| 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 |
$3$ |
$9$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.63812$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$214.5630492$ |
0.377847309 |
\( 5032 a^{3} + 108 a^{2} - 21852 a - 10233 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - 4 a\) , \( a^{2} - a - 2\) , \( a^{3} + a^{2} - 5 a - 1\) , \( a^{2} - a - 1\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(a^{3}+a^{2}-5a-1\right){x}+a^{2}-a-1$ |
| 1.1-a2 |
1.1-a |
$3$ |
$9$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.63812$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$2.648926534$ |
0.377847309 |
\( 3994239657835 a^{3} - 838913630729 a^{2} - 16660517039629 a - 5161701786020 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - 4 a\) , \( a^{2} - a - 2\) , \( a^{3} - 14 a^{2} + 5 a - 1\) , \( 2 a^{3} - 62 a^{2} + 32 a + 10\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(a^{3}-14a^{2}+5a-1\right){x}+2a^{3}-62a^{2}+32a+10$ |
| 1.1-a3 |
1.1-a |
$3$ |
$9$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.63812$ |
$\textsf{none}$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1931.067443$ |
0.377847309 |
\( 2999 a^{3} - 8848 a^{2} + 2922 a + 3305 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - 3 a\) , \( -6 a^{3} + 24 a + 13\) , \( -3 a^{3} - a^{2} + 12 a + 7\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-6a^{3}+24a+13\right){x}-3a^{3}-a^{2}+12a+7$ |
| 9.2-a1 |
9.2-a |
$3$ |
$9$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$7.42019$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.020323483$ |
$481.2851658$ |
1.240207984 |
\( 2999 a^{3} - 8848 a^{2} + 2922 a + 3305 \) |
\( \bigl[a^{2} - a - 1\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{3} - 4 a - 1\) , \( 2 a^{3} - 3 a^{2} - 6 a + 4\) , \( a^{3} - 6 a + 1\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+3\right){x}^{2}+\left(2a^{3}-3a^{2}-6a+4\right){x}+a^{3}-6a+1$ |
| 9.2-a2 |
9.2-a |
$3$ |
$9$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$7.42019$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.020323483$ |
$481.2851658$ |
1.240207984 |
\( 3994239657835 a^{3} - 838913630729 a^{2} - 16660517039629 a - 5161701786020 \) |
\( \bigl[a^{2} - 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - a - 1\) , \( -49 a^{3} + 65 a^{2} + 174 a - 165\) , \( 239 a^{3} - 320 a^{2} - 851 a + 767\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-49a^{3}+65a^{2}+174a-165\right){x}+239a^{3}-320a^{2}-851a+767$ |
| 9.2-a3 |
9.2-a |
$3$ |
$9$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$7.42019$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2 \) |
$0.006774494$ |
$1443.855497$ |
1.240207984 |
\( 5032 a^{3} + 108 a^{2} - 21852 a - 10233 \) |
\( \bigl[a^{2} - 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - a - 1\) , \( a^{3} - a\) , \( a^{3} - a\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(a^{3}-a\right){x}+a^{3}-a$ |
| 15.1-a1 |
15.1-a |
$8$ |
$12$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5^{12} \) |
$7.90945$ |
$(a+1), (a^3-a^2-3a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$273.6514143$ |
1.445707232 |
\( \frac{6935488597286792192}{732421875} a^{3} - \frac{9145436876739566566}{732421875} a^{2} - \frac{24831990659561275366}{732421875} a + \frac{21789556188562103261}{732421875} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -14 a^{3} - 62 a^{2} - 86 a - 27\) , \( 355 a^{3} + 634 a^{2} + a - 43\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(-14a^{3}-62a^{2}-86a-27\right){x}+355a^{3}+634a^{2}+a-43$ |
| 15.1-a2 |
15.1-a |
$8$ |
$12$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{3} \) |
$7.90945$ |
$(a+1), (a^3-a^2-3a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$273.6514143$ |
1.445707232 |
\( \frac{111482851679585337445376}{1125} a^{3} + \frac{47714581371317338065134}{375} a^{2} - \frac{118991400037913313650998}{1125} a - \frac{16270133630882176611689}{375} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 4 a\) , \( a^{3} - 3 a\) , \( 19 a^{3} - 77 a^{2} + 99 a - 50\) , \( -329 a^{3} + 872 a^{2} - 164 a - 256\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(19a^{3}-77a^{2}+99a-50\right){x}-329a^{3}+872a^{2}-164a-256$ |
| 15.1-a3 |
15.1-a |
$8$ |
$12$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{6} \cdot 5^{2} \) |
$7.90945$ |
$(a+1), (a^3-a^2-3a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$121.6228508$ |
1.445707232 |
\( -\frac{2672856399197}{675} a^{3} + \frac{7351669304531}{675} a^{2} - \frac{2179706314169}{675} a - \frac{1526037435976}{675} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - 4 a\) , \( a\) , \( -4 a^{3} - 7 a^{2} + 54 a - 37\) , \( 4 a^{3} - 70 a^{2} + 186 a - 107\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-4a^{3}-7a^{2}+54a-37\right){x}+4a^{3}-70a^{2}+186a-107$ |
| 15.1-a4 |
15.1-a |
$8$ |
$12$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{3} \cdot 5 \) |
$7.90945$ |
$(a+1), (a^3-a^2-3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$121.6228508$ |
1.445707232 |
\( \frac{795694}{45} a^{3} - \frac{1967582}{45} a^{2} + \frac{511333}{45} a + \frac{390022}{45} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - 4 a\) , \( a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( -a^{3} + 8 a - 6\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(a^{3}-2a^{2}-a+3\right){x}-a^{3}+8a-6$ |
| 15.1-a5 |
15.1-a |
$8$ |
$12$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{12} \cdot 5 \) |
$7.90945$ |
$(a+1), (a^3-a^2-3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$30.40571270$ |
1.445707232 |
\( -\frac{3591878697880259}{3645} a^{3} + \frac{771051619573382}{3645} a^{2} + \frac{14973349192271482}{3645} a + \frac{4575189587437043}{3645} \) |
\( \bigl[a^{3} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 1\) , \( 86 a^{3} - 235 a^{2} + 62 a + 40\) , \( 1137 a^{3} - 3116 a^{2} + 912 a + 625\bigr] \) |
${y}^2+\left(a^{3}-3a-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(86a^{3}-235a^{2}+62a+40\right){x}+1137a^{3}-3116a^{2}+912a+625$ |
| 15.1-a6 |
15.1-a |
$8$ |
$12$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5^{3} \) |
$7.90945$ |
$(a+1), (a^3-a^2-3a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$1094.605657$ |
1.445707232 |
\( \frac{4681208}{375} a^{3} + \frac{6157616}{375} a^{2} - \frac{4844584}{375} a - \frac{2032561}{375} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + 2\) , \( 1\) , \( -a^{3} + 3 a - 1\) , \( 4 a^{3} - 5 a^{2} - 14 a + 12\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-a^{3}+3a-1\right){x}+4a^{3}-5a^{2}-14a+12$ |
| 15.1-a7 |
15.1-a |
$8$ |
$12$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{6} \) |
$7.90945$ |
$(a+1), (a^3-a^2-3a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1094.605657$ |
1.445707232 |
\( \frac{39209436896364}{15625} a^{3} + \frac{151028756530984}{46875} a^{2} - \frac{41852106216772}{15625} a - \frac{51492956620289}{46875} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 3 a + 2\) , \( a^{2} - 1\) , \( 86 a^{3} - 21 a^{2} - 354 a - 106\) , \( -358 a^{3} + 69 a^{2} + 1506 a + 461\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{3}+3a+2\right){x}^{2}+\left(86a^{3}-21a^{2}-354a-106\right){x}-358a^{3}+69a^{2}+1506a+461$ |
| 15.1-a8 |
15.1-a |
$8$ |
$12$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{3} \cdot 5^{4} \) |
$7.90945$ |
$(a+1), (a^3-a^2-3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$30.40571270$ |
1.445707232 |
\( -\frac{1292376637714733533491449}{5625} a^{3} + \frac{3555070200487356367478002}{5625} a^{2} - \frac{1054711856610514200550898}{5625} a - \frac{738163311723126622608167}{5625} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a\) , \( -15 a^{3} + 43 a^{2} + 62 a - 103\) , \( 147 a^{3} - 101 a^{2} - 455 a + 302\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(-15a^{3}+43a^{2}+62a-103\right){x}+147a^{3}-101a^{2}-455a+302$ |
| 25.1-a1 |
25.1-a |
$2$ |
$3$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{10} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$141.1384953$ |
2.236914549 |
\( -86229 a^{3} + 236300 a^{2} - 69470 a - 47257 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( a^{3} - 3 a\) , \( -2 a^{3} - 5 a^{2} - 5 a + 6\) , \( -19 a^{3} - 21 a^{2} + 22 a + 4\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-4\right){x}^{2}+\left(-2a^{3}-5a^{2}-5a+6\right){x}-19a^{3}-21a^{2}+22a+4$ |
| 25.1-a2 |
25.1-a |
$2$ |
$3$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{10} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$141.1384953$ |
2.236914549 |
\( -561763038 a^{3} - 57829358 a^{2} + 1972488848 a + 615872329 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a\) , \( 16 a^{3} + 3 a^{2} - 75 a - 53\) , \( -72 a^{3} - 3 a^{2} + 301 a + 149\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(16a^{3}+3a^{2}-75a-53\right){x}-72a^{3}-3a^{2}+301a+149$ |
| 25.1-b1 |
25.1-b |
$3$ |
$9$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$114.7208231$ |
1.818218891 |
\( 2999 a^{3} - 8848 a^{2} + 2922 a + 3305 \) |
\( \bigl[a^{2} - a - 1\) , \( a - 1\) , \( a^{2} - a - 2\) , \( -2 a^{2} + 1\) , \( -2 a^{3} - 3 a^{2} + 2 a\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a^{2}+1\right){x}-2a^{3}-3a^{2}+2a$ |
| 25.1-b2 |
25.1-b |
$3$ |
$9$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$12.74675813$ |
1.818218891 |
\( 3994239657835 a^{3} - 838913630729 a^{2} - 16660517039629 a - 5161701786020 \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - 3 a - 1\) , \( a^{2} - 2\) , \( -30 a^{3} + 33 a^{2} + 135 a - 114\) , \( -226 a^{3} + 336 a^{2} + 697 a - 646\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(-30a^{3}+33a^{2}+135a-114\right){x}-226a^{3}+336a^{2}+697a-646$ |
| 25.1-b3 |
25.1-b |
$3$ |
$9$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$114.7208231$ |
1.818218891 |
\( 5032 a^{3} + 108 a^{2} - 21852 a - 10233 \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - 3 a - 1\) , \( a^{2} - 2\) , \( 3 a^{2} + 1\) , \( a^{3} + 2 a^{2} - 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(3a^{2}+1\right){x}+a^{3}+2a^{2}-3$ |
| 25.1-c1 |
25.1-c |
$4$ |
$15$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 5$ |
3B.1.1, 5B.4.1 |
$1$ |
\( 3 \) |
$0.074011784$ |
$1313.335988$ |
2.054089519 |
\( -1931693 a^{3} + 2483692 a^{2} + 6948943 a - 5812156 \) |
\( \bigl[a^{2} - a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a + 1\) , \( -2 a^{2} + 4 a - 1\) , \( -a\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-2a^{2}+4a-1\right){x}-a$ |
| 25.1-c2 |
25.1-c |
$4$ |
$15$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 5$ |
3B.1.2, 5B.4.2 |
$1$ |
\( 1 \) |
$1.110176762$ |
$29.18524419$ |
2.054089519 |
\( -137052798212356529505 a^{3} + 29430519368025128508 a^{2} + 571321845118279428507 a + 174531423228883445992 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 2\) , \( -60 a^{3} - 76 a^{2} + 68 a + 23\) , \( 773 a^{3} + 1002 a^{2} - 821 a - 356\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-60a^{3}-76a^{2}+68a+23\right){x}+773a^{3}+1002a^{2}-821a-356$ |
| 25.1-c3 |
25.1-c |
$4$ |
$15$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 5$ |
3B.1.1, 5B.4.2 |
$1$ |
\( 3 \) |
$0.370058920$ |
$262.6671977$ |
2.054089519 |
\( -12443416333009 a^{3} + 34188653134010 a^{2} - 10136096453467 a - 7097092032021 \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 93 a^{3} - 130 a^{2} - 328 a + 291\) , \( 97 a^{3} - 110 a^{2} - 360 a + 303\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(93a^{3}-130a^{2}-328a+291\right){x}+97a^{3}-110a^{2}-360a+303$ |
| 25.1-c4 |
25.1-c |
$4$ |
$15$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 5$ |
3B.1.2, 5B.4.1 |
$1$ |
\( 1 \) |
$0.222035352$ |
$145.9262209$ |
2.054089519 |
\( -4639449 a^{3} + 12753162 a^{2} - 3768507 a - 2643329 \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a^{2} - a - 2\) , \( 4 a^{3} - a^{2} - 18 a - 3\) , \( 7 a^{3} - 2 a^{2} - 30 a - 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-2\right){x}^{2}+\left(4a^{3}-a^{2}-18a-3\right){x}+7a^{3}-2a^{2}-30a-10$ |
| 25.1-d1 |
25.1-d |
$4$ |
$15$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{10} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 5$ |
3B, 5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$2.738022339$ |
1.084878011 |
\( -137052798212356529505 a^{3} + 29430519368025128508 a^{2} + 571321845118279428507 a + 174531423228883445992 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -71 a^{3} + 76 a^{2} + 231 a - 207\) , \( -481 a^{3} + 534 a^{2} + 1614 a - 1410\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(-71a^{3}+76a^{2}+231a-207\right){x}-481a^{3}+534a^{2}+1614a-1410$ |
| 25.1-d2 |
25.1-d |
$4$ |
$15$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1711.263962$ |
1.084878011 |
\( -4639449 a^{3} + 12753162 a^{2} - 3768507 a - 2643329 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + a + 3\) , \( a^{3} - a^{2} - 4 a + 5\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(-a^{3}+a^{2}+a+3\right){x}+a^{3}-a^{2}-4a+5$ |
| 25.1-d3 |
25.1-d |
$4$ |
$15$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{10} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 5$ |
3B, 5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$2.738022339$ |
1.084878011 |
\( -12443416333009 a^{3} + 34188653134010 a^{2} - 10136096453467 a - 7097092032021 \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 59 a^{3} - 144 a^{2} - 77 a + 118\) , \( 290 a^{3} - 892 a^{2} + 210 a + 244\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a\right){x}^{2}+\left(59a^{3}-144a^{2}-77a+118\right){x}+290a^{3}-892a^{2}+210a+244$ |
| 25.1-d4 |
25.1-d |
$4$ |
$15$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1711.263962$ |
1.084878011 |
\( -1931693 a^{3} + 2483692 a^{2} + 6948943 a - 5812156 \) |
\( \bigl[a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - 3 a - 1\) , \( -2 a^{2} + a + 3\) , \( -a^{3} - 2 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(-2a^{2}+a+3\right){x}-a^{3}-2a$ |
| 25.1-e1 |
25.1-e |
$2$ |
$3$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.003896615$ |
$1598.430407$ |
1.184585685 |
\( -86229 a^{3} + 236300 a^{2} - 69470 a - 47257 \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + 4 a + 2\) , \( a^{3} - 4 a - 1\) , \( -a^{3} - 3 a^{2} + 2 a + 7\) , \( 2 a^{3} + 2 a^{2} - 2 a + 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-a^{3}-3a^{2}+2a+7\right){x}+2a^{3}+2a^{2}-2a+1$ |
| 25.1-e2 |
25.1-e |
$2$ |
$3$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$8.43096$ |
$(a^3-a^2-3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.011689847$ |
$1598.430407$ |
1.184585685 |
\( -561763038 a^{3} - 57829358 a^{2} + 1972488848 a + 615872329 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{2} - a - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -22 a^{3} - 28 a^{2} + 29 a + 7\) , \( 151 a^{3} + 185 a^{2} - 159 a - 63\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-22a^{3}-28a^{2}+29a+7\right){x}+151a^{3}+185a^{2}-159a-63$ |
| 27.1-a1 |
27.1-a |
$4$ |
$6$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{8} \) |
$8.51246$ |
$(a+1), (-a^2+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$67.41695018$ |
1.602744415 |
\( -\frac{882593}{27} a^{3} - \frac{924556}{27} a^{2} + \frac{1138906}{27} a + \frac{93197}{27} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -3 a^{3} - 5 a^{2} + a + 3\) , \( -11 a^{3} - 14 a^{2} + 12 a + 4\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(-3a^{3}-5a^{2}+a+3\right){x}-11a^{3}-14a^{2}+12a+4$ |
| 27.1-a2 |
27.1-a |
$4$ |
$6$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{7} \) |
$8.51246$ |
$(a+1), (-a^2+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$67.41695018$ |
1.602744415 |
\( \frac{126200840218}{9} a^{3} + \frac{53687768389}{3} a^{2} - \frac{135642284054}{9} a - \frac{53904008452}{9} \) |
\( \bigl[a^{3} - 3 a\) , \( 0\) , \( a^{2} - 2\) , \( 25 a^{3} - 52 a^{2} - 9 a - 1\) , \( -101 a^{3} + 315 a^{2} - 151 a - 89\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(25a^{3}-52a^{2}-9a-1\right){x}-101a^{3}+315a^{2}-151a-89$ |
| 27.1-a3 |
27.1-a |
$4$ |
$6$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{8} \) |
$8.51246$ |
$(a+1), (-a^2+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$606.7525517$ |
1.602744415 |
\( \frac{336796}{3} a^{3} - \frac{8324996}{27} a^{2} + \frac{2433176}{27} a + \frac{1763683}{27} \) |
\( \bigl[1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a + 1\) , \( 2 a^{3} - 3 a^{2} - 5 a + 4\) , \( -a^{3} + 3 a^{2} - 4 a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(2a^{3}-3a^{2}-5a+4\right){x}-a^{3}+3a^{2}-4a+1$ |
| 27.1-a4 |
27.1-a |
$4$ |
$6$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{13} \) |
$8.51246$ |
$(a+1), (-a^2+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$606.7525517$ |
1.602744415 |
\( -\frac{133914571970734}{729} a^{3} + \frac{368372259892138}{729} a^{2} - \frac{109288018528498}{729} a - \frac{25495875248035}{243} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{2} + a + 2\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -28 a^{3} + 34 a^{2} + 106 a - 91\) , \( -36 a^{3} + 50 a^{2} + 119 a - 107\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-28a^{3}+34a^{2}+106a-91\right){x}-36a^{3}+50a^{2}+119a-107$ |
| 27.2-a1 |
27.2-a |
$2$ |
$3$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{9} \) |
$8.51246$ |
$(a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$813.6606381$ |
1.432863133 |
\( 14864 a^{3} - 6745 a^{2} - 60113 a - 4784 \) |
\( \bigl[a^{2} - a - 1\) , \( a^{2} - a - 3\) , \( a^{3} - 4 a\) , \( 6 a^{3} - 28 a - 10\) , \( -21 a^{3} + 4 a^{2} + 86 a + 31\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(6a^{3}-28a-10\right){x}-21a^{3}+4a^{2}+86a+31$ |
| 27.2-a2 |
27.2-a |
$2$ |
$3$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{3} \) |
$8.51246$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$90.40673757$ |
1.432863133 |
\( -18036172 a^{3} - 23338947 a^{2} + 19077141 a + 8145869 \) |
\( \bigl[a^{2} - 1\) , \( 0\) , \( a + 1\) , \( -4 a^{3} + 3 a^{2} + 14 a - 5\) , \( -4 a^{3} + 3 a^{2} + 13 a - 8\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-4a^{3}+3a^{2}+14a-5\right){x}-4a^{3}+3a^{2}+13a-8$ |
| 27.2-b1 |
27.2-b |
$2$ |
$3$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{3} \) |
$8.51246$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.053122209$ |
$563.6065380$ |
1.898086749 |
\( 14864 a^{3} - 6745 a^{2} - 60113 a - 4784 \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 2 a^{3} - a^{2} - 10 a + 3\) , \( a^{3} - a^{2} - 3 a\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(2a^{3}-a^{2}-10a+3\right){x}+a^{3}-a^{2}-3a$ |
| 27.2-b2 |
27.2-b |
$2$ |
$3$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{9} \) |
$8.51246$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.017707403$ |
$563.6065380$ |
1.898086749 |
\( -18036172 a^{3} - 23338947 a^{2} + 19077141 a + 8145869 \) |
\( \bigl[a^{3} - 3 a - 1\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( a^{3} - 4 a\) , \( -a^{3} + 2 a^{2} - 3\) , \( 11 a^{3} - 26 a^{2} - 4 a + 12\bigr] \) |
${y}^2+\left(a^{3}-3a-1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+a-3\right){x}^{2}+\left(-a^{3}+2a^{2}-3\right){x}+11a^{3}-26a^{2}-4a+12$ |
| 37.1-a1 |
37.1-a |
$3$ |
$9$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
37.1 |
\( 37 \) |
\( 37^{3} \) |
$8.85441$ |
$(a^3-4a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.259527247$ |
$374.7416087$ |
2.055216250 |
\( \frac{6402086}{50653} a^{3} + \frac{5680026}{50653} a^{2} - \frac{9059472}{50653} a + \frac{1247121}{50653} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 1\) , \( a^{2} - a - 2\) , \( 2 a^{2} - 2 a - 2\) , \( a^{2} - a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(2a^{2}-2a-2\right){x}+a^{2}-a-1$ |
| 37.1-a2 |
37.1-a |
$3$ |
$9$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
37.1 |
\( 37 \) |
\( 37^{9} \) |
$8.85441$ |
$(a^3-4a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$0.778581742$ |
$4.626439614$ |
2.055216250 |
\( \frac{50956086371369039072}{129961739795077} a^{3} - \frac{140694288212823259279}{129961739795077} a^{2} + \frac{41839264940005369726}{129961739795077} a + \frac{29226475929028326308}{129961739795077} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 1\) , \( a^{2} - a - 2\) , \( 5 a^{3} - 23 a^{2} + 8 a + 3\) , \( 39 a^{3} - 141 a^{2} + 48 a + 29\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(5a^{3}-23a^{2}+8a+3\right){x}+39a^{3}-141a^{2}+48a+29$ |
| 37.1-a3 |
37.1-a |
$3$ |
$9$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
37.1 |
\( 37 \) |
\( 37 \) |
$8.85441$ |
$(a^3-4a+1)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.778581742$ |
$3372.674478$ |
2.055216250 |
\( \frac{19234086}{37} a^{3} + \frac{9255030}{37} a^{2} - \frac{87396751}{37} a - \frac{78159660}{37} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{2} - 2 a - 3\) , \( 0\) , \( -2 a^{3} + 3 a^{2} + 3 a + 1\) , \( -3 a^{3} + 9 a^{2} - 4 a - 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-2a^{3}+3a^{2}+3a+1\right){x}-3a^{3}+9a^{2}-4a-2$ |
| 39.1-a1 |
39.1-a |
$2$ |
$2$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{26} \cdot 13^{2} \) |
$8.91287$ |
$(a+1), (a^3-a^2-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$107.1813771$ |
1.698725648 |
\( -\frac{11251711838749}{269440587} a^{3} + \frac{10223262997580}{89813529} a^{2} - \frac{663812869246}{20726199} a - \frac{2073854813744}{89813529} \) |
\( \bigl[a^{3} - 3 a - 1\) , \( a^{2} - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 5 a^{3} - 5 a^{2} - 16 a + 12\) , \( 153 a^{3} - 205 a^{2} - 551 a + 485\bigr] \) |
${y}^2+\left(a^{3}-3a-1\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(5a^{3}-5a^{2}-16a+12\right){x}+153a^{3}-205a^{2}-551a+485$ |
| 39.1-a2 |
39.1-a |
$2$ |
$2$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{13} \cdot 13 \) |
$8.91287$ |
$(a+1), (a^3-a^2-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$428.7255085$ |
1.698725648 |
\( \frac{354398677}{28431} a^{3} - \frac{172286069}{28431} a^{2} - \frac{75764297}{2187} a + \frac{757175593}{28431} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{3} - 3 a\) , \( 7 a^{3} - 19 a^{2} + 9 a + 4\) , \( 10 a^{3} - 25 a^{2} + 7 a + 5\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(7a^{3}-19a^{2}+9a+4\right){x}+10a^{3}-25a^{2}+7a+5$ |
| 39.1-b1 |
39.1-b |
$6$ |
$18$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{2} \cdot 13^{2} \) |
$8.91287$ |
$(a+1), (a^3-a^2-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2^{2} \) |
$1$ |
$1.390924576$ |
1.785634263 |
\( \frac{38409969423367873510476474}{169} a^{3} + \frac{147954956795479381309554835}{507} a^{2} - \frac{3153610945707113393174394}{13} a - \frac{50450970106612171291054136}{507} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + a - 2\) , \( 1\) , \( -804 a^{3} + 992 a^{2} + 2833 a - 2456\) , \( -16498 a^{3} + 21201 a^{2} + 58815 a - 51281\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+2a^{2}+a-2\right){x}^{2}+\left(-804a^{3}+992a^{2}+2833a-2456\right){x}-16498a^{3}+21201a^{2}+58815a-51281$ |
| 39.1-b2 |
39.1-b |
$6$ |
$18$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{2} \cdot 13^{2} \) |
$8.91287$ |
$(a+1), (a^3-a^2-4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1013.984015$ |
1.785634263 |
\( \frac{26441365867233467}{507} a^{3} - \frac{11620620263431943}{169} a^{2} - \frac{7281799408058719}{39} a + \frac{27676386409512356}{169} \) |
\( \bigl[a^{2} - 1\) , \( a - 1\) , \( a^{3} - 4 a - 1\) , \( 86 a^{3} - 16 a^{2} - 358 a - 117\) , \( -643 a^{3} + 136 a^{2} + 2682 a + 831\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(86a^{3}-16a^{2}-358a-117\right){x}-643a^{3}+136a^{2}+2682a+831$ |
| 39.1-b3 |
39.1-b |
$6$ |
$18$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3 \cdot 13 \) |
$8.91287$ |
$(a+1), (a^3-a^2-4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$4055.936063$ |
1.785634263 |
\( \frac{139097386}{39} a^{3} - \frac{180699914}{39} a^{2} - \frac{38352917}{3} a + \frac{435345142}{39} \) |
\( \bigl[a^{2} - 1\) , \( a - 1\) , \( a^{3} - 4 a - 1\) , \( 6 a^{3} - a^{2} - 23 a - 7\) , \( -10 a^{3} + 3 a^{2} + 42 a + 13\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6a^{3}-a^{2}-23a-7\right){x}-10a^{3}+3a^{2}+42a+13$ |
| 39.1-b4 |
39.1-b |
$6$ |
$18$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3 \cdot 13 \) |
$8.91287$ |
$(a+1), (a^3-a^2-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$5.563698304$ |
1.785634263 |
\( -\frac{6795312330173}{39} a^{3} + \frac{37633447680268}{39} a^{2} - \frac{1112831844398}{3} a - \frac{8555464024919}{39} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a - 1\) , \( a + 1\) , \( 7 a^{3} - 24 a^{2} - 76 a - 33\) , \( a^{3} - 138 a^{2} - 265 a - 84\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(7a^{3}-24a^{2}-76a-33\right){x}+a^{3}-138a^{2}-265a-84$ |
| 39.1-b5 |
39.1-b |
$6$ |
$18$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{6} \cdot 13^{6} \) |
$8.91287$ |
$(a+1), (a^3-a^2-4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$112.6648906$ |
1.785634263 |
\( \frac{1268322618541402}{130323843} a^{3} + \frac{1623613163163278}{130323843} a^{2} - \frac{104492000461466}{10024911} a - \frac{548391428940157}{130323843} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a - 1\) , \( a + 1\) , \( 2 a^{3} - 4 a^{2} - 21 a - 8\) , \( -8 a^{3} - 9 a^{2} + 9 a + 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a^{3}-4a^{2}-21a-8\right){x}-8a^{3}-9a^{2}+9a+4$ |
| 39.1-b6 |
39.1-b |
$6$ |
$18$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{3} \cdot 13^{3} \) |
$8.91287$ |
$(a+1), (a^3-a^2-4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$450.6595626$ |
1.785634263 |
\( -\frac{3568348}{19773} a^{3} + \frac{72045356}{19773} a^{2} - \frac{3256984}{1521} a + \frac{22939493}{19773} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a - 1\) , \( a + 1\) , \( -3 a^{3} + a^{2} + 9 a + 2\) , \( a^{3} - 6 a - 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a^{3}+a^{2}+9a+2\right){x}+a^{3}-6a-2$ |
| 39.1-c1 |
39.1-c |
$2$ |
$2$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{22} \cdot 13^{2} \) |
$8.91287$ |
$(a+1), (a^3-a^2-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$65.44525388$ |
1.037246714 |
\( -\frac{39868770271085}{29937843} a^{3} - \frac{25955803247761}{29937843} a^{2} + \frac{14201873335798}{2302911} a + \frac{188836842261947}{29937843} \) |
\( \bigl[a\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{2} - 1\) , \( -46 a^{3} - 57 a^{2} + 47 a + 19\) , \( -302 a^{3} - 389 a^{2} + 326 a + 131\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+2\right){x}^{2}+\left(-46a^{3}-57a^{2}+47a+19\right){x}-302a^{3}-389a^{2}+326a+131$ |
| 39.1-c2 |
39.1-c |
$2$ |
$2$ |
4.4.3981.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{11} \cdot 13 \) |
$8.91287$ |
$(a+1), (a^3-a^2-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$261.7810155$ |
1.037246714 |
\( \frac{2500916636}{9477} a^{3} + \frac{3628419299}{9477} a^{2} - \frac{223878391}{729} a - \frac{1186410439}{9477} \) |
\( \bigl[1\) , \( a^{2} - 3\) , \( a^{3} - 4 a\) , \( -5 a^{3} + 2 a^{2} + 15 a - 8\) , \( -4 a^{3} - 5 a^{2} + 4 a\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-5a^{3}+2a^{2}+15a-8\right){x}-4a^{3}-5a^{2}+4a$ |
*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.
