| 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 |
| 8.2-a1 |
8.2-a |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{4} \) |
$14.44098$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$577.0468467$ |
2.315310980 |
\( 13248223492222193 a^{3} - 23508409183253015 a^{2} - 61283077778025158 a + 34212914079218048 \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + 2 a^{2} + 5 a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 120 a^{3} - 58 a^{2} - 737 a - 480\) , \( -1239 a^{3} + 641 a^{2} + 7775 a + 5059\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-2\right){x}^{2}+\left(120a^{3}-58a^{2}-737a-480\right){x}-1239a^{3}+641a^{2}+7775a+5059$ |
| 8.2-a2 |
8.2-a |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$14.44098$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$577.0468467$ |
2.315310980 |
\( -1191486939 a^{3} + 3315222345 a^{2} + 1291767576 a - 1293622444 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 2\) , \( -a^{2} + 2 a + 4\) , \( a\) , \( 8 a^{3} - 23 a^{2} - 9 a + 16\) , \( 23 a^{3} - 64 a^{2} - 27 a + 29\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(8a^{3}-23a^{2}-9a+16\right){x}+23a^{3}-64a^{2}-27a+29$ |
| 8.2-a3 |
8.2-a |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$14.44098$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$36.06542792$ |
2.315310980 |
\( -15878775660750025413 a^{3} + 43494248145076889731 a^{2} + 19629906781804479190 a - 18260452840524552892 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 2\) , \( -a^{2} + 2 a + 4\) , \( a\) , \( 123 a^{3} - 338 a^{2} - 154 a + 146\) , \( 1623 a^{3} - 4446 a^{2} - 2012 a + 1863\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(123a^{3}-338a^{2}-154a+146\right){x}+1623a^{3}-4446a^{2}-2012a+1863$ |
| 8.2-a4 |
8.2-a |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$14.44098$ |
$(-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$577.0468467$ |
2.315310980 |
\( 105745 a^{3} + 174313 a^{2} + 13204 a - 60216 \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( 2 a^{3} - 3 a^{2} - 8 a + 2\) , \( 2 a^{3} - 21 a^{2} - 8 a + 9\) , \( 28 a^{3} - 10 a^{2} - 15 a + 5\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(2a^{3}-3a^{2}-8a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+2\right){x}^{2}+\left(2a^{3}-21a^{2}-8a+9\right){x}+28a^{3}-10a^{2}-15a+5$ |
| 8.2-b1 |
8.2-b |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$14.44098$ |
$(-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.440349113$ |
$152.0389114$ |
2.977384800 |
\( -1191486939 a^{3} + 3315222345 a^{2} + 1291767576 a - 1293622444 \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( 2 a^{3} - 3 a^{2} - 10 a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -4 a^{3} - 14 a^{2} - 4 a + 10\) , \( 19 a^{3} + 41 a^{2} + 6 a - 17\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-10a\right){x}^{2}+\left(-4a^{3}-14a^{2}-4a+10\right){x}+19a^{3}+41a^{2}+6a-17$ |
| 8.2-b2 |
8.2-b |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$14.44098$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$4.880698226$ |
$38.00972786$ |
2.977384800 |
\( -15878775660750025413 a^{3} + 43494248145076889731 a^{2} + 19629906781804479190 a - 18260452840524552892 \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( 2 a^{3} - 3 a^{2} - 10 a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -24 a^{3} - 99 a^{2} - 19 a + 40\) , \( -490 a^{3} - 1138 a^{2} - 93 a + 377\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-10a\right){x}^{2}+\left(-24a^{3}-99a^{2}-19a+40\right){x}-490a^{3}-1138a^{2}-93a+377$ |
| 8.2-b3 |
8.2-b |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$14.44098$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.220174556$ |
$152.0389114$ |
2.977384800 |
\( 105745 a^{3} + 174313 a^{2} + 13204 a - 60216 \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 2\) , \( -a^{2} + 2\) , \( a\) , \( 59 a^{3} - 158 a^{2} - 91 a + 80\) , \( 534 a^{3} - 1458 a^{2} - 678 a + 623\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(59a^{3}-158a^{2}-91a+80\right){x}+534a^{3}-1458a^{2}-678a+623$ |
| 8.2-b4 |
8.2-b |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{4} \) |
$14.44098$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$4.880698226$ |
$38.00972786$ |
2.977384800 |
\( 13248223492222193 a^{3} - 23508409183253015 a^{2} - 61283077778025158 a + 34212914079218048 \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 6 a - 2\) , \( a^{3} - a^{2} - 5 a\) , \( -47 a^{3} + 85 a^{2} + 215 a - 124\) , \( -319 a^{3} + 567 a^{2} + 1475 a - 826\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a-2\right){x}^{2}+\left(-47a^{3}+85a^{2}+215a-124\right){x}-319a^{3}+567a^{2}+1475a-826$ |
| 9.2-a1 |
9.2-a |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$14.65516$ |
$(-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$126.5236133$ |
2.030625506 |
\( \frac{337535631604}{9} a^{3} - \frac{598947315488}{9} a^{2} - \frac{1561352884649}{9} a + \frac{871696686907}{9} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 9 a + 1\) , \( 2 a^{3} - 3 a^{2} - 9 a\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( 10 a^{3} - 19 a^{2} - 39 a + 15\) , \( 4 a^{3} - 43 a + 13\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-9a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+3\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-9a\right){x}^{2}+\left(10a^{3}-19a^{2}-39a+15\right){x}+4a^{3}-43a+13$ |
| 9.2-a2 |
9.2-a |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$14.65516$ |
$(-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$506.0944534$ |
2.030625506 |
\( -\frac{2809}{9} a^{3} + \frac{6182}{9} a^{2} + \frac{12005}{9} a + \frac{2861}{9} \) |
\( \bigl[1\) , \( a^{2} - 3\) , \( 2 a^{3} - 3 a^{2} - 8 a + 2\) , \( -a^{3} + 2 a^{2} + 6 a + 1\) , \( -a^{3} + 2 a^{2} + 5 a - 6\bigr] \) |
${y}^2+{x}{y}+\left(2a^{3}-3a^{2}-8a+2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{3}+2a^{2}+6a+1\right){x}-a^{3}+2a^{2}+5a-6$ |
| 9.2-a3 |
9.2-a |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$14.65516$ |
$(-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$506.0944534$ |
2.030625506 |
\( \frac{7404848}{81} a^{3} - \frac{12594191}{81} a^{2} - \frac{33539950}{81} a + \frac{18854041}{81} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a^{3} - a^{2} - 4 a - 1\) , \( 6 a^{3} - 18 a^{2} - 3 a + 12\) , \( -2 a^{2} + 3 a - 1\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(6a^{3}-18a^{2}-3a+12\right){x}-2a^{2}+3a-1$ |
| 9.2-a4 |
9.2-a |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{32} \) |
$14.65516$ |
$(-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$31.63090333$ |
2.030625506 |
\( -\frac{8880954382979771}{43046721} a^{3} + \frac{501671290675028}{4782969} a^{2} + \frac{55507815273710893}{43046721} a + \frac{1339397560769671}{1594323} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a^{3} - a^{2} - 4 a - 1\) , \( 26 a^{3} - 83 a^{2} + 2 a + 22\) , \( 1544 a^{3} - 4217 a^{2} - 1956 a + 1795\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(26a^{3}-83a^{2}+2a+22\right){x}+1544a^{3}-4217a^{2}-1956a+1795$ |
| 9.2-a5 |
9.2-a |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{16} \) |
$14.65516$ |
$(-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$126.5236133$ |
2.030625506 |
\( \frac{1012761232322}{6561} a^{3} + \frac{227650135462}{729} a^{2} + \frac{113755555913}{6561} a - \frac{8275598185}{81} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( a^{3} - a^{2} - 4 a - 1\) , \( 71 a^{3} - 198 a^{2} - 83 a + 87\) , \( 786 a^{3} - 2155 a^{2} - 969 a + 903\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(71a^{3}-198a^{2}-83a+87\right){x}+786a^{3}-2155a^{2}-969a+903$ |
| 9.2-a6 |
9.2-a |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$14.65516$ |
$(-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$7.907725834$ |
2.030625506 |
\( \frac{88337427239397557611}{81} a^{3} + \frac{178643397563268268748}{81} a^{2} + \frac{9886574331766691587}{81} a - \frac{58457390752199491645}{81} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{2} - 2 a - 2\) , \( 2 a^{3} - 3 a^{2} - 8 a + 1\) , \( 48 a^{3} - 106 a^{2} - 203 a + 228\) , \( -2566 a^{3} + 1268 a^{2} + 16066 a + 10613\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(2a^{3}-3a^{2}-8a+1\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(48a^{3}-106a^{2}-203a+228\right){x}-2566a^{3}+1268a^{2}+16066a+10613$ |
| 9.2-b1 |
9.2-b |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$14.65516$ |
$(-a^3+2a^2+3a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.213910911$ |
$1240.886061$ |
1.065033097 |
\( \frac{337535631604}{9} a^{3} - \frac{598947315488}{9} a^{2} - \frac{1561352884649}{9} a + \frac{871696686907}{9} \) |
\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 5 a - 1\) , \( 2 a^{3} - 3 a^{2} - 8 a + 1\) , \( -42 a^{3} + 74 a^{2} + 198 a - 108\) , \( 259 a^{3} - 460 a^{2} - 1197 a + 670\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a-1\right){x}{y}+\left(2a^{3}-3a^{2}-8a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-1\right){x}^{2}+\left(-42a^{3}+74a^{2}+198a-108\right){x}+259a^{3}-460a^{2}-1197a+670$ |
| 9.2-b2 |
9.2-b |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$14.65516$ |
$(-a^3+2a^2+3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1.711287293$ |
$4.847211176$ |
1.065033097 |
\( \frac{88337427239397557611}{81} a^{3} + \frac{178643397563268268748}{81} a^{2} + \frac{9886574331766691587}{81} a - \frac{58457390752199491645}{81} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 9 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( -153 a^{3} + 11 a^{2} + 1044 a + 968\) , \( 136288 a^{3} - 69560 a^{2} - 851490 a - 553568\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-9a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+1\right){x}^{2}+\left(-153a^{3}+11a^{2}+1044a+968\right){x}+136288a^{3}-69560a^{2}-851490a-553568$ |
| 9.2-b3 |
9.2-b |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$14.65516$ |
$(-a^3+2a^2+3a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.427821823$ |
$1240.886061$ |
1.065033097 |
\( \frac{7404848}{81} a^{3} - \frac{12594191}{81} a^{2} - \frac{33539950}{81} a + \frac{18854041}{81} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 27 a^{3} - 73 a^{2} - 36 a + 35\) , \( -7 a^{3} + 21 a^{2} + 3 a - 6\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+1\right){x}^{2}+\left(27a^{3}-73a^{2}-36a+35\right){x}-7a^{3}+21a^{2}+3a-6$ |
| 9.2-b4 |
9.2-b |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{32} \) |
$14.65516$ |
$(-a^3+2a^2+3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.711287293$ |
$4.847211176$ |
1.065033097 |
\( -\frac{8880954382979771}{43046721} a^{3} + \frac{501671290675028}{4782969} a^{2} + \frac{55507815273710893}{43046721} a + \frac{1339397560769671}{1594323} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 142 a^{3} - 373 a^{2} - 221 a + 125\) , \( 10669 a^{3} - 29170 a^{2} - 13355 a + 12116\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+1\right){x}^{2}+\left(142a^{3}-373a^{2}-221a+125\right){x}+10669a^{3}-29170a^{2}-13355a+12116$ |
| 9.2-b5 |
9.2-b |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{16} \) |
$14.65516$ |
$(-a^3+2a^2+3a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.855643646$ |
$77.55537882$ |
1.065033097 |
\( \frac{1012761232322}{6561} a^{3} + \frac{227650135462}{729} a^{2} + \frac{113755555913}{6561} a - \frac{8275598185}{81} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 267 a^{3} - 733 a^{2} - 336 a + 310\) , \( 5342 a^{3} - 14646 a^{2} - 6618 a + 6148\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+1\right){x}^{2}+\left(267a^{3}-733a^{2}-336a+310\right){x}+5342a^{3}-14646a^{2}-6618a+6148$ |
| 9.2-b6 |
9.2-b |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$14.65516$ |
$(-a^3+2a^2+3a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.213910911$ |
$1240.886061$ |
1.065033097 |
\( -\frac{2809}{9} a^{3} + \frac{6182}{9} a^{2} + \frac{12005}{9} a + \frac{2861}{9} \) |
\( \bigl[a + 1\) , \( 2 a^{3} - 3 a^{2} - 9 a\) , \( 0\) , \( -2 a^{3} + a^{2} + 13 a + 14\) , \( 2 a^{3} - 2 a^{2} - 10 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(2a^{3}-3a^{2}-9a\right){x}^{2}+\left(-2a^{3}+a^{2}+13a+14\right){x}+2a^{3}-2a^{2}-10a-3$ |
| 10.1-a1 |
10.1-a |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{10} \cdot 5^{2} \) |
$14.84945$ |
$(-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$810.9198740$ |
1.626845116 |
\( -\frac{10480002733}{25600} a^{3} + \frac{5744130759}{5120} a^{2} + \frac{3270189017}{6400} a - \frac{11918569419}{25600} \) |
\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 61 a^{3} - 167 a^{2} - 75 a + 70\) , \( 576 a^{3} - 1578 a^{2} - 711 a + 662\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a-1\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a-1\right){x}^{2}+\left(61a^{3}-167a^{2}-75a+70\right){x}+576a^{3}-1578a^{2}-711a+662$ |
| 10.1-a2 |
10.1-a |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{5} \cdot 5 \) |
$14.84945$ |
$(-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$202.7299685$ |
1.626845116 |
\( -\frac{274408606271677}{160} a^{3} + \frac{150330411057943}{32} a^{2} + \frac{84810481011233}{40} a - \frac{315565570668091}{160} \) |
\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 976 a^{3} - 2672 a^{2} - 1210 a + 1120\) , \( 37351 a^{3} - 102311 a^{2} - 46172 a + 42956\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a-1\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a-1\right){x}^{2}+\left(976a^{3}-2672a^{2}-1210a+1120\right){x}+37351a^{3}-102311a^{2}-46172a+42956$ |
| 10.1-a3 |
10.1-a |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{5} \cdot 5 \) |
$14.84945$ |
$(-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$810.9198740$ |
1.626845116 |
\( \frac{6208797}{160} a^{3} - \frac{2209015}{32} a^{2} - \frac{7159353}{40} a + \frac{16039291}{160} \) |
\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - 2 a^{2} - 5 a + 1\) , \( 2 a^{3} - 3 a^{2} - 8 a + 2\) , \( -2 a^{3} + a^{2} + 12 a + 7\) , \( -11 a^{3} + 6 a^{2} + 67 a + 37\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a-1\right){x}{y}+\left(2a^{3}-3a^{2}-8a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-5a+1\right){x}^{2}+\left(-2a^{3}+a^{2}+12a+7\right){x}-11a^{3}+6a^{2}+67a+37$ |
| 10.1-a4 |
10.1-a |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{20} \cdot 5^{4} \) |
$14.84945$ |
$(-a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$202.7299685$ |
1.626845116 |
\( \frac{65473675802867}{655360000} a^{3} - \frac{23356298648601}{131072000} a^{2} - \frac{75509147443783}{163840000} a + \frac{174238423128981}{655360000} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 9 a + 1\) , \( a\) , \( a^{3} - a^{2} - 4 a - 1\) , \( -3 a^{3} + 9 a - 4\) , \( -18 a^{3} + 15 a^{2} + 63 a - 32\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-9a+1\right){x}{y}+\left(a^{3}-a^{2}-4a-1\right){y}={x}^{3}+a{x}^{2}+\left(-3a^{3}+9a-4\right){x}-18a^{3}+15a^{2}+63a-32$ |
| 10.1-a5 |
10.1-a |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{40} \cdot 5^{2} \) |
$14.84945$ |
$(-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$50.68249212$ |
1.626845116 |
\( -\frac{87810629781261733}{27487790694400} a^{3} + \frac{47997871295480239}{5497558138880} a^{2} + \frac{29298276815704817}{6871947673600} a - \frac{99054093272640019}{27487790694400} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 1\) , \( a^{2} - a - 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -8 a^{3} + 19 a^{2} + 32 a - 23\) , \( -66 a^{3} + 123 a^{2} + 301 a - 176\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+1\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-8a^{3}+19a^{2}+32a-23\right){x}-66a^{3}+123a^{2}+301a-176$ |
| 10.1-a6 |
10.1-a |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{10} \cdot 5^{8} \) |
$14.84945$ |
$(-a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$12.67062303$ |
1.626845116 |
\( \frac{18955788412509050133}{400000000} a^{3} - \frac{6728003511675238399}{80000000} a^{2} - \frac{21919882110070253217}{100000000} a + \frac{48973186135175370019}{400000000} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( 2 a^{3} - 3 a^{2} - 8 a + 2\) , \( 189 a^{3} - 83 a^{2} - 1216 a - 803\) , \( 3164 a^{3} - 1656 a^{2} - 19681 a - 12787\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(2a^{3}-3a^{2}-8a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+1\right){x}^{2}+\left(189a^{3}-83a^{2}-1216a-803\right){x}+3164a^{3}-1656a^{2}-19681a-12787$ |
| 10.1-b1 |
10.1-b |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{10} \cdot 5^{2} \) |
$14.84945$ |
$(-a), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.142614250$ |
$598.2737651$ |
3.423427547 |
\( -\frac{10480002733}{25600} a^{3} + \frac{5744130759}{5120} a^{2} + \frac{3270189017}{6400} a - \frac{11918569419}{25600} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 1\) , \( -a\) , \( 2 a^{3} - 3 a^{2} - 9 a + 2\) , \( 3 a^{3} - 10 a^{2} - 4 a + 1\) , \( 24 a^{3} - 65 a^{2} - 28 a + 25\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+1\right){x}{y}+\left(2a^{3}-3a^{2}-9a+2\right){y}={x}^{3}-a{x}^{2}+\left(3a^{3}-10a^{2}-4a+1\right){x}+24a^{3}-65a^{2}-28a+25$ |
| 10.1-b2 |
10.1-b |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{5} \cdot 5 \) |
$14.84945$ |
$(-a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 5 \) |
$0.285228500$ |
$74.78422064$ |
3.423427547 |
\( -\frac{274408606271677}{160} a^{3} + \frac{150330411057943}{32} a^{2} + \frac{84810481011233}{40} a - \frac{315565570668091}{160} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 1\) , \( -a\) , \( 2 a^{3} - 3 a^{2} - 9 a + 2\) , \( 73 a^{3} - 225 a^{2} - 99 a + 91\) , \( 1091 a^{3} - 2855 a^{2} - 1313 a + 1203\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+1\right){x}{y}+\left(2a^{3}-3a^{2}-9a+2\right){y}={x}^{3}-a{x}^{2}+\left(73a^{3}-225a^{2}-99a+91\right){x}+1091a^{3}-2855a^{2}-1313a+1203$ |
| 10.1-b3 |
10.1-b |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{5} \cdot 5 \) |
$14.84945$ |
$(-a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.285228500$ |
$299.1368825$ |
3.423427547 |
\( \frac{6208797}{160} a^{3} - \frac{2209015}{32} a^{2} - \frac{7159353}{40} a + \frac{16039291}{160} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 1\) , \( -2 a^{3} + 3 a^{2} + 9 a\) , \( 2 a^{3} - 3 a^{2} - 9 a + 2\) , \( -8 a^{3} + 14 a^{2} + 33 a - 2\) , \( -7 a^{3} + 15 a^{2} + 30 a\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+1\right){x}{y}+\left(2a^{3}-3a^{2}-9a+2\right){y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a\right){x}^{2}+\left(-8a^{3}+14a^{2}+33a-2\right){x}-7a^{3}+15a^{2}+30a$ |
| 10.1-b4 |
10.1-b |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{10} \cdot 5^{8} \) |
$14.84945$ |
$(-a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.142614250$ |
$149.5684412$ |
3.423427547 |
\( \frac{18955788412509050133}{400000000} a^{3} - \frac{6728003511675238399}{80000000} a^{2} - \frac{21919882110070253217}{100000000} a + \frac{48973186135175370019}{400000000} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 3\) , \( -a\) , \( 2 a^{3} - 3 a^{2} - 9 a + 2\) , \( -48 a^{3} + 90 a^{2} + 211 a - 139\) , \( 181 a^{3} - 329 a^{2} - 825 a + 499\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+3\right){x}{y}+\left(2a^{3}-3a^{2}-9a+2\right){y}={x}^{3}-a{x}^{2}+\left(-48a^{3}+90a^{2}+211a-139\right){x}+181a^{3}-329a^{2}-825a+499$ |
| 10.1-b5 |
10.1-b |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{20} \cdot 5^{4} \) |
$14.84945$ |
$(-a), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.071307125$ |
$598.2737651$ |
3.423427547 |
\( \frac{65473675802867}{655360000} a^{3} - \frac{23356298648601}{131072000} a^{2} - \frac{75509147443783}{163840000} a + \frac{174238423128981}{655360000} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 3\) , \( -a\) , \( 2 a^{3} - 3 a^{2} - 9 a + 2\) , \( -3 a^{3} + 5 a^{2} + 16 a - 9\) , \( -a^{3} + a^{2} + 7 a - 5\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+3\right){x}{y}+\left(2a^{3}-3a^{2}-9a+2\right){y}={x}^{3}-a{x}^{2}+\left(-3a^{3}+5a^{2}+16a-9\right){x}-a^{3}+a^{2}+7a-5$ |
| 10.1-b6 |
10.1-b |
$6$ |
$8$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{40} \cdot 5^{2} \) |
$14.84945$ |
$(-a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.035653562$ |
$149.5684412$ |
3.423427547 |
\( -\frac{87810629781261733}{27487790694400} a^{3} + \frac{47997871295480239}{5497558138880} a^{2} + \frac{29298276815704817}{6871947673600} a - \frac{99054093272640019}{27487790694400} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( -25 a^{3} + 17 a^{2} + 148 a + 87\) , \( -299 a^{3} + 155 a^{2} + 1862 a + 1207\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-1\right){x}^{2}+\left(-25a^{3}+17a^{2}+148a+87\right){x}-299a^{3}+155a^{2}+1862a+1207$ |
| 16.2-a1 |
16.2-a |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{10} \) |
$15.74800$ |
$(-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$563.0611636$ |
2.259195596 |
\( 105745 a^{3} + 174313 a^{2} + 13204 a - 60216 \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 4\) , \( a^{3} - a^{2} - 5 a\) , \( 28 a^{3} - 81 a^{2} - 31 a + 40\) , \( -214 a^{3} + 586 a^{2} + 268 a - 245\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(28a^{3}-81a^{2}-31a+40\right){x}-214a^{3}+586a^{2}+268a-245$ |
| 16.2-a2 |
16.2-a |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.74800$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$563.0611636$ |
2.259195596 |
\( -1191486939 a^{3} + 3315222345 a^{2} + 1291767576 a - 1293622444 \) |
\( \bigl[2 a^{3} - 3 a^{2} - 9 a + 2\) , \( -a^{3} + a^{2} + 5 a\) , \( a\) , \( -17 a^{3} + 26 a^{2} + 83 a - 37\) , \( -125 a^{3} + 224 a^{2} + 577 a - 319\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-9a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-17a^{3}+26a^{2}+83a-37\right){x}-125a^{3}+224a^{2}+577a-319$ |
| 16.2-a3 |
16.2-a |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{10} \) |
$15.74800$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$281.5305818$ |
2.259195596 |
\( -15878775660750025413 a^{3} + 43494248145076889731 a^{2} + 19629906781804479190 a - 18260452840524552892 \) |
\( \bigl[2 a^{3} - 3 a^{2} - 9 a + 2\) , \( -a^{3} + a^{2} + 5 a\) , \( a\) , \( -2 a^{3} - 24 a^{2} + 63 a - 17\) , \( -222 a^{3} + 457 a^{2} + 681 a - 415\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-9a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-2a^{3}-24a^{2}+63a-17\right){x}-222a^{3}+457a^{2}+681a-415$ |
| 16.2-a4 |
16.2-a |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{4} \) |
$15.74800$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$70.38264546$ |
2.259195596 |
\( 13248223492222193 a^{3} - 23508409183253015 a^{2} - 61283077778025158 a + 34212914079218048 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 5 a - 2\) , \( a^{3} - a^{2} - 4 a\) , \( 4 a^{3} + 8 a^{2} - 8 a - 19\) , \( 10 a^{3} + 36 a^{2} + 13 a - 34\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a-2\right){x}^{2}+\left(4a^{3}+8a^{2}-8a-19\right){x}+10a^{3}+36a^{2}+13a-34$ |
| 16.2-b1 |
16.2-b |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{10} \) |
$15.74800$ |
$(-a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.028078005$ |
$2137.036274$ |
3.852089635 |
\( 105745 a^{3} + 174313 a^{2} + 13204 a - 60216 \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( 2 a^{3} - 3 a^{2} - 8 a + 2\) , \( 2 a^{3} - 3 a^{2} - 8 a + 2\) , \( 10 a^{3} - 24 a^{2} - 21 a + 12\) , \( -36 a^{3} + 100 a^{2} + 40 a - 41\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(2a^{3}-3a^{2}-8a+2\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-8a+2\right){x}^{2}+\left(10a^{3}-24a^{2}-21a+12\right){x}-36a^{3}+100a^{2}+40a-41$ |
| 16.2-b2 |
16.2-b |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{4} \) |
$15.74800$ |
$(-a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.112312020$ |
$1068.518137$ |
3.852089635 |
\( 13248223492222193 a^{3} - 23508409183253015 a^{2} - 61283077778025158 a + 34212914079218048 \) |
\( \bigl[a\) , \( -a^{2} + 2\) , \( 0\) , \( 52 a^{3} - 25 a^{2} - 324 a - 219\) , \( -365 a^{3} + 185 a^{2} + 2280 a + 1490\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(52a^{3}-25a^{2}-324a-219\right){x}-365a^{3}+185a^{2}+2280a+1490$ |
| 16.2-b3 |
16.2-b |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.74800$ |
$(-a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.112312020$ |
$2137.036274$ |
3.852089635 |
\( -1191486939 a^{3} + 3315222345 a^{2} + 1291767576 a - 1293622444 \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( a\) , \( 12 a^{3} - 23 a^{2} - 38 a + 22\) , \( -a^{3} + 9 a^{2} - 21 a + 9\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(12a^{3}-23a^{2}-38a+22\right){x}-a^{3}+9a^{2}-21a+9$ |
| 16.2-b4 |
16.2-b |
$4$ |
$4$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{10} \) |
$15.74800$ |
$(-a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.112312020$ |
$267.1295343$ |
3.852089635 |
\( -15878775660750025413 a^{3} + 43494248145076889731 a^{2} + 19629906781804479190 a - 18260452840524552892 \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( a\) , \( 72 a^{3} - 203 a^{2} - 123 a + 92\) , \( -663 a^{3} + 1619 a^{2} + 732 a - 681\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(72a^{3}-203a^{2}-123a+92\right){x}-663a^{3}+1619a^{2}+732a-681$ |
| 18.2-a1 |
18.2-a |
$2$ |
$2$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{2} \) |
$15.98157$ |
$(-a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 1 \) |
$1$ |
$82.59959772$ |
1.491381341 |
\( \frac{60338226833}{96} a^{3} - \frac{106789563871}{96} a^{2} - \frac{23339153135}{8} a + \frac{156229457351}{96} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 4 a\) , \( -9 a^{3} - 2 a^{2} + 26 a - 4\) , \( -28 a^{3} - 40 a^{2} + 22 a + 4\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+1\right){x}^{2}+\left(-9a^{3}-2a^{2}+26a-4\right){x}-28a^{3}-40a^{2}+22a+4$ |
| 18.2-a2 |
18.2-a |
$2$ |
$2$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$15.98157$ |
$(-a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2^{2} \) |
$1$ |
$20.64989943$ |
1.491381341 |
\( -\frac{831656172914791205}{9216} a^{3} + \frac{759341919204247801}{3072} a^{2} + \frac{257030729310271345}{2304} a - \frac{956397309964116115}{9216} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( 2 a^{3} - 3 a^{2} - 10 a + 2\) , \( 2 a^{3} - 3 a^{2} - 8 a + 1\) , \( -6 a^{3} + 7 a^{2} + 35 a - 13\) , \( -73 a^{3} + 126 a^{2} + 349 a - 198\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(2a^{3}-3a^{2}-8a+1\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-10a+2\right){x}^{2}+\left(-6a^{3}+7a^{2}+35a-13\right){x}-73a^{3}+126a^{2}+349a-198$ |
| 18.2-b1 |
18.2-b |
$2$ |
$2$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{2} \) |
$15.98157$ |
$(-a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$1$ |
$488.5386890$ |
4.900464311 |
\( \frac{60338226833}{96} a^{3} - \frac{106789563871}{96} a^{2} - \frac{23339153135}{8} a + \frac{156229457351}{96} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 7 a^{3} - 22 a^{2} + 6 a + 5\) , \( 46 a^{3} - 119 a^{2} - 75 a + 57\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a^{3}-22a^{2}+6a+5\right){x}+46a^{3}-119a^{2}-75a+57$ |
| 18.2-b2 |
18.2-b |
$2$ |
$2$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$15.98157$ |
$(-a), (a^3-a^2-5a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$122.1346722$ |
4.900464311 |
\( -\frac{831656172914791205}{9216} a^{3} + \frac{759341919204247801}{3072} a^{2} + \frac{257030729310271345}{2304} a - \frac{956397309964116115}{9216} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 3\) , \( a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 6 a^{3} - 18 a^{2} - 7 a + 15\) , \( -40 a^{3} - 18 a^{2} + 332 a + 257\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+3\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a-1\right){x}^{2}+\left(6a^{3}-18a^{2}-7a+15\right){x}-40a^{3}-18a^{2}+332a+257$ |
| 18.2-c1 |
18.2-c |
$2$ |
$2$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{2} \) |
$15.98157$ |
$(-a), (a^3-a^2-5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.187664541$ |
$1982.839791$ |
2.986057069 |
\( \frac{65063}{6} a^{3} - \frac{119497}{6} a^{2} - 45626 a + \frac{267575}{6} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 1\) , \( -2 a^{3} + 3 a^{2} + 9 a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( -6 a^{3} + 5 a^{2} + 22 a + 2\) , \( -6 a^{3} - 3 a^{2} + 9 a + 4\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a-2\right){x}^{2}+\left(-6a^{3}+5a^{2}+22a+2\right){x}-6a^{3}-3a^{2}+9a+4$ |
| 18.2-c2 |
18.2-c |
$2$ |
$2$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{4} \) |
$15.98157$ |
$(-a), (a^3-a^2-5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.093832270$ |
$991.4198957$ |
2.986057069 |
\( \frac{30043579015}{36} a^{3} - \frac{5923449537}{4} a^{2} - \frac{34743603287}{9} a + \frac{77586311981}{36} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 3\) , \( a^{2} - a - 3\) , \( a^{3} - a^{2} - 4 a\) , \( -16 a^{3} + 28 a^{2} + 75 a - 38\) , \( 33 a^{3} - 59 a^{2} - 154 a + 84\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+3\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-16a^{3}+28a^{2}+75a-38\right){x}+33a^{3}-59a^{2}-154a+84$ |
| 18.2-d1 |
18.2-d |
$2$ |
$2$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{8} \) |
$15.98157$ |
$(-a), (a^3-a^2-5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.096891251$ |
$344.0831877$ |
5.350646643 |
\( \frac{843835421}{82944} a^{3} + \frac{73623671}{3072} a^{2} + \frac{74118263}{20736} a - \frac{919245605}{82944} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 1\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( 2 a^{3} - 3 a^{2} - 8 a + 2\) , \( 17 a^{3} - 3 a^{2} - 113 a - 97\) , \( 215 a^{3} - 108 a^{2} - 1345 a - 879\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+1\right){x}{y}+\left(2a^{3}-3a^{2}-8a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+2\right){x}^{2}+\left(17a^{3}-3a^{2}-113a-97\right){x}+215a^{3}-108a^{2}-1345a-879$ |
| 18.2-d2 |
18.2-d |
$2$ |
$2$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{4} \) |
$15.98157$ |
$(-a), (a^3-a^2-5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.048445625$ |
$344.0831877$ |
5.350646643 |
\( \frac{36999460049867}{9437184} a^{3} - \frac{8984257447741}{1048576} a^{2} - \frac{37911292146367}{2359296} a + \frac{175476256277245}{9437184} \) |
\( \bigl[1\) , \( a^{2} - a - 2\) , \( 2 a^{3} - 3 a^{2} - 9 a + 2\) , \( -13 a^{3} + 20 a^{2} + 60 a - 30\) , \( 38 a^{3} - 55 a^{2} - 158 a + 84\bigr] \) |
${y}^2+{x}{y}+\left(2a^{3}-3a^{2}-9a+2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-13a^{3}+20a^{2}+60a-30\right){x}+38a^{3}-55a^{2}-158a+84$ |
| 18.2-e1 |
18.2-e |
$2$ |
$2$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{4} \) |
$15.98157$ |
$(-a), (a^3-a^2-5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.245319521$ |
$324.3746490$ |
2.554272696 |
\( \frac{36999460049867}{9437184} a^{3} - \frac{8984257447741}{1048576} a^{2} - \frac{37911292146367}{2359296} a + \frac{175476256277245}{9437184} \) |
\( \bigl[2 a^{3} - 3 a^{2} - 8 a + 1\) , \( -a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 2 a^{3} - 12 a^{2} - 6 a + 5\) , \( 18 a^{3} + 10 a^{2} - 7 a - 1\bigr] \) |
${y}^2+\left(2a^{3}-3a^{2}-8a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a^{3}-12a^{2}-6a+5\right){x}+18a^{3}+10a^{2}-7a-1$ |
| 18.2-e2 |
18.2-e |
$2$ |
$2$ |
4.4.15529.1 |
$4$ |
$[4, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{8} \) |
$15.98157$ |
$(-a), (a^3-a^2-5a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.122659760$ |
$324.3746490$ |
2.554272696 |
\( \frac{843835421}{82944} a^{3} + \frac{73623671}{3072} a^{2} + \frac{74118263}{20736} a - \frac{919245605}{82944} \) |
\( \bigl[a + 1\) , \( a^{3} - a^{2} - 4 a - 2\) , \( 1\) , \( -2 a^{3} + 7 a^{2} + 8 a - 14\) , \( -10 a^{3} + 13 a^{2} + 56 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-4a-2\right){x}^{2}+\left(-2a^{3}+7a^{2}+8a-14\right){x}-10a^{3}+13a^{2}+56a+4$ |
*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.
