| 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 |
| 1.1-a1 |
1.1-a |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$7.37361$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$46.16896912$ |
0.559510847 |
\( -21033460516913055 a^{3} + 43531437358120952 a^{2} + 15073423980297778 a - 10162918758743358 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 5 a - 2\) , \( a^{3} - 4 a - 1\) , \( -10 a^{3} + 3 a^{2} + 53 a - 20\) , \( -18 a^{3} + 4 a^{2} + 100 a - 35\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(-10a^{3}+3a^{2}+53a-20\right){x}-18a^{3}+4a^{2}+100a-35$ |
| 1.1-a2 |
1.1-a |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.37361$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$738.7035059$ |
0.559510847 |
\( -36526459 a^{3} + 75590368 a^{2} + 26171681 a - 17605509 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 5 a - 2\) , \( a^{3} - 4 a - 1\) , \( -5 a^{3} + 3 a^{2} + 23 a - 10\) , \( 8 a^{3} - 5 a^{2} - 37 a + 14\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(-5a^{3}+3a^{2}+23a-10\right){x}+8a^{3}-5a^{2}-37a+14$ |
| 1.1-a3 |
1.1-a |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.37361$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$184.6758764$ |
0.559510847 |
\( 869555956172596077 a^{3} - 506752841808147273 a^{2} - 4052458425046051917 a + 1492103245592240456 \) |
\( \bigl[a^{2} + a - 3\) , \( -1\) , \( a^{3} - 4 a\) , \( -33 a^{3} + 71 a^{2} + 19 a - 22\) , \( 3482 a^{3} - 7202 a^{2} - 2504 a + 1678\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}-{x}^{2}+\left(-33a^{3}+71a^{2}+19a-22\right){x}+3482a^{3}-7202a^{2}-2504a+1678$ |
| 1.1-a4 |
1.1-a |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.37361$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$738.7035059$ |
0.559510847 |
\( 101155137 a^{3} - 401898414 a^{2} - 395694666 a + 1799295860 \) |
\( \bigl[a^{2} + a - 3\) , \( -1\) , \( a^{3} - 4 a\) , \( 77 a^{3} - 154 a^{2} - 66 a + 33\) , \( 926 a^{3} - 1913 a^{2} - 669 a + 442\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}-{x}^{2}+\left(77a^{3}-154a^{2}-66a+33\right){x}+926a^{3}-1913a^{2}-669a+442$ |
| 1.1-a5 |
1.1-a |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$7.37361$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$738.7035059$ |
0.559510847 |
\( 949 a^{3} - 3135 a^{2} + 1797 a + 2300 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{2} - 4\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a + 1\) , \( 2 a^{3} + a^{2} - 9 a - 6\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(a^{3}-4a+1\right){x}+2a^{3}+a^{2}-9a-6$ |
| 1.1-a6 |
1.1-a |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.37361$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$184.6758764$ |
0.559510847 |
\( -583790480364966797 a^{3} - 211325898519474007 a^{2} + 2842454690938643917 a + 1612728621302066216 \) |
\( \bigl[a\) , \( a^{3} + a^{2} - 6 a - 4\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -2 a^{3} + 2 a^{2} + 6 a - 4\) , \( 4 a^{3} + 2 a^{2} - 14 a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-4\right){x}^{2}+\left(-2a^{3}+2a^{2}+6a-4\right){x}+4a^{3}+2a^{2}-14a-1$ |
| 5.1-a1 |
5.1-a |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{16} \) |
$9.01678$ |
$(a^3-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$135.2702818$ |
0.819654320 |
\( -\frac{830432300890820238694}{152587890625} a^{3} - \frac{300608695483940061258}{152587890625} a^{2} + \frac{4043349064576805798114}{152587890625} a + \frac{2294087903896782953517}{152587890625} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 6 a - 5\) , \( 1\) , \( -213 a^{3} - 259 a^{2} + 338 a - 76\) , \( 3469 a^{3} + 6333 a^{2} - 1901 a - 307\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+{y}={x}^{3}+\left(a^{3}+a^{2}-6a-5\right){x}^{2}+\left(-213a^{3}-259a^{2}+338a-76\right){x}+3469a^{3}+6333a^{2}-1901a-307$ |
| 5.1-a2 |
5.1-a |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{8} \) |
$9.01678$ |
$(a^3-4a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$541.0811274$ |
0.819654320 |
\( -\frac{33199685017384}{390625} a^{3} + \frac{68678090471412}{390625} a^{2} + \frac{23848316311004}{390625} a - \frac{15996423941063}{390625} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 6 a - 5\) , \( 1\) , \( -28 a^{3} - 29 a^{2} + 53 a - 11\) , \( -57 a^{3} - 88 a^{2} + 58 a - 7\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+{y}={x}^{3}+\left(a^{3}+a^{2}-6a-5\right){x}^{2}+\left(-28a^{3}-29a^{2}+53a-11\right){x}-57a^{3}-88a^{2}+58a-7$ |
| 5.1-a3 |
5.1-a |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{2} \) |
$9.01678$ |
$(a^3-4a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$541.0811274$ |
0.819654320 |
\( -\frac{3096698}{25} a^{3} - \frac{1114386}{25} a^{2} + \frac{15073288}{25} a + \frac{8517339}{25} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 2 a^{3} - a^{2} - 11 a + 1\) , \( -a^{3} + 3 a - 2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(2a^{3}-a^{2}-11a+1\right){x}-a^{3}+3a-2$ |
| 5.1-a4 |
5.1-a |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{4} \) |
$9.01678$ |
$(a^3-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$135.2702818$ |
0.819654320 |
\( -\frac{71109854727042243754}{625} a^{3} + \frac{147170941466637547322}{625} a^{2} + \frac{50960182639085118974}{625} a - \frac{34358762598847250653}{625} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} + a^{2} - 6 a - 4\) , \( a^{2} - 3\) , \( 5 a^{3} - 12 a^{2} - a + 9\) , \( -12 a^{3} + 29 a^{2} + 2 a - 13\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-4\right){x}^{2}+\left(5a^{3}-12a^{2}-a+9\right){x}-12a^{3}+29a^{2}+2a-13$ |
| 5.1-a5 |
5.1-a |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{2} \) |
$9.01678$ |
$(a^3-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$33.81757046$ |
0.819654320 |
\( \frac{90906856652898}{25} a^{3} - \frac{48651091967314}{25} a^{2} - \frac{416271466497588}{25} a + \frac{152748816811661}{25} \) |
\( \bigl[1\) , \( a^{3} + a^{2} - 4 a - 5\) , \( a^{3} + a^{2} - 5 a - 4\) , \( -98 a^{3} + 52 a^{2} + 459 a - 146\) , \( -625 a^{3} + 370 a^{2} + 2911 a - 1102\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-5\right){x}^{2}+\left(-98a^{3}+52a^{2}+459a-146\right){x}-625a^{3}+370a^{2}+2911a-1102$ |
| 5.1-a6 |
5.1-a |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$9.01678$ |
$(a^3-4a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$541.0811274$ |
0.819654320 |
\( \frac{617917504}{625} a^{3} - \frac{268416072}{625} a^{2} - \frac{2732295224}{625} a + \frac{996043153}{625} \) |
\( \bigl[1\) , \( a^{3} + a^{2} - 4 a - 5\) , \( a^{3} + a^{2} - 5 a - 4\) , \( -8 a^{3} + 2 a^{2} + 39 a - 1\) , \( -4 a^{3} + 5 a^{2} + 18 a - 19\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-5\right){x}^{2}+\left(-8a^{3}+2a^{2}+39a-1\right){x}-4a^{3}+5a^{2}+18a-19$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$9.56239$ |
$(a^3-a^2-4a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.004022804$ |
$1993.121133$ |
1.166009917 |
\( \frac{517695}{4} a^{3} - \frac{562409}{2} a^{2} - \frac{718077}{8} a + \frac{519415}{8} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{2} + a - 2\) , \( 3 a^{3} - 6 a^{2} - a + 2\) , \( -6 a^{3} + 12 a^{2} + 6 a - 3\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(3a^{3}-6a^{2}-a+2\right){x}-6a^{3}+12a^{2}+6a-3$ |
| 8.2-a1 |
8.2-a |
$2$ |
$2$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$9.56239$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.033380399$ |
$2243.544078$ |
1.815158151 |
\( -13651 a^{3} + 275 a^{2} + 64243 a + 11017 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - a^{2} - 6 a + 1\) , \( a^{3} + a^{2} - 5 a - 3\) , \( 10 a^{3} + 3 a^{2} - 48 a - 21\) , \( -13 a^{3} - 6 a^{2} + 63 a + 39\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a+1\right){x}^{2}+\left(10a^{3}+3a^{2}-48a-21\right){x}-13a^{3}-6a^{2}+63a+39$ |
| 8.2-a2 |
8.2-a |
$2$ |
$2$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{8} \) |
$9.56239$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.016690199$ |
$2243.544078$ |
1.815158151 |
\( 148148865 a^{3} - 83210084 a^{2} - 685093029 a + 251872624 \) |
\( \bigl[a + 1\) , \( a^{3} + a^{2} - 4 a - 5\) , \( a + 1\) , \( -2 a^{3} - 2 a^{2} + 13 a + 6\) , \( 2 a^{3} + 2 a^{2} - 14 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-5\right){x}^{2}+\left(-2a^{3}-2a^{2}+13a+6\right){x}+2a^{3}+2a^{2}-14a-3$ |
| 10.1-a1 |
10.1-a |
$8$ |
$12$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{12} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$6.651747425$ |
0.725498623 |
\( -\frac{29680136547293972884912463281149}{1000000000000} a^{3} - \frac{10743891404527057493816436480193}{1000000000000} a^{2} + \frac{36127877292472047530434122176711}{250000000000} a + \frac{81991754411705431499391332784457}{1000000000000} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( -a^{2} - a + 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -8 a^{3} - 63 a^{2} - 56 a - 7\) , \( -7157 a^{3} - 16545 a^{2} - 2241 a + 2899\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-8a^{3}-63a^{2}-56a-7\right){x}-7157a^{3}-16545a^{2}-2241a+2899$ |
| 10.1-a2 |
10.1-a |
$8$ |
$12$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{24} \cdot 5^{6} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$26.60698970$ |
0.725498623 |
\( -\frac{678517704977060049519}{262144000000} a^{3} - \frac{245615709965117088283}{262144000000} a^{2} + \frac{825920095618752590141}{65536000000} a + \frac{1874427482107438730867}{262144000000} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 5 a - 2\) , \( a^{3} - 4 a\) , \( 52 a^{3} + 8 a^{2} - 277 a - 149\) , \( 268 a^{3} + 49 a^{2} - 1434 a - 803\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(52a^{3}+8a^{2}-277a-149\right){x}+268a^{3}+49a^{2}-1434a-803$ |
| 10.1-a3 |
10.1-a |
$8$ |
$12$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5^{4} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$538.7915414$ |
0.725498623 |
\( \frac{5889170773051}{10000} a^{3} + \frac{1220733099207}{10000} a^{2} - \frac{9953288127089}{2500} a + \frac{14023486993857}{10000} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 5 a - 2\) , \( a^{3} - 4 a\) , \( 12 a^{3} + 3 a^{2} - 57 a - 29\) , \( 23 a^{3} + 13 a^{2} - 103 a - 61\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(12a^{3}+3a^{2}-57a-29\right){x}+23a^{3}+13a^{2}-103a-61$ |
| 10.1-a4 |
10.1-a |
$8$ |
$12$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2155.166165$ |
0.725498623 |
\( \frac{73374961}{6400} a^{3} + \frac{23899077}{6400} a^{2} - \frac{101756579}{1600} a + \frac{160507027}{6400} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 5 a - 2\) , \( a^{3} - 4 a\) , \( 2 a^{3} - 2 a^{2} - 12 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(2a^{3}-2a^{2}-12a+1\right){x}$ |
| 10.1-a5 |
10.1-a |
$8$ |
$12$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1077.583082$ |
0.725498623 |
\( -\frac{18231}{80} a^{3} + \frac{36733}{80} a^{2} + \frac{22569}{20} a + \frac{36523}{80} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a^{2} + a - 2\) , \( a^{2} + 2 a - 2\) , \( 2 a^{3} - 7 a + 2\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-2\right){x}^{2}+\left(a^{2}+2a-2\right){x}+2a^{3}-7a+2$ |
| 10.1-a6 |
10.1-a |
$8$ |
$12$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{12} \cdot 5^{3} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$13.30349485$ |
0.725498623 |
\( \frac{81783144871609}{512000} a^{3} + \frac{420834417530413}{512000} a^{2} + \frac{17904015425349}{128000} a - \frac{85002532745237}{512000} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a^{2} + a - 2\) , \( 10 a^{3} - 19 a^{2} - 8 a + 3\) , \( a^{3} - 72 a^{2} + 186 a - 59\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-2\right){x}^{2}+\left(10a^{3}-19a^{2}-8a+3\right){x}+a^{3}-72a^{2}+186a-59$ |
| 10.1-a7 |
10.1-a |
$8$ |
$12$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{16} \cdot 5 \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1077.583082$ |
0.725498623 |
\( \frac{17586495260821}{327680} a^{3} + \frac{40283826796857}{327680} a^{2} + \frac{1083948522481}{81920} a - \frac{7673047800193}{327680} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - 6 a - 1\) , \( a^{2} + a - 3\) , \( -a^{3} + 3 a^{2} + 4 a - 11\) , \( -10 a^{3} + 4 a^{2} + 46 a - 10\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}-6a-1\right){x}^{2}+\left(-a^{3}+3a^{2}+4a-11\right){x}-10a^{3}+4a^{2}+46a-10$ |
| 10.1-a8 |
10.1-a |
$8$ |
$12$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{48} \cdot 5^{3} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$13.30349485$ |
0.725498623 |
\( \frac{19274834808997077816929901}{35184372088832000} a^{3} - \frac{11233634119410594126435343}{35184372088832000} a^{2} - \frac{22456950071220457925225239}{8796093022208000} a + \frac{33078231255184044057612807}{35184372088832000} \) |
\( \bigl[1\) , \( -a^{3} + 5 a\) , \( 1\) , \( -37 a^{3} + 16 a^{2} + 161 a - 59\) , \( -116 a^{3} + 55 a^{2} + 605 a - 222\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-37a^{3}+16a^{2}+161a-59\right){x}-116a^{3}+55a^{2}+605a-222$ |
| 10.1-b1 |
10.1-b |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{32} \cdot 5^{2} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.010052227$ |
$332.2358862$ |
2.590282729 |
\( -\frac{37164002414207649319}{107374182400} a^{3} + \frac{76915611213513607117}{107374182400} a^{2} + \frac{6658302257169235941}{26843545600} a - \frac{17956842241208970933}{107374182400} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 0\) , \( a^{3} - 4 a^{2} - 3 a + 18\) , \( 788 a^{3} - 463 a^{2} - 3672 a + 1371\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-4\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(a^{3}-4a^{2}-3a+18\right){x}+788a^{3}-463a^{2}-3672a+1371$ |
| 10.1-b2 |
10.1-b |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.020104455$ |
$1328.943545$ |
2.590282729 |
\( \frac{15697121267681}{40960000} a^{3} + \frac{36432105152117}{40960000} a^{2} + \frac{1092521899341}{10240000} a - \frac{4796898008733}{40960000} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 1\) , \( -3 a^{3} - 4 a^{2} + 2 a - 5\) , \( -a^{3} + 5 a^{2} + 22 a + 15\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+{y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(-3a^{3}-4a^{2}+2a-5\right){x}-a^{3}+5a^{2}+22a+15$ |
| 10.1-b3 |
10.1-b |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.040208911$ |
$1328.943545$ |
2.590282729 |
\( -\frac{4448396724991}{6400} a^{3} - \frac{1610271569387}{6400} a^{2} + \frac{5414771247149}{1600} a + \frac{12288769447363}{6400} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -38 a^{3} + 22 a^{2} + 176 a - 67\) , \( -190 a^{3} + 111 a^{2} + 884 a - 330\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(-38a^{3}+22a^{2}+176a-67\right){x}-190a^{3}+111a^{2}+884a-330$ |
| 10.1-b4 |
10.1-b |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$0.080417822$ |
$166.1179431$ |
2.590282729 |
\( -\frac{171220932691152078127}{80} a^{3} - \frac{61980142984982690699}{80} a^{2} + \frac{208417128954628671113}{20} a + \frac{473000002576989611571}{80} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 142 a^{3} - 83 a^{2} - 659 a + 233\) , \( -538 a^{3} + 311 a^{2} + 2511 a - 925\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(142a^{3}-83a^{2}-659a+233\right){x}-538a^{3}+311a^{2}+2511a-925$ |
| 10.1-b5 |
10.1-b |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.080417822$ |
$664.4717725$ |
2.590282729 |
\( \frac{49122607}{80} a^{3} - \frac{27675861}{80} a^{2} - \frac{57288373}{20} a + \frac{79867549}{80} \) |
\( \bigl[a\) , \( a^{2} - 3\) , \( a^{3} - 5 a\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( a^{2} + a - 2\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{3}+a^{2}+5a+1\right){x}+a^{2}+a-2$ |
| 10.1-b6 |
10.1-b |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{8} \cdot 5^{8} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.040208911$ |
$332.2358862$ |
2.590282729 |
\( \frac{365603532600104788471}{100000000} a^{3} + \frac{837230314352276174147}{100000000} a^{2} + \frac{22418016027494639531}{25000000} a - \frac{159509774553019178203}{100000000} \) |
\( \bigl[a\) , \( -a^{3} - a^{2} + 4 a + 5\) , \( a^{2} - 2\) , \( -41 a^{3} + 24 a^{2} + 203 a - 101\) , \( -259 a^{3} + 953 a^{2} - 858 a + 75\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+5\right){x}^{2}+\left(-41a^{3}+24a^{2}+203a-101\right){x}-259a^{3}+953a^{2}-858a+75$ |
| 10.1-c1 |
10.1-c |
$8$ |
$16$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{4} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1024$ |
\( 2^{2} \) |
$1$ |
$0.171933065$ |
2.133623059 |
\( -\frac{838872200657736899845813}{1250} a^{3} - \frac{290731155390614664958991}{1250} a^{2} + \frac{2031177927459941001131514}{625} a + \frac{2300134192065821501411809}{1250} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 3\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -3313 a^{3} - 316 a^{2} + 11602 a - 4042\) , \( -177734 a^{3} - 19498 a^{2} + 618172 a - 212855\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-3313a^{3}-316a^{2}+11602a-4042\right){x}-177734a^{3}-19498a^{2}+618172a-212855$ |
| 10.1-c2 |
10.1-c |
$8$ |
$16$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{16} \cdot 5^{4} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/16\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$704.2378368$ |
2.133623059 |
\( \frac{4752624697430737}{40960000} a^{3} - \frac{2765657876476891}{40960000} a^{2} - \frac{5539826641613443}{10240000} a + \frac{8158468803972659}{40960000} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 5 a + 4\) , \( a\) , \( -15 a^{3} + 4 a^{2} + 71 a - 9\) , \( 20 a^{3} - 14 a^{2} - 95 a + 50\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}-a^{2}+5a+4\right){x}^{2}+\left(-15a^{3}+4a^{2}+71a-9\right){x}+20a^{3}-14a^{2}-95a+50$ |
| 10.1-c3 |
10.1-c |
$8$ |
$16$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5^{4} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$704.2378368$ |
2.133623059 |
\( -\frac{801166897}{10000} a^{3} - \frac{287122229}{10000} a^{2} + \frac{974622183}{2500} a + \frac{2211064221}{10000} \) |
\( \bigl[1\) , \( a^{2} + a - 2\) , \( a^{2} - 3\) , \( 2 a^{2} - a + 2\) , \( 2 a^{2} - a - 2\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(2a^{2}-a+2\right){x}+2a^{2}-a-2$ |
| 10.1-c4 |
10.1-c |
$8$ |
$16$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{8} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$64$ |
\( 2^{4} \) |
$1$ |
$2.750929050$ |
2.133623059 |
\( \frac{3841268121600576869}{1562500} a^{3} + \frac{8838580121599664733}{1562500} a^{2} + \frac{260924774399323834}{390625} a - \frac{1633261669198976917}{1562500} \) |
\( \bigl[1\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( -342 a^{3} - 944 a^{2} - 436 a - 3\) , \( -15444 a^{3} - 36457 a^{2} - 6453 a + 5559\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-342a^{3}-944a^{2}-436a-3\right){x}-15444a^{3}-36457a^{2}-6453a+5559$ |
| 10.1-c5 |
10.1-c |
$8$ |
$16$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5^{16} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$44.01486480$ |
2.133623059 |
\( \frac{640044657840357761}{2441406250000} a^{3} + \frac{1769974043680010677}{2441406250000} a^{2} + \frac{204947664659575721}{610351562500} a + \frac{11954122104281827}{2441406250000} \) |
\( \bigl[1\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( -22 a^{3} - 59 a^{2} - 26 a + 2\) , \( -235 a^{3} - 558 a^{2} - 111 a + 77\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-22a^{3}-59a^{2}-26a+2\right){x}-235a^{3}-558a^{2}-111a+77$ |
| 10.1-c6 |
10.1-c |
$8$ |
$16$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5^{8} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$704.2378368$ |
2.133623059 |
\( \frac{518213471009}{100000000} a^{3} - \frac{277620339787}{100000000} a^{2} - \frac{595789147251}{25000000} a + \frac{1047960694563}{100000000} \) |
\( \bigl[1\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( -2 a^{3} - 4 a^{2} - a + 2\) , \( -3 a^{3} - 7 a^{2} - a\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-2a^{3}-4a^{2}-a+2\right){x}-3a^{3}-7a^{2}-a$ |
| 10.1-c7 |
10.1-c |
$8$ |
$16$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{32} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{6} \) |
$1$ |
$2.750929050$ |
2.133623059 |
\( \frac{11054134169533563912802939}{93132257461547851562500} a^{3} - \frac{28546574205003378223953277}{93132257461547851562500} a^{2} - \frac{22876153429256832149841146}{23283064365386962890625} a + \frac{30591223930858315021155573}{93132257461547851562500} \) |
\( \bigl[1\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( -22 a^{3} - 54 a^{2} - 16 a + 7\) , \( -274 a^{3} - 663 a^{2} - 149 a + 83\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-22a^{3}-54a^{2}-16a+7\right){x}-274a^{3}-663a^{2}-149a+83$ |
| 10.1-c8 |
10.1-c |
$8$ |
$16$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{4} \) |
$9.83287$ |
$(a+1), (a^3-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1024$ |
\( 2^{2} \) |
$1$ |
$0.171933065$ |
2.133623059 |
\( \frac{184408363025485712456162565813}{1250} a^{3} + \frac{422370873250253843174859518991}{1250} a^{2} + \frac{22680459454963084844770388486}{625} a - \frac{80513232581668014960899231809}{1250} \) |
\( \bigl[1\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( -6602 a^{3} - 15244 a^{2} - 1911 a + 2702\) , \( -1026911 a^{3} - 2353003 a^{2} - 255035 a + 447068\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-6602a^{3}-15244a^{2}-1911a+2702\right){x}-1026911a^{3}-2353003a^{2}-255035a+447068$ |
| 16.1-a1 |
16.1-a |
$2$ |
$3$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{36} \) |
$10.42786$ |
$(a+1), (a^3-a^2-4a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$8.142347374$ |
0.888076685 |
\( -\frac{660020704386731466440865}{134217728} a^{3} + \frac{384641569708596430889419}{134217728} a^{2} + \frac{768986298632194620762355}{33554432} a - \frac{1132553952889340970681251}{134217728} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 6 a + 2\) , \( 1\) , \( -19 a^{3} + 38 a^{2} + 15 a - 6\) , \( -1350 a^{3} + 2788 a^{2} + 990 a - 660\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-6a+2\right){x}^{2}+\left(-19a^{3}+38a^{2}+15a-6\right){x}-1350a^{3}+2788a^{2}+990a-660$ |
| 16.1-a2 |
16.1-a |
$2$ |
$3$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$10.42786$ |
$(a+1), (a^3-a^2-4a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$659.5301373$ |
0.888076685 |
\( -\frac{346507681}{512} a^{3} - \frac{1199941173}{512} a^{2} - \frac{7725901}{128} a + \frac{182693213}{512} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( 6 a^{3} - 2 a^{2} - 20 a - 11\) , \( -10 a^{3} + 8 a^{2} + 30 a + 12\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-5a-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a^{3}-2a^{2}-20a-11\right){x}-10a^{3}+8a^{2}+30a+12$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{7} \) |
$10.42786$ |
$(a+1), (a^3-a^2-4a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.009566586$ |
$1552.346764$ |
1.439773098 |
\( -\frac{3781781}{16} a^{3} + \frac{2203391}{16} a^{2} + \frac{4405271}{4} a - \frac{6490567}{16} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 5 a + 4\) , \( a^{2} - 3\) , \( -12 a^{3} + 4 a^{2} + 56 a - 9\) , \( 14 a^{3} - 10 a^{2} - 65 a + 32\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+4\right){x}^{2}+\left(-12a^{3}+4a^{2}+56a-9\right){x}+14a^{3}-10a^{2}-65a+32$ |
| 16.1-c1 |
16.1-c |
$2$ |
$2$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{14} \) |
$10.42786$ |
$(a+1), (a^3-a^2-4a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$70.81979311$ |
0.858248368 |
\( -\frac{993393}{2} a^{3} - \frac{3080951}{16} a^{2} + \frac{19188621}{8} a + \frac{21839297}{16} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + a^{2} + 5 a - 3\) , \( a\) , \( 10 a^{3} - a^{2} - 43 a - 15\) , \( 18 a^{3} + 2 a^{2} - 79 a - 47\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+5a-3\right){x}^{2}+\left(10a^{3}-a^{2}-43a-15\right){x}+18a^{3}+2a^{2}-79a-47$ |
| 16.1-c2 |
16.1-c |
$2$ |
$2$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{10} \) |
$10.42786$ |
$(a+1), (a^3-a^2-4a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$70.81979311$ |
0.858248368 |
\( \frac{9106495465}{16} a^{3} + \frac{22912277149}{16} a^{2} + 168334223 a - \frac{4409270297}{16} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} - a^{2} + 5 a + 4\) , \( a^{3} - 4 a - 1\) , \( -11 a^{3} - 7 a^{2} + 31 a - 3\) , \( -9 a^{3} - 39 a^{2} - 36 a + 12\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+4\right){x}^{2}+\left(-11a^{3}-7a^{2}+31a-3\right){x}-9a^{3}-39a^{2}-36a+12$ |
| 16.2-a1 |
16.2-a |
$2$ |
$2$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{10} \) |
$10.42786$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$182.4799322$ |
1.105715629 |
\( -13651 a^{3} + 275 a^{2} + 64243 a + 11017 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( -a^{3} + 4 a + 1\) , \( a^{2} + a - 2\) , \( -7 a^{3} - 2 a^{2} + 31 a + 14\) , \( -7 a^{3} - 3 a^{2} + 33 a + 17\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-7a^{3}-2a^{2}+31a+14\right){x}-7a^{3}-3a^{2}+33a+17$ |
| 16.2-a2 |
16.2-a |
$2$ |
$2$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{8} \) |
$10.42786$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$182.4799322$ |
1.105715629 |
\( 148148865 a^{3} - 83210084 a^{2} - 685093029 a + 251872624 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -10 a^{3} - 9 a^{2} + 34 a + 20\) , \( -29 a^{3} - 24 a^{2} + 105 a + 63\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+3\right){x}^{2}+\left(-10a^{3}-9a^{2}+34a+20\right){x}-29a^{3}-24a^{2}+105a+63$ |
| 16.2-b1 |
16.2-b |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{12} \) |
$10.42786$ |
$(a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.426082305$ |
$395.6849226$ |
2.043155088 |
\( -21033460516913055 a^{3} + 43531437358120952 a^{2} + 15073423980297778 a - 10162918758743358 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( -a^{3} + 4 a + 2\) , \( a + 1\) , \( -94 a^{3} + 40 a^{2} + 455 a - 126\) , \( 330 a^{3} - 187 a^{2} - 1573 a + 617\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-94a^{3}+40a^{2}+455a-126\right){x}+330a^{3}-187a^{2}-1573a+617$ |
| 16.2-b2 |
16.2-b |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$10.42786$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.852164610$ |
$791.3698452$ |
2.043155088 |
\( -36526459 a^{3} + 75590368 a^{2} + 26171681 a - 17605509 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( -a^{3} + 4 a + 2\) , \( a + 1\) , \( -49 a^{3} + 20 a^{2} + 230 a - 46\) , \( -210 a^{3} + 115 a^{2} + 980 a - 326\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-49a^{3}+20a^{2}+230a-46\right){x}-210a^{3}+115a^{2}+980a-326$ |
| 16.2-b3 |
16.2-b |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$10.42786$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.704329220$ |
$98.92123065$ |
2.043155088 |
\( 101155137 a^{3} - 401898414 a^{2} - 395694666 a + 1799295860 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( -a\) , \( a^{3} - 4 a - 1\) , \( -13 a^{3} - 30 a^{2} - 9 a + 1\) , \( -88 a^{3} - 211 a^{2} - 48 a + 25\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}-a{x}^{2}+\left(-13a^{3}-30a^{2}-9a+1\right){x}-88a^{3}-211a^{2}-48a+25$ |
| 16.2-b4 |
16.2-b |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$10.42786$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$3.408658441$ |
$6.182576916$ |
2.043155088 |
\( 869555956172596077 a^{3} - 506752841808147273 a^{2} - 4052458425046051917 a + 1492103245592240456 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( -a\) , \( a^{3} - 4 a - 1\) , \( -223 a^{3} - 495 a^{2} - 34 a + 81\) , \( -6080 a^{3} - 13901 a^{2} - 1465 a + 2616\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}-a{x}^{2}+\left(-223a^{3}-495a^{2}-34a+81\right){x}-6080a^{3}-13901a^{2}-1465a+2616$ |
| 16.2-b5 |
16.2-b |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{12} \) |
$10.42786$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.408658441$ |
$12.36515383$ |
2.043155088 |
\( -583790480364966797 a^{3} - 211325898519474007 a^{2} + 2842454690938643917 a + 1612728621302066216 \) |
\( \bigl[a^{2} - 3\) , \( -a + 1\) , \( a^{3} + a^{2} - 5 a - 3\) , \( 10 a^{2} - 3 a - 49\) , \( -9 a^{3} + 38 a^{2} + 34 a - 176\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-5a-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a^{2}-3a-49\right){x}-9a^{3}+38a^{2}+34a-176$ |
| 16.2-b6 |
16.2-b |
$6$ |
$8$ |
4.4.6809.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{12} \) |
$10.42786$ |
$(a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.426082305$ |
$791.3698452$ |
2.043155088 |
\( 949 a^{3} - 3135 a^{2} + 1797 a + 2300 \) |
\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+{x}$ |
*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.
