| 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 |
| 9.1-a1 |
9.1-a |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$14.04951$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.132937508$ |
$998.3560553$ |
2.221879845 |
\( -8192 a^{3} + 960 a^{2} + 63488 a + 66368 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{3} + 3 a^{2} + a - 4\) , \( a^{3} - 3 a^{2} - 2 a + 3\) , \( -4 a^{3} + 12 a^{2} + 10 a - 18\) , \( 6 a^{3} - 16 a^{2} - 19 a + 23\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(a^{3}-3a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+a-4\right){x}^{2}+\left(-4a^{3}+12a^{2}+10a-18\right){x}+6a^{3}-16a^{2}-19a+23$ |
| 9.1-a2 |
9.1-a |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$14.04951$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.066468754$ |
$1996.712110$ |
2.221879845 |
\( 8192 a^{3} + 9152 a^{2} - 8064 a - 4096 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( 3 a^{3} - 15 a^{2} + 13 a + 13\) , \( -7 a^{3} + 21 a^{2} + 9 a - 10\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(a^{3}-3a^{2}-2a+4\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-1\right){x}^{2}+\left(3a^{3}-15a^{2}+13a+13\right){x}-7a^{3}+21a^{2}+9a-10$ |
| 9.1-a3 |
9.1-a |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$14.04951$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.398812526$ |
$332.7853517$ |
2.221879845 |
\( 2863051917056 a^{3} - 7777078581056 a^{2} - 8744074634496 a + 11990005718336 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{2} + a + 2\) , \( 2 a^{3} - 5 a^{2} - 6 a + 4\) , \( -56 a^{3} + 154 a^{2} + 173 a - 236\) , \( 295 a^{3} - 814 a^{2} - 906 a + 1251\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(2a^{3}-5a^{2}-6a+4\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-56a^{3}+154a^{2}+173a-236\right){x}+295a^{3}-814a^{2}-906a+1251$ |
| 9.1-a4 |
9.1-a |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$14.04951$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.199406263$ |
$665.5707035$ |
2.221879845 |
\( -74976000 a^{3} + 87518656 a^{2} + 436386432 a + 243770624 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -2 a^{3} + 5 a^{2} + 7 a - 4\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( a^{3} + 3 a^{2} - 8 a - 23\) , \( 3 a^{3} - 15 a^{2} + 17 a + 12\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+5\right){x}{y}+\left(2a^{3}-5a^{2}-6a+5\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+7a-4\right){x}^{2}+\left(a^{3}+3a^{2}-8a-23\right){x}+3a^{3}-15a^{2}+17a+12$ |
| 9.1-b1 |
9.1-b |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$14.04951$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$4.767388381$ |
$42.85755496$ |
3.420546522 |
\( 2863051917056 a^{3} - 7777078581056 a^{2} - 8744074634496 a + 11990005718336 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 5 a + 2\) , \( a + 1\) , \( 3 a^{3} - a^{2} - 10 a - 2\) , \( -17 a^{3} - 14 a^{2} + 12 a - 4\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-5a+2\right){x}^{2}+\left(3a^{3}-a^{2}-10a-2\right){x}-17a^{3}-14a^{2}+12a-4$ |
| 9.1-b2 |
9.1-b |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$14.04951$ |
$(-a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.794564730$ |
$2314.307968$ |
3.420546522 |
\( 8192 a^{3} + 9152 a^{2} - 8064 a - 4096 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( 2 a^{3} - 4 a^{2} - 8 a + 1\) , \( a^{3} - 2 a^{2} - 4 a\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(a^{3}-3a^{2}-2a+4\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+2\right){x}^{2}+\left(2a^{3}-4a^{2}-8a+1\right){x}+a^{3}-2a^{2}-4a$ |
| 9.1-b3 |
9.1-b |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$14.04951$ |
$(-a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1.589129460$ |
$1157.153984$ |
3.420546522 |
\( -8192 a^{3} + 960 a^{2} + 63488 a + 66368 \) |
\( \bigl[a^{3} - 3 a^{2} - a + 4\) , \( -a^{3} + 3 a^{2} + a - 4\) , \( a^{3} - 3 a^{2} - 2 a + 3\) , \( -3 a^{3} + 9 a^{2} + 5 a - 9\) , \( -2 a^{3} + 7 a^{2} + 2 a - 6\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+4\right){x}{y}+\left(a^{3}-3a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+a-4\right){x}^{2}+\left(-3a^{3}+9a^{2}+5a-9\right){x}-2a^{3}+7a^{2}+2a-6$ |
| 9.1-b4 |
9.1-b |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$14.04951$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$2.383694190$ |
$85.71510993$ |
3.420546522 |
\( -74976000 a^{3} + 87518656 a^{2} + 436386432 a + 243770624 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 68 a^{3} - 230 a^{2} - 13 a + 145\) , \( 568 a^{3} - 1968 a^{2} + 37 a + 1132\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+5\right){x}{y}+\left(2a^{3}-5a^{2}-6a+5\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-6a+5\right){x}^{2}+\left(68a^{3}-230a^{2}-13a+145\right){x}+568a^{3}-1968a^{2}+37a+1132$ |
| 11.1-a1 |
11.1-a |
$2$ |
$2$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$14.40639$ |
$(a^3-3a^2-2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.088579032$ |
$2312.258632$ |
3.428900792 |
\( \frac{43119360}{121} a^{3} - \frac{117339456}{121} a^{2} - \frac{131340160}{121} a + \frac{182355456}{121} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( -2 a^{2} - a\) , \( -a^{2} - a\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+5\right){x}{y}+\left(a^{3}-2a^{2}-3a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a^{2}-a\right){x}-a^{2}-a$ |
| 11.1-a2 |
11.1-a |
$2$ |
$2$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$14.40639$ |
$(a^3-3a^2-2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.177158065$ |
$578.0646580$ |
3.428900792 |
\( -\frac{2670848}{14641} a^{3} + \frac{8059584}{14641} a^{2} + \frac{7064320}{14641} a - \frac{10057152}{14641} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( a^{3} - 3 a^{2} - 2 a + 3\) , \( 4 a^{3} - 12 a^{2} - 7 a + 20\) , \( 10 a^{3} - 19 a^{2} - 44 a + 3\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+5\right){x}{y}+\left(a^{3}-3a^{2}-2a+3\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+2\right){x}^{2}+\left(4a^{3}-12a^{2}-7a+20\right){x}+10a^{3}-19a^{2}-44a+3$ |
| 11.1-b1 |
11.1-b |
$2$ |
$2$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$14.40639$ |
$(a^3-3a^2-2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.080333014$ |
$1554.184841$ |
2.090182996 |
\( \frac{43119360}{121} a^{3} - \frac{117339456}{121} a^{2} - \frac{131340160}{121} a + \frac{182355456}{121} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 4\) , \( a^{3} - 3 a^{2} - a + 2\) , \( a\) , \( -3 a^{3} + 9 a^{2} + 8 a - 17\) , \( -12 a^{3} + 32 a^{2} + 38 a - 48\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+4\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-3a^{2}-a+2\right){x}^{2}+\left(-3a^{3}+9a^{2}+8a-17\right){x}-12a^{3}+32a^{2}+38a-48$ |
| 11.1-b2 |
11.1-b |
$2$ |
$2$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$14.40639$ |
$(a^3-3a^2-2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.160666029$ |
$388.5462104$ |
2.090182996 |
\( -\frac{2670848}{14641} a^{3} + \frac{8059584}{14641} a^{2} + \frac{7064320}{14641} a - \frac{10057152}{14641} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - 4 a^{2} - 3 a + 9\) , \( a^{3} - 3 a^{2} - 5 a + 8\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+5\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(a^{3}-4a^{2}-3a+9\right){x}+a^{3}-3a^{2}-5a+8$ |
| 12.1-a1 |
12.1-a |
$2$ |
$3$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{6} \cdot 3^{3} \) |
$14.56393$ |
$(-a), (a^2+a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$292.8345218$ |
2.451206249 |
\( \frac{342720401}{108} a^{3} - \frac{386496913}{108} a^{2} - \frac{2024767477}{108} a - \frac{281557157}{27} \) |
\( \bigl[a\) , \( 1\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 36 a^{3} - 41 a^{2} - 213 a - 116\) , \( -230 a^{3} + 257 a^{2} + 1373 a + 758\bigr] \) |
${y}^2+a{x}{y}+\left(2a^{3}-5a^{2}-6a+5\right){y}={x}^{3}+{x}^{2}+\left(36a^{3}-41a^{2}-213a-116\right){x}-230a^{3}+257a^{2}+1373a+758$ |
| 12.1-a2 |
12.1-a |
$2$ |
$3$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$14.56393$ |
$(-a), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 3^{2} \) |
$1$ |
$3.615241010$ |
2.451206249 |
\( \frac{77666324667431929}{24} a^{3} - \frac{1067757750578273159}{96} a^{2} - \frac{18954796339204835}{96} a + \frac{648568860602329529}{96} \) |
\( \bigl[a\) , \( 1\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 6 a^{3} - 6 a^{2} - 33 a - 41\) , \( -608 a^{3} + 679 a^{2} + 3638 a + 1967\bigr] \) |
${y}^2+a{x}{y}+\left(2a^{3}-5a^{2}-6a+5\right){y}={x}^{3}+{x}^{2}+\left(6a^{3}-6a^{2}-33a-41\right){x}-608a^{3}+679a^{2}+3638a+1967$ |
| 12.1-b1 |
12.1-b |
$2$ |
$3$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$14.56393$ |
$(-a), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$13.88774049$ |
1.046240876 |
\( \frac{77666324667431929}{24} a^{3} - \frac{1067757750578273159}{96} a^{2} - \frac{18954796339204835}{96} a + \frac{648568860602329529}{96} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 3\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( -11 a^{3} - 26 a^{2} + 15 a + 14\) , \( -89 a^{3} - 165 a^{2} + 65 a + 96\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+3\right){x}{y}+\left(a^{3}-3a^{2}-2a+4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+2\right){x}^{2}+\left(-11a^{3}-26a^{2}+15a+14\right){x}-89a^{3}-165a^{2}+65a+96$ |
| 12.1-b2 |
12.1-b |
$2$ |
$3$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{6} \cdot 3^{3} \) |
$14.56393$ |
$(-a), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$124.9896644$ |
1.046240876 |
\( \frac{342720401}{108} a^{3} - \frac{386496913}{108} a^{2} - \frac{2024767477}{108} a - \frac{281557157}{27} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( -a^{3} + 3 a^{2} + 3 a - 2\) , \( 2 a^{3} - 5 a^{2} - 6 a + 4\) , \( -a^{3} + 3 a^{2} + 6 a - 7\) , \( 4 a^{3} - 12 a^{2} - 4 a + 8\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-6a+5\right){x}{y}+\left(2a^{3}-5a^{2}-6a+4\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-2\right){x}^{2}+\left(-a^{3}+3a^{2}+6a-7\right){x}+4a^{3}-12a^{2}-4a+8$ |
| 12.1-c1 |
12.1-c |
$1$ |
$1$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3^{7} \) |
$14.56393$ |
$(-a), (a^2+a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.064880680$ |
$1286.292807$ |
2.794298582 |
\( -\frac{9205433}{4374} a^{3} + \frac{13489763}{2187} a^{2} + \frac{14773841}{2187} a - \frac{39480439}{4374} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 2\) , \( -2 a^{3} + 5 a^{2} + 5 a - 5\) , \( a^{3} - 3 a^{2} - a + 4\) , \( -8 a^{3} + 12 a^{2} + 40 a + 16\) , \( -33 a^{3} + 37 a^{2} + 197 a + 108\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+2\right){x}{y}+\left(a^{3}-3a^{2}-a+4\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+5a-5\right){x}^{2}+\left(-8a^{3}+12a^{2}+40a+16\right){x}-33a^{3}+37a^{2}+197a+108$ |
| 12.1-d1 |
12.1-d |
$1$ |
$1$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3^{7} \) |
$14.56393$ |
$(-a), (a^2+a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.041997182$ |
$324.8870463$ |
3.197924209 |
\( -\frac{9205433}{4374} a^{3} + \frac{13489763}{2187} a^{2} + \frac{14773841}{2187} a - \frac{39480439}{4374} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 3\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( -5 a^{3} + 12 a^{2} + 17 a - 11\) , \( -6 a^{3} + 15 a^{2} + 20 a - 22\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{2}+3a+3\right){x}^{2}+\left(-5a^{3}+12a^{2}+17a-11\right){x}-6a^{3}+15a^{2}+20a-22$ |
| 16.1-a1 |
16.1-a |
$4$ |
$4$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$15.09718$ |
$(a^2+a-1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 3 \) |
$0.129007054$ |
$1295.106030$ |
4.195634234 |
\( -8192 a^{3} + 28672 a^{2} + 4096 a - 12288 \) |
\( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( a^{2} - 2 a - 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(a^{2}-2a-4\right){x}$ |
| 16.1-a2 |
16.1-a |
$4$ |
$4$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.09718$ |
$(a^2+a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.129007054$ |
$323.7765075$ |
4.195634234 |
\( 10248160 a^{3} + 12869728 a^{2} - 9199584 a - 9383184 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( 2 a^{3} - 5 a^{2} - 7 a + 5\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( 10 a^{3} - 30 a^{2} - 17 a + 26\) , \( 8 a^{3} - 24 a^{2} - 14 a + 23\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-7a+5\right){x}^{2}+\left(10a^{3}-30a^{2}-17a+26\right){x}+8a^{3}-24a^{2}-14a+23$ |
| 16.1-a3 |
16.1-a |
$4$ |
$4$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.09718$ |
$(a^2+a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.032251763$ |
$1295.106030$ |
4.195634234 |
\( -6053856 a^{3} + 5767040 a^{2} + 37945344 a + 24654672 \) |
\( \bigl[a^{3} - 3 a^{2} - a + 4\) , \( -a^{3} + 3 a^{2} + a - 4\) , \( 2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -3 a^{3} + 8 a^{2} + 6 a - 9\) , \( -15 a^{3} + 50 a^{2} + 5 a - 34\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+4\right){x}{y}+\left(2a^{3}-5a^{2}-5a+5\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+a-4\right){x}^{2}+\left(-3a^{3}+8a^{2}+6a-9\right){x}-15a^{3}+50a^{2}+5a-34$ |
| 16.1-a4 |
16.1-a |
$4$ |
$4$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.09718$ |
$(a^2+a-1)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$0.129007054$ |
$1295.106030$ |
4.195634234 |
\( -528875520 a^{3} + 1817747488 a^{2} + 32268256 a - 1104121200 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -a^{2} + a + 2\) , \( 0\) , \( 38 a^{3} - 104 a^{2} - 116 a + 163\) , \( 208 a^{3} - 565 a^{2} - 635 a + 872\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+5\right){x}{y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(38a^{3}-104a^{2}-116a+163\right){x}+208a^{3}-565a^{2}-635a+872$ |
| 16.1-b1 |
16.1-b |
$4$ |
$4$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$15.09718$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 1 \) |
$1$ |
$772.7780485$ |
1.617157678 |
\( -8192 a^{3} + 28672 a^{2} + 4096 a - 12288 \) |
\( \bigl[0\) , \( -a^{2} + 3 a + 3\) , \( 0\) , \( -2 a^{3} + 2 a^{2} + 6 a + 2\) , \( -2 a^{3} - 2 a^{2} + 4 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(-a^{2}+3a+3\right){x}^{2}+\left(-2a^{3}+2a^{2}+6a+2\right){x}-2a^{3}-2a^{2}+4a+3$ |
| 16.1-b2 |
16.1-b |
$4$ |
$4$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.09718$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$772.7780485$ |
1.617157678 |
\( 10248160 a^{3} + 12869728 a^{2} - 9199584 a - 9383184 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( 0\) , \( 10 a^{3} - 11 a^{2} - 62 a - 32\) , \( -27 a^{3} + 29 a^{2} + 163 a + 93\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}={x}^{3}+\left(a^{3}-3a^{2}-2a+2\right){x}^{2}+\left(10a^{3}-11a^{2}-62a-32\right){x}-27a^{3}+29a^{2}+163a+93$ |
| 16.1-b3 |
16.1-b |
$4$ |
$4$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.09718$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$193.1945121$ |
1.617157678 |
\( -6053856 a^{3} + 5767040 a^{2} + 37945344 a + 24654672 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -2 a^{3} + 5 a^{2} + 7 a - 4\) , \( a^{3} - 3 a^{2} - a + 4\) , \( -3 a^{3} + 8 a^{2} + 13 a - 3\) , \( -17 a^{3} + 56 a^{2} + 7 a - 32\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+5\right){x}{y}+\left(a^{3}-3a^{2}-a+4\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+7a-4\right){x}^{2}+\left(-3a^{3}+8a^{2}+13a-3\right){x}-17a^{3}+56a^{2}+7a-32$ |
| 16.1-b4 |
16.1-b |
$4$ |
$4$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.09718$ |
$(a^2+a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$772.7780485$ |
1.617157678 |
\( -528875520 a^{3} + 1817747488 a^{2} + 32268256 a - 1104121200 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( 2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -2 a^{3} + 2 a^{2} + 6 a + 2\) , \( a^{3} - a^{2} - 6 a\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+5\right){x}{y}+\left(2a^{3}-5a^{2}-5a+5\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-1\right){x}^{2}+\left(-2a^{3}+2a^{2}+6a+2\right){x}+a^{3}-a^{2}-6a$ |
| 17.1-a1 |
17.1-a |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$15.21203$ |
$(a^3-3a^2-2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$94.42352016$ |
3.556724957 |
\( \frac{13834806373280509636740011174}{289} a^{3} - \frac{37580309182394739748115559673}{289} a^{2} - \frac{42253016405658218695644998246}{289} a + \frac{57937966910413693362695212289}{289} \) |
\( \bigl[a\) , \( -2 a^{3} + 5 a^{2} + 5 a - 4\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 436 a^{3} - 541 a^{2} - 2889 a - 1731\) , \( -12800 a^{3} + 12436 a^{2} + 73729 a + 42292\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+5a-4\right){x}^{2}+\left(436a^{3}-541a^{2}-2889a-1731\right){x}-12800a^{3}+12436a^{2}+73729a+42292$ |
| 17.1-a2 |
17.1-a |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$15.21203$ |
$(a^3-3a^2-2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 1 \) |
$1$ |
$188.8470403$ |
3.556724957 |
\( -\frac{64062278444570}{17} a^{3} + \frac{159030677714743}{17} a^{2} + \frac{222959298472246}{17} a - \frac{198097673386670}{17} \) |
\( \bigl[a\) , \( -2 a^{3} + 5 a^{2} + 5 a - 4\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 496 a^{3} - 551 a^{2} - 2989 a - 1676\) , \( -12292 a^{3} + 13558 a^{2} + 73547 a + 41221\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+5a-4\right){x}^{2}+\left(496a^{3}-551a^{2}-2989a-1676\right){x}-12292a^{3}+13558a^{2}+73547a+41221$ |
| 17.1-a3 |
17.1-a |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$15.21203$ |
$(a^3-3a^2-2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$849.8116814$ |
3.556724957 |
\( \frac{3160780786477234}{24137569} a^{3} - \frac{8584784275986769}{24137569} a^{2} - \frac{9657653990723062}{24137569} a + \frac{13239950045973032}{24137569} \) |
\( \bigl[a\) , \( -2 a^{3} + 5 a^{2} + 5 a - 4\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 16 a^{3} - 21 a^{2} - 109 a - 56\) , \( 92 a^{3} - 88 a^{2} - 533 a - 305\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+5a-4\right){x}^{2}+\left(16a^{3}-21a^{2}-109a-56\right){x}+92a^{3}-88a^{2}-533a-305$ |
| 17.1-a4 |
17.1-a |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$15.21203$ |
$(a^3-3a^2-2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1699.623362$ |
3.556724957 |
\( -\frac{36228926}{4913} a^{3} + \frac{83659129}{4913} a^{2} + \frac{136209514}{4913} a - \frac{75851327}{4913} \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 3\) , \( a^{2} - 3 a - 1\) , \( 1\) , \( -5 a^{3} + 16 a^{2} + 6 a - 16\) , \( -2 a^{3} + 6 a^{2} + a + 2\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+3\right){x}{y}+{y}={x}^{3}+\left(a^{2}-3a-1\right){x}^{2}+\left(-5a^{3}+16a^{2}+6a-16\right){x}-2a^{3}+6a^{2}+a+2$ |
| 17.1-b1 |
17.1-b |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$15.21203$ |
$(a^3-3a^2-2a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$3.490744549$ |
$4.207340861$ |
2.212869756 |
\( \frac{13834806373280509636740011174}{289} a^{3} - \frac{37580309182394739748115559673}{289} a^{2} - \frac{42253016405658218695644998246}{289} a + \frac{57937966910413693362695212289}{289} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( -848 a^{3} + 2260 a^{2} + 2564 a - 3510\) , \( -22808 a^{3} + 61558 a^{2} + 69436 a - 95032\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-6a+5\right){x}{y}+\left(2a^{3}-5a^{2}-6a+5\right){y}={x}^{3}+\left(-848a^{3}+2260a^{2}+2564a-3510\right){x}-22808a^{3}+61558a^{2}+69436a-95032$ |
| 17.1-b2 |
17.1-b |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$15.21203$ |
$(a^3-3a^2-2a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$6.981489099$ |
$4.207340861$ |
2.212869756 |
\( -\frac{64062278444570}{17} a^{3} + \frac{159030677714743}{17} a^{2} + \frac{222959298472246}{17} a - \frac{198097673386670}{17} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( -48 a^{3} + 130 a^{2} + 144 a - 215\) , \( -466 a^{3} + 1261 a^{2} + 1414 a - 1971\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-6a+5\right){x}{y}+\left(2a^{3}-5a^{2}-6a+5\right){y}={x}^{3}+\left(-48a^{3}+130a^{2}+144a-215\right){x}-466a^{3}+1261a^{2}+1414a-1971$ |
| 17.1-b3 |
17.1-b |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$15.21203$ |
$(a^3-3a^2-2a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.163581516$ |
$340.7946097$ |
2.212869756 |
\( \frac{3160780786477234}{24137569} a^{3} - \frac{8584784275986769}{24137569} a^{2} - \frac{9657653990723062}{24137569} a + \frac{13239950045973032}{24137569} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( -8 a^{3} + 20 a^{2} + 24 a - 35\) , \( -54 a^{3} + 149 a^{2} + 166 a - 231\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-6a+5\right){x}{y}+\left(2a^{3}-5a^{2}-6a+5\right){y}={x}^{3}+\left(-8a^{3}+20a^{2}+24a-35\right){x}-54a^{3}+149a^{2}+166a-231$ |
| 17.1-b4 |
17.1-b |
$4$ |
$6$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$15.21203$ |
$(a^3-3a^2-2a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$2.327163033$ |
$340.7946097$ |
2.212869756 |
\( -\frac{36228926}{4913} a^{3} + \frac{83659129}{4913} a^{2} + \frac{136209514}{4913} a - \frac{75851327}{4913} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 2 a^{3} - 5 a^{2} - 6 a + 6\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-6a+5\right){x}{y}+\left(2a^{3}-5a^{2}-6a+5\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-6a+5\right){x}+2a^{3}-5a^{2}-6a+6$ |
| 23.1-a1 |
23.1-a |
$2$ |
$2$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$15.79781$ |
$(a^2-2a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.075786706$ |
$919.2072240$ |
4.665025598 |
\( \frac{1262080}{529} a^{3} - \frac{8120064}{529} a^{2} + \frac{5079040}{529} a + \frac{26007360}{529} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( -2 a^{3} + 5 a^{2} + 7 a - 4\) , \( 2 a^{3} - 5 a^{2} - 5 a + 4\) , \( -a^{3} + 9 a + 6\) , \( -2 a^{3} + 3 a^{2} + 11 a - 1\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(2a^{3}-5a^{2}-5a+4\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+7a-4\right){x}^{2}+\left(-a^{3}+9a+6\right){x}-2a^{3}+3a^{2}+11a-1$ |
| 23.1-a2 |
23.1-a |
$2$ |
$2$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$15.79781$ |
$(a^2-2a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.075786706$ |
$1838.414448$ |
4.665025598 |
\( -\frac{49178112}{23} a^{3} + \frac{169106688}{23} a^{2} + \frac{3020800}{23} a - \frac{102695232}{23} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 4\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 2 a^{3} - 5 a^{2} - 5 a + 4\) , \( 8 a^{3} - 17 a^{2} - 31 a + 5\) , \( -4 a^{3} - 2 a^{2} + 37 a + 39\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+4\right){x}{y}+\left(2a^{3}-5a^{2}-5a+4\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-6a+5\right){x}^{2}+\left(8a^{3}-17a^{2}-31a+5\right){x}-4a^{3}-2a^{2}+37a+39$ |
| 23.1-b1 |
23.1-b |
$2$ |
$2$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$15.79781$ |
$(a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.065141793$ |
$2601.503755$ |
2.837081085 |
\( \frac{1262080}{529} a^{3} - \frac{8120064}{529} a^{2} + \frac{5079040}{529} a + \frac{26007360}{529} \) |
\( \bigl[a^{3} - 3 a^{2} - a + 4\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -a^{2} + 2 a + 1\) , \( -a^{3} + 4 a^{2} - 4\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-a+4\right){x}{y}+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+2\right){x}^{2}+\left(-a^{2}+2a+1\right){x}-a^{3}+4a^{2}-4$ |
| 23.1-b2 |
23.1-b |
$2$ |
$2$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$15.79781$ |
$(a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.032570896$ |
$2601.503755$ |
2.837081085 |
\( -\frac{49178112}{23} a^{3} + \frac{169106688}{23} a^{2} + \frac{3020800}{23} a - \frac{102695232}{23} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -a^{3} + 3 a^{2} + 3 a - 4\) , \( 2 a^{3} - 5 a^{2} - 5 a + 4\) , \( -a^{3} + 4 a^{2} + 3 a - 9\) , \( a^{2} - 4\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+5\right){x}{y}+\left(2a^{3}-5a^{2}-5a+4\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-4\right){x}^{2}+\left(-a^{3}+4a^{2}+3a-9\right){x}+a^{2}-4$ |
| 27.2-a1 |
27.2-a |
$2$ |
$3$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{11} \) |
$16.11764$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$28.39623037$ |
2.139246262 |
\( 2601469299 a^{3} + 979846000 a^{2} - 1845097523 a - 868242642 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 2\) , \( -2 a^{3} + 5 a^{2} + 5 a - 4\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( 155 a^{3} - 211 a^{2} - 829 a - 434\) , \( -1557 a^{3} + 1446 a^{2} + 10025 a + 5864\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+2\right){x}{y}+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+5a-4\right){x}^{2}+\left(155a^{3}-211a^{2}-829a-434\right){x}-1557a^{3}+1446a^{2}+10025a+5864$ |
| 27.2-a2 |
27.2-a |
$2$ |
$3$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{9} \) |
$16.11764$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$255.5660733$ |
2.139246262 |
\( 24 a^{3} + 14 a^{2} + 1119 a + 702 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 2\) , \( -2 a^{3} + 5 a^{2} + 5 a - 4\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( 4 a^{2} - 9 a - 14\) , \( 3 a^{3} - 2 a^{2} - 21 a - 16\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+2\right){x}{y}+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+5a-4\right){x}^{2}+\left(4a^{2}-9a-14\right){x}+3a^{3}-2a^{2}-21a-16$ |
| 27.2-b1 |
27.2-b |
$2$ |
$3$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{9} \) |
$16.11764$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$24.07650104$ |
1.813816981 |
\( -239246708898838021 a^{3} - 301268551509204475 a^{2} + 214356574729728562 a + 220208013181338423 \) |
\( \bigl[1\) , \( a^{3} - 3 a^{2} - a + 2\) , \( 2 a^{3} - 5 a^{2} - 5 a + 4\) , \( -134 a^{3} + 79 a^{2} + 278 a - 218\) , \( -1211 a^{3} - 2856 a^{2} + 217 a + 2956\bigr] \) |
${y}^2+{x}{y}+\left(2a^{3}-5a^{2}-5a+4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+2\right){x}^{2}+\left(-134a^{3}+79a^{2}+278a-218\right){x}-1211a^{3}-2856a^{2}+217a+2956$ |
| 27.2-b2 |
27.2-b |
$2$ |
$3$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{3} \) |
$16.11764$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$216.6885094$ |
1.813816981 |
\( 10859688666169 a^{3} - 37324787338606 a^{2} - 662596359841 a + 22671530225877 \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 4\) , \( -1\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( 37 a^{3} - 37 a^{2} - 228 a - 146\) , \( -312 a^{3} + 353 a^{2} + 1854 a + 1009\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+4\right){x}{y}+\left(a^{3}-3a^{2}-2a+4\right){y}={x}^{3}-{x}^{2}+\left(37a^{3}-37a^{2}-228a-146\right){x}-312a^{3}+353a^{2}+1854a+1009$ |
| 27.2-c1 |
27.2-c |
$2$ |
$3$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{9} \) |
$16.11764$ |
$(-a)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
|
\( 3 \) |
$1$ |
$1.770053263$ |
2.792467069 |
\( -239246708898838021 a^{3} - 301268551509204475 a^{2} + 214356574729728562 a + 220208013181338423 \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 1\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( -282 a^{3} + 772 a^{2} + 854 a - 1264\) , \( -3630 a^{3} + 9955 a^{2} + 10840 a - 15521\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-282a^{3}+772a^{2}+854a-1264\right){x}-3630a^{3}+9955a^{2}+10840a-15521$ |
| 27.2-c2 |
27.2-c |
$2$ |
$3$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{3} \) |
$16.11764$ |
$(-a)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
|
\( 1 \) |
$1$ |
$143.3743143$ |
2.792467069 |
\( 10859688666169 a^{3} - 37324787338606 a^{2} - 662596359841 a + 22671530225877 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 2\) , \( -a^{3} + 2 a^{2} + 5 a - 1\) , \( a^{3} - 3 a^{2} - a + 3\) , \( -4 a^{3} - a^{2} + 5 a - 3\) , \( -12 a^{3} - 29 a^{2} - 13 a + 2\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+2\right){x}{y}+\left(a^{3}-3a^{2}-a+3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-1\right){x}^{2}+\left(-4a^{3}-a^{2}+5a-3\right){x}-12a^{3}-29a^{2}-13a+2$ |
| 27.2-d1 |
27.2-d |
$2$ |
$3$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{9} \) |
$16.11764$ |
$(-a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.570985337$ |
$519.7693715$ |
3.312317496 |
\( 24 a^{3} + 14 a^{2} + 1119 a + 702 \) |
\( \bigl[1\) , \( -2 a^{3} + 5 a^{2} + 7 a - 4\) , \( 2 a^{3} - 5 a^{2} - 6 a + 4\) , \( 6 a^{3} - 22 a^{2} + 2 a + 22\) , \( 30 a^{3} - 105 a^{2} + 6 a + 58\bigr] \) |
${y}^2+{x}{y}+\left(2a^{3}-5a^{2}-6a+4\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+7a-4\right){x}^{2}+\left(6a^{3}-22a^{2}+2a+22\right){x}+30a^{3}-105a^{2}+6a+58$ |
| 27.2-d2 |
27.2-d |
$2$ |
$3$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{11} \) |
$16.11764$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1.712956013$ |
$6.416905822$ |
3.312317496 |
\( 2601469299 a^{3} + 979846000 a^{2} - 1845097523 a - 868242642 \) |
\( \bigl[1\) , \( -2 a^{3} + 5 a^{2} + 7 a - 4\) , \( 2 a^{3} - 5 a^{2} - 6 a + 4\) , \( 581 a^{3} - 1997 a^{2} - 38 a + 1222\) , \( 15566 a^{3} - 53503 a^{2} - 937 a + 32479\bigr] \) |
${y}^2+{x}{y}+\left(2a^{3}-5a^{2}-6a+4\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+7a-4\right){x}^{2}+\left(581a^{3}-1997a^{2}-38a+1222\right){x}+15566a^{3}-53503a^{2}-937a+32479$ |
| 33.1-a1 |
33.1-a |
$2$ |
$2$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{16} \cdot 11^{4} \) |
$16.52705$ |
$(-a), (a^3-3a^2-2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$40.13875187$ |
1.343944816 |
\( -\frac{37218889768960}{630247042161} a^{3} - \frac{577789941869632}{630247042161} a^{2} - \frac{208677623294464}{630247042161} a + \frac{124443860676160}{630247042161} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{3} - 3 a^{2} - a + 4\) , \( 2 a^{3} - 5 a^{2} - 6 a + 4\) , \( -4 a^{3} + 11 a^{2} + 12 a - 17\) , \( -80 a^{3} + 217 a^{2} + 246 a - 337\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(2a^{3}-5a^{2}-6a+4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+4\right){x}^{2}+\left(-4a^{3}+11a^{2}+12a-17\right){x}-80a^{3}+217a^{2}+246a-337$ |
| 33.1-a2 |
33.1-a |
$2$ |
$2$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{8} \cdot 11^{2} \) |
$16.52705$ |
$(-a), (a^3-3a^2-2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$160.5550075$ |
1.343944816 |
\( \frac{2763974729728}{793881} a^{3} + \frac{5197091868352}{793881} a^{2} - \frac{1742926646144}{793881} a - \frac{2796704681728}{793881} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -a^{3} + 3 a^{2} + 2 a - 2\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( 17 a^{3} - 49 a^{2} - 20 a + 15\) , \( 123 a^{3} - 396 a^{2} - 71 a + 194\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-5a+5\right){x}{y}+\left(a^{3}-3a^{2}-2a+4\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-2\right){x}^{2}+\left(17a^{3}-49a^{2}-20a+15\right){x}+123a^{3}-396a^{2}-71a+194$ |
| 33.1-b1 |
33.1-b |
$4$ |
$4$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{2} \cdot 11^{2} \) |
$16.52705$ |
$(-a), (a^3-3a^2-2a+5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.449522905$ |
$1073.479197$ |
4.039271451 |
\( \frac{61931264390}{1089} a^{3} - \frac{89066640709}{1089} a^{2} - \frac{517920426016}{1089} a + \frac{490053006958}{1089} \) |
\( \bigl[a\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( a\) , \( -10 a^{3} + 24 a^{2} + 42 a - 47\) , \( 55 a^{3} - 143 a^{2} - 195 a + 249\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-2\right){x}^{2}+\left(-10a^{3}+24a^{2}+42a-47\right){x}+55a^{3}-143a^{2}-195a+249$ |
| 33.1-b2 |
33.1-b |
$4$ |
$4$ |
4.4.14272.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3 \cdot 11 \) |
$16.52705$ |
$(-a), (a^3-3a^2-2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.224761452$ |
$2146.958394$ |
4.039271451 |
\( \frac{313606}{33} a^{3} - \frac{927911}{33} a^{2} - \frac{601646}{33} a + \frac{1075541}{33} \) |
\( \bigl[a\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( a\) , \( -a^{2} + 2 a + 3\) , \( a^{3} - 3 a^{2} - 3 a + 6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-2\right){x}^{2}+\left(-a^{2}+2a+3\right){x}+a^{3}-3a^{2}-3a+6$ |
*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.
