a^{2} + 1078 a - 2185\) , \( -7153 a^{3} + 16767 a^{2} + 23042 a - 43919\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+2\right){x}^{2}+\left(-339a^{3}+815a^{2}+1078a-2185\right){x}-7153a^{3}+16767a^{2}+23042a-43919$ |
| 4.1-a5 |
4.1-a |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{18} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.428193739$ |
$1057.517052$ |
2.439212162 |
\( -\frac{775099}{4096} a^{3} + \frac{325913}{1024} a^{2} + \frac{1405713}{1024} a + \frac{9152113}{4096} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 5 a + 2\) , \( a^{3} - 5 a - 2\) , \( -4 a^{3} + 15 a^{2} + 8 a - 45\) , \( -2 a^{3} + 9 a^{2} + 4 a - 27\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+2\right){x}^{2}+\left(-4a^{3}+15a^{2}+8a-45\right){x}-2a^{3}+9a^{2}+4a-27$ |
| 4.1-a6 |
4.1-a |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{17} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$2.569162434$ |
$1.631970760$ |
2.439212162 |
\( -\frac{280401766250925363}{512} a^{3} + \frac{1034629287445097955}{512} a^{2} - \frac{629865483106281211}{512} a - \frac{20638781304796925}{32} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -213 a^{3} + 305 a^{2} + 615 a - 867\) , \( -2875 a^{3} + 4341 a^{2} + 8409 a - 12175\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(-213a^{3}+305a^{2}+615a-867\right){x}-2875a^{3}+4341a^{2}+8409a-12175$ |
| 4.1-a7 |
4.1-a |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{27} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.856387478$ |
$132.1896315$ |
2.439212162 |
\( -\frac{237926148587}{16777216} a^{3} + \frac{189399317433}{4194304} a^{2} - \frac{64016324079}{4194304} a - \frac{147860638399}{16777216} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 12 a^{3} - 25 a^{2} - 35 a + 73\) , \( 2 a^{3} - 31 a^{2} - 13 a + 77\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(12a^{3}-25a^{2}-35a+73\right){x}+2a^{3}-31a^{2}-13a+77$ |
| 4.1-a8 |
4.1-a |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{19} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$5.138324868$ |
$3.263941520$ |
2.439212162 |
\( \frac{242040755788705504414306661066662661}{262144} a^{3} - \frac{563888926547782432185802163326932659}{262144} a^{2} - \frac{782233519623267834773636928774173349}{262144} a + \frac{734063714311722039417478948314159089}{131072} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 5\) , \( a^{3} - 5 a - 1\) , \( -187 a^{3} + 626 a^{2} - 349 a - 222\) , \( 12566 a^{3} - 46564 a^{2} + 28613 a + 14737\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+5\right){x}^{2}+\left(-187a^{3}+626a^{2}-349a-222\right){x}+12566a^{3}-46564a^{2}+28613a+14737$ |
| 4.1-a9 |
4.1-a |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{9} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.712774956$ |
$264.3792631$ |
2.439212162 |
\( -\frac{1211116029998867}{64} a^{3} + \frac{811492257554189}{64} a^{2} + \frac{5924196660024347}{64} a + \frac{911455142569285}{32} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 5\) , \( a^{3} - 5 a - 1\) , \( 13 a^{3} - 84 a^{2} + 46 a + 38\) , \( -471 a^{3} + 1907 a^{2} - 1237 a - 623\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+5\right){x}^{2}+\left(13a^{3}-84a^{2}+46a+38\right){x}-471a^{3}+1907a^{2}-1237a-623$ |
| 4.1-a10 |
4.1-a |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{18} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.856387478$ |
$1057.517052$ |
2.439212162 |
\( -\frac{6814982421}{4096} a^{3} + \frac{4701382115}{4096} a^{2} + \frac{32854186741}{4096} a + \frac{5318720799}{2048} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 5\) , \( a^{3} - 5 a - 1\) , \( 33 a^{3} - 119 a^{2} + 61 a + 48\) , \( -301 a^{3} + 1114 a^{2} - 690 a - 349\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+5\right){x}^{2}+\left(33a^{3}-119a^{2}+61a+48\right){x}-301a^{3}+1114a^{2}-690a-349$ |
| 4.1-a11 |
4.1-a |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{38} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$2.569162434$ |
$13.05576608$ |
2.439212162 |
\( \frac{25244062543252502649437931}{68719476736} a^{3} - \frac{58811778546102253618393565}{68719476736} a^{2} - \frac{81584408494612303988948299}{68719476736} a + \frac{76560454679459868202267199}{34359738368} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 5\) , \( a^{3} - 5 a - 1\) , \( 138 a^{3} - 549 a^{2} + 341 a + 188\) , \( 2457 a^{3} - 9401 a^{2} + 5861 a + 3045\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+5\right){x}^{2}+\left(138a^{3}-549a^{2}+341a+188\right){x}+2457a^{3}-9401a^{2}+5861a+3045$ |
| 4.1-a12 |
4.1-a |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{73} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$5.138324868$ |
$3.263941520$ |
2.439212162 |
\( -\frac{34604215282042281704676226101}{4722366482869645213696} a^{3} + \frac{80619066741497191268959792643}{4722366482869645213696} a^{2} + \frac{111827495038782804569975667157}{4722366482869645213696} a - \frac{104940827717958463993588143201}{2361183241434822606848} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 5 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -81 a^{3} + 24 a^{2} + 464 a + 146\) , \( 642 a^{3} - 317 a^{2} - 3434 a - 1078\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(-81a^{3}+24a^{2}+464a+146\right){x}+642a^{3}-317a^{2}-3434a-1078$ |
| 4.1-b1 |
4.1-b |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{17} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$2.569162434$ |
$1.631970760$ |
2.439212162 |
\( \frac{280401766250925363}{512} a^{3} + \frac{96711994346160933}{256} a^{2} - \frac{299093896515569305}{256} a - \frac{205858462788859419}{512} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( a^{2} - a - 3\) , \( 210 a^{3} - 330 a^{2} - 576 a - 161\) , \( 3369 a^{3} - 5116 a^{2} - 9720 a - 2540\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-4\right){x}^{2}+\left(210a^{3}-330a^{2}-576a-161\right){x}+3369a^{3}-5116a^{2}-9720a-2540$ |
| 4.1-b2 |
4.1-b |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{27} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.856387478$ |
$132.1896315$ |
2.439212162 |
\( \frac{237926148587}{16777216} a^{3} + \frac{43818823971}{16777216} a^{2} - \frac{545350797387}{16777216} a + \frac{57872593215}{8388608} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( a^{2} - a - 3\) , \( -15 a^{3} + 15 a^{2} + 59 a + 24\) , \( -38 a^{3} + 18 a^{2} + 205 a + 60\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-4\right){x}^{2}+\left(-15a^{3}+15a^{2}+59a+24\right){x}-38a^{3}+18a^{2}+205a+60$ |
| 4.1-b3 |
4.1-b |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{19} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$5.138324868$ |
$3.263941520$ |
2.439212162 |
\( -\frac{242040755788705504414306661066662661}{262144} a^{3} + \frac{40558335204583520264279454968263831}{65536} a^{2} + \frac{295972276338179046475580318057012671}{65536} a + \frac{364045738241099316289825465593874831}{262144} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{2} + a + 4\) , \( a^{3} - 4 a - 1\) , \( 186 a^{3} + 62 a^{2} - 334 a - 122\) , \( -12129 a^{3} - 8459 a^{2} + 25756 a + 8984\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(186a^{3}+62a^{2}-334a-122\right){x}-12129a^{3}-8459a^{2}+25756a+8984$ |
| 4.1-b4 |
4.1-b |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{9} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.712774956$ |
$264.3792631$ |
2.439212162 |
\( \frac{1211116029998867}{64} a^{3} - \frac{705463958110603}{16} a^{2} - \frac{978458271284031}{16} a + \frac{7347483172718239}{64} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{2} + a + 4\) , \( a^{3} - 4 a - 1\) , \( -14 a^{3} - 48 a^{2} + 91 a + 23\) , \( 398 a^{3} + 526 a^{2} - 1080 a - 392\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-14a^{3}-48a^{2}+91a+23\right){x}+398a^{3}+526a^{2}-1080a-392$ |
| 4.1-b5 |
4.1-b |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{18} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.856387478$ |
$1057.517052$ |
2.439212162 |
\( \frac{6814982421}{4096} a^{3} - \frac{3935891287}{1024} a^{2} - \frac{5453000927}{1024} a + \frac{41378028033}{4096} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{2} + a + 4\) , \( a^{3} - 4 a - 1\) , \( -34 a^{3} - 23 a^{2} + 86 a + 33\) , \( 213 a^{3} + 158 a^{2} - 441 a - 154\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-34a^{3}-23a^{2}+86a+33\right){x}+213a^{3}+158a^{2}-441a-154$ |
| 4.1-b6 |
4.1-b |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{38} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$2.569162434$ |
$13.05576608$ |
2.439212162 |
\( -\frac{25244062543252502649437931}{68719476736} a^{3} + \frac{4230102270913813582480057}{17179869184} a^{2} + \frac{30868944489264825819355409}{17179869184} a + \frac{37968784861457681446630465}{68719476736} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{2} + a + 4\) , \( a^{3} - 4 a - 1\) , \( -139 a^{3} - 138 a^{2} + 351 a + 128\) , \( -2870 a^{3} - 2238 a^{2} + 6384 a + 2244\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-139a^{3}-138a^{2}+351a+128\right){x}-2870a^{3}-2238a^{2}+6384a+2244$ |
| 4.1-b7 |
4.1-b |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{22} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$1.284581217$ |
$13.05576608$ |
2.439212162 |
\( -\frac{761611006401787}{262144} a^{3} + \frac{703414656269161}{65536} a^{2} - \frac{427635170725311}{65536} a - \frac{896652222286223}{262144} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 2 a - 2\) , \( 1\) , \( 341 a^{3} - 207 a^{2} - 1698 a - 620\) , \( 6813 a^{3} - 4488 a^{2} - 33422 a - 10636\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(341a^{3}-207a^{2}-1698a-620\right){x}+6813a^{3}-4488a^{2}-33422a-10636$ |
| 4.1-b8 |
4.1-b |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{18} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.428193739$ |
$1057.517052$ |
2.439212162 |
\( \frac{775099}{4096} a^{3} - \frac{1021645}{4096} a^{2} - \frac{5904859}{4096} a + \frac{7651759}{2048} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 2 a - 2\) , \( 1\) , \( 6 a^{3} - 2 a^{2} - 33 a - 15\) , \( -3 a^{3} + 2 a^{2} + 14 a + 6\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(6a^{3}-2a^{2}-33a-15\right){x}-3a^{3}+2a^{2}+14a+6$ |
| 4.1-b9 |
4.1-b |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{27} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.712774956$ |
$264.3792631$ |
2.439212162 |
\( \frac{137939962377536181}{16777216} a^{3} + \frac{23916215098746073}{4194304} a^{2} - \frac{73521046073389519}{4194304} a - \frac{102423413622775967}{16777216} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 5 a + 2\) , \( a^{3} - 5 a - 1\) , \( a^{3} - 14 a + 2\) , \( -3 a^{3} + 31 a^{2} - 55 a - 18\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+2\right){x}^{2}+\left(a^{3}-14a+2\right){x}-3a^{3}+31a^{2}-55a-18$ |
| 4.1-b10 |
4.1-b |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{9} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.856387478$ |
$528.7585263$ |
2.439212162 |
\( -\frac{55551499}{64} a^{3} + \frac{187267205}{64} a^{2} - \frac{82905629}{64} a - \frac{24823675}{32} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{2} + a + 4\) , \( a^{3} - 4 a - 1\) , \( 3 a^{3} - 4 a + 6\) , \( a^{3} + 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(3a^{3}-4a+6\right){x}+a^{3}+4$ |
| 4.1-b11 |
4.1-b |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{11} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$2.569162434$ |
$6.527883041$ |
2.439212162 |
\( -\frac{78090946968383133271389}{512} a^{3} + \frac{72107720173390849966079}{128} a^{2} - \frac{44025294420449469081049}{128} a - \frac{92222952295782345809129}{512} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{2} + a + 4\) , \( a^{3} - 4 a - 1\) , \( -37 a^{3} - 65 a^{2} + 116 a + 51\) , \( -522 a^{3} - 534 a^{2} + 1277 a + 464\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-37a^{3}-65a^{2}+116a+51\right){x}-522a^{3}-534a^{2}+1277a+464$ |
| 4.1-b12 |
4.1-b |
$12$ |
$24$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{73} \) |
$13.15173$ |
$(-a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$5.138324868$ |
$3.263941520$ |
2.439212162 |
\( \frac{34604215282042281704676226101}{4722366482869645213696} a^{3} - \frac{5798394776157413461267221415}{1180591620717411303424} a^{2} - \frac{42313245668912585498466643535}{1180591620717411303424} a - \frac{52039308937679213852917052703}{4722366482869645213696} \) |
\( \bigl[1\) , \( -a^{3} + 2 a^{2} + 4 a - 5\) , \( a^{3} - 5 a - 2\) , \( 80 a^{3} - 218 a^{2} - 265 a + 553\) , \( -641 a^{3} + 1608 a^{2} + 2136 a - 4187\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-5\right){x}^{2}+\left(80a^{3}-218a^{2}-265a+553\right){x}-641a^{3}+1608a^{2}+2136a-4187$ |
| 8.1-a1 |
8.1-a |
$4$ |
$4$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{46} \) |
$14.34206$ |
$(-a), (-a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$225.2337538$ |
0.909948101 |
\( \frac{133425326437522565}{1099511627776} a^{3} - \frac{82385904144071959}{274877906944} a^{2} - \frac{101331943756558911}{274877906944} a + \frac{887810214505548273}{1099511627776} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 5 a\) , \( a^{2} - 3\) , \( 12 a^{3} + a^{2} - 69 a - 63\) , \( 73 a^{3} - 68 a^{2} - 339 a - 24\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(12a^{3}+a^{2}-69a-63\right){x}+73a^{3}-68a^{2}-339a-24$ |
| 8.1-a2 |
8.1-a |
$4$ |
$4$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{16} \) |
$14.34206$ |
$(-a), (-a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$225.2337538$ |
0.909948101 |
\( -\frac{5905819933813793759}{1024} a^{3} + \frac{5453323691191835349}{256} a^{2} - \frac{3329521173035041619}{256} a - \frac{6974587594585785187}{1024} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 5 a\) , \( a + 1\) , \( -14 a^{3} + 47 a^{2} + 46 a - 125\) , \( -104 a^{3} + 184 a^{2} + 317 a - 496\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-14a^{3}+47a^{2}+46a-125\right){x}-104a^{3}+184a^{2}+317a-496$ |
| 8.1-a3 |
8.1-a |
$4$ |
$4$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{34} \) |
$14.34206$ |
$(-a), (-a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$112.6168769$ |
0.909948101 |
\( \frac{5626580555}{4096} a^{3} + \frac{3919129353}{4096} a^{2} - \frac{6006498917}{2048} a - \frac{1044761257}{1024} \) |
\( \bigl[1\) , \( a\) , \( a^{3} - 4 a - 1\) , \( -247 a^{3} + 165 a^{2} + 1208 a + 373\) , \( -1955 a^{3} + 1309 a^{2} + 9560 a + 2940\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+a{x}^{2}+\left(-247a^{3}+165a^{2}+1208a+373\right){x}-1955a^{3}+1309a^{2}+9560a+2940$ |
| 8.1-a4 |
8.1-a |
$4$ |
$4$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{32} \) |
$14.34206$ |
$(-a), (-a^2+a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$450.4675076$ |
0.909948101 |
\( -\frac{18723427264355}{1048576} a^{3} + \frac{17289087332577}{262144} a^{2} - \frac{10555894729991}{262144} a - \frac{22110121674327}{1048576} \) |
\( \bigl[1\) , \( -a + 1\) , \( a^{3} - 4 a - 2\) , \( 6 a^{3} - 8 a^{2} - 28 a - 7\) , \( -9 a^{3} + 5 a^{2} + 36 a + 11\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a^{3}-8a^{2}-28a-7\right){x}-9a^{3}+5a^{2}+36a+11$ |
| 8.1-b1 |
8.1-b |
$2$ |
$3$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{19} \) |
$14.34206$ |
$(-a), (-a^2+a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 3^{2} \) |
$1$ |
$3.119887243$ |
2.041912186 |
\( \frac{2630452712385}{256} a^{3} - \frac{19877155534545}{512} a^{2} + \frac{13657658639923}{512} a + \frac{2307922386793}{256} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a^{3} - 5 a - 1\) , \( 21 a^{3} - 83 a - 36\) , \( 111 a^{3} - 15 a^{2} - 427 a - 143\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(21a^{3}-83a-36\right){x}+111a^{3}-15a^{2}-427a-143$ |
| 8.1-b2 |
8.1-b |
$2$ |
$3$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$14.34206$ |
$(-a), (-a^2+a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$252.7108667$ |
2.041912186 |
\( -3709 a^{3} - \frac{25851}{8} a^{2} + \frac{19173}{2} a + \frac{19007}{8} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a^{3} - 5 a - 1\) , \( -4 a^{3} + 12 a + 4\) , \( 3 a^{3} - 9 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a^{3}+12a+4\right){x}+3a^{3}-9a-3$ |
| 8.1-c1 |
8.1-c |
$4$ |
$4$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$14.34206$ |
$(-a), (-a^2+a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.219435829$ |
$426.3764159$ |
1.511972368 |
\( -\frac{256356035}{16} a^{3} + \frac{237868897}{4} a^{2} - \frac{145464061}{4} a - \frac{304488127}{16} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 4 a + 2\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -13 a^{3} - a^{2} + 43 a + 13\) , \( -38 a^{3} - 15 a^{2} + 105 a + 36\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-13a^{3}-a^{2}+43a+13\right){x}-38a^{3}-15a^{2}+105a+36$ |
| 8.1-c2 |
8.1-c |
$4$ |
$4$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$14.34206$ |
$(-a), (-a^2+a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.054858957$ |
$852.7528318$ |
1.511972368 |
\( -\frac{1231}{16} a^{3} + \frac{2891}{8} a^{2} - \frac{8749}{16} a + \frac{14187}{8} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -1\) , \( a^{2} - 2\) , \( a + 2\) , \( -a^{3} + 3 a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}-{x}^{2}+\left(a+2\right){x}-a^{3}+3a$ |
| 8.1-c3 |
8.1-c |
$4$ |
$4$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$14.34206$ |
$(-a), (-a^2+a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.219435829$ |
$852.7528318$ |
1.511972368 |
\( 1080811380 a^{3} - 2518236540 a^{2} - \frac{6985472877}{2} a + \frac{13113837841}{2} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{2} - a - 3\) , \( -20 a^{3} - 25 a^{2} + 23 a + 13\) , \( 320 a^{3} + 190 a^{2} - 748 a - 258\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(-20a^{3}-25a^{2}+23a+13\right){x}+320a^{3}+190a^{2}-748a-258$ |
| 8.1-c4 |
8.1-c |
$4$ |
$4$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$14.34206$ |
$(-a), (-a^2+a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.109717914$ |
$1705.505663$ |
1.511972368 |
\( 11520 a^{3} - \frac{102503}{4} a^{2} - \frac{84053}{2} a + \frac{304353}{4} \) |
\( \bigl[1\) , \( a^{3} - 2 a^{2} - 2 a + 5\) , \( 0\) , \( 2 a^{3} - 4 a^{2} - 3 a + 6\) , \( a^{3} - 2 a^{2} - a + 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{3}-2a^{2}-2a+5\right){x}^{2}+\left(2a^{3}-4a^{2}-3a+6\right){x}+a^{3}-2a^{2}-a+2$ |
| 8.2-a1 |
8.2-a |
$4$ |
$4$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{16} \) |
$14.34206$ |
$(a-1), (-a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$225.2337538$ |
0.909948101 |
\( \frac{5905819933813793759}{1024} a^{3} + \frac{4095834963325960119}{1024} a^{2} - \frac{12591045035953135039}{1024} a - \frac{2192598727886202013}{512} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 5\) , \( 0\) , \( 8 a^{3} + 16 a^{2} - 75 a - 64\) , \( 182 a^{3} - 232 a^{2} - 700 a + 15\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-5\right){x}^{2}+\left(8a^{3}+16a^{2}-75a-64\right){x}+182a^{3}-232a^{2}-700a+15$ |
| 8.2-a2 |
8.2-a |
$4$ |
$4$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{46} \) |
$14.34206$ |
$(a-1), (-a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$225.2337538$ |
0.909948101 |
\( -\frac{133425326437522565}{1099511627776} a^{3} + \frac{70732362736279859}{1099511627776} a^{2} + \frac{664139028866243621}{1099511627776} a + \frac{143182074670273679}{549755813888} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -13 a^{3} + 39 a^{2} + 30 a - 120\) , \( -86 a^{3} + 190 a^{2} + 287 a - 477\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}-a{x}^{2}+\left(-13a^{3}+39a^{2}+30a-120\right){x}-86a^{3}+190a^{2}+287a-477$ |
| 8.2-a3 |
8.2-a |
$4$ |
$4$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{32} \) |
$14.34206$ |
$(a-1), (-a^2+a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$450.4675076$ |
0.909948101 |
\( \frac{18723427264355}{1048576} a^{3} + \frac{12986067537243}{1048576} a^{2} - \frac{39918837947587}{1048576} a - \frac{6950389264169}{524288} \) |
\( \bigl[1\) , \( a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -7 a^{3} + 12 a^{2} + 28 a - 40\) , \( 9 a^{3} - 22 a^{2} - 23 a + 47\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+a{x}^{2}+\left(-7a^{3}+12a^{2}+28a-40\right){x}+9a^{3}-22a^{2}-23a+47$ |
| 8.2-a4 |
8.2-a |
$4$ |
$4$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{34} \) |
$14.34206$ |
$(a-1), (-a^2+a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$112.6168769$ |
0.909948101 |
\( -\frac{5626580555}{4096} a^{3} + \frac{10399435509}{2048} a^{2} - \frac{12705002537}{4096} a - \frac{3323166477}{2048} \) |
\( \bigl[1\) , \( -a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 246 a^{3} - 574 a^{2} - 795 a + 1496\) , \( 1954 a^{3} - 4554 a^{2} - 6315 a + 11855\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(246a^{3}-574a^{2}-795a+1496\right){x}+1954a^{3}-4554a^{2}-6315a+11855$ |
*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.
