| 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 |
| 3.1-a1 |
3.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{8} \) |
$13.79056$ |
$(1/2a^3-1/2a^2-5/2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$5.823176666$ |
1.385181399 |
\( -\frac{12371881828153183}{13122} a^{3} - \frac{1639313099076769}{4374} a^{2} + \frac{80290491123814561}{13122} a + \frac{18977711698065041}{6561} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 1\) , \( a^{2} + a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -10 a^{3} + 43 a^{2} - 20 a - 31\) , \( \frac{4623}{2} a^{3} - \frac{16427}{2} a^{2} + \frac{8359}{2} a + 3763\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-10a^{3}+43a^{2}-20a-31\right){x}+\frac{4623}{2}a^{3}-\frac{16427}{2}a^{2}+\frac{8359}{2}a+3763$ |
| 3.1-a2 |
3.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$13.79056$ |
$(1/2a^3-1/2a^2-5/2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1490.733226$ |
1.385181399 |
\( \frac{12420053}{162} a^{3} + \frac{3369131}{54} a^{2} - \frac{47076827}{162} a + \frac{6787868}{81} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( -a^{3} + 6 a\) , \( a\) , \( -6 a^{3} - 6 a^{2} + 28 a + 14\) , \( \frac{3}{2} a^{3} + \frac{11}{2} a^{2} + \frac{9}{2} a + 1\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+6a\right){x}^{2}+\left(-6a^{3}-6a^{2}+28a+14\right){x}+\frac{3}{2}a^{3}+\frac{11}{2}a^{2}+\frac{9}{2}a+1$ |
| 3.1-a3 |
3.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$13.79056$ |
$(1/2a^3-1/2a^2-5/2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$93.17082666$ |
1.385181399 |
\( -\frac{25637486733503}{86093442} a^{3} - \frac{4677525455849}{28697814} a^{2} + \frac{167554420555829}{86093442} a + \frac{54282517880836}{43046721} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 1\) , \( \frac{47}{2} a^{3} + \frac{27}{2} a^{2} - \frac{311}{2} a - 101\) , \( 122 a^{3} + 56 a^{2} - 797 a - 434\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-1\right){x}^{2}+\left(\frac{47}{2}a^{3}+\frac{27}{2}a^{2}-\frac{311}{2}a-101\right){x}+122a^{3}+56a^{2}-797a-434$ |
| 3.1-a4 |
3.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{32} \) |
$13.79056$ |
$(1/2a^3-1/2a^2-5/2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$5.823176666$ |
1.385181399 |
\( -\frac{102288071412608069844353}{3706040377703682} a^{3} + \frac{119389510916945748781441}{1235346792567894} a^{2} - \frac{179959387802949567169921}{3706040377703682} a - \frac{81780932195665608478625}{1853020188851841} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 1\) , \( 21 a^{3} + 11 a^{2} - 138 a - 81\) , \( \frac{337}{2} a^{3} + \frac{161}{2} a^{2} - \frac{2201}{2} a - 619\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-1\right){x}^{2}+\left(21a^{3}+11a^{2}-138a-81\right){x}+\frac{337}{2}a^{3}+\frac{161}{2}a^{2}-\frac{2201}{2}a-619$ |
| 3.1-a5 |
3.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$13.79056$ |
$(1/2a^3-1/2a^2-5/2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$1490.733226$ |
1.385181399 |
\( -\frac{1432433}{13122} a^{3} + \frac{341449}{4374} a^{2} + \frac{7045667}{13122} a + \frac{12831643}{6561} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 1\) , \( a^{3} + a^{2} - 8 a - 6\) , \( -a^{3} - a^{2} + 4 a + 1\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-1\right){x}^{2}+\left(a^{3}+a^{2}-8a-6\right){x}-a^{3}-a^{2}+4a+1$ |
| 3.1-a6 |
3.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$13.79056$ |
$(1/2a^3-1/2a^2-5/2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1490.733226$ |
1.385181399 |
\( -\frac{16173269}{162} a^{3} + \frac{17888725}{54} a^{2} - \frac{22156141}{162} a - \frac{11068556}{81} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( -a^{3} + 4 a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( 2 a^{3} - 2 a^{2} - 15 a + 23\) , \( \frac{3}{2} a^{3} - \frac{5}{2} a^{2} - \frac{27}{2} a + 18\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(2a^{3}-2a^{2}-15a+23\right){x}+\frac{3}{2}a^{3}-\frac{5}{2}a^{2}-\frac{27}{2}a+18$ |
| 3.1-b1 |
3.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{8} \) |
$13.79056$ |
$(1/2a^3-1/2a^2-5/2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.458806839$ |
$86.19187725$ |
2.351705403 |
\( -\frac{12371881828153183}{13122} a^{3} - \frac{1639313099076769}{4374} a^{2} + \frac{80290491123814561}{13122} a + \frac{18977711698065041}{6561} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -226 a^{3} + 332 a^{2} + 1435 a - 2025\) , \( 4202 a^{3} - 6092 a^{2} - 26640 a + 37153\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+2\right){y}={x}^{3}+{x}^{2}+\left(-226a^{3}+332a^{2}+1435a-2025\right){x}+4202a^{3}-6092a^{2}-26640a+37153$ |
| 3.1-b2 |
3.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$13.79056$ |
$(1/2a^3-1/2a^2-5/2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.057350854$ |
$1379.070036$ |
2.351705403 |
\( -\frac{16173269}{162} a^{3} + \frac{17888725}{54} a^{2} - \frac{22156141}{162} a - \frac{11068556}{81} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 3\) , \( \frac{3}{2} a^{3} - \frac{17}{2} a^{2} + \frac{23}{2} a + 2\) , \( -9 a^{3} + 31 a^{2} - 15 a - 17\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}^{2}+\left(\frac{3}{2}a^{3}-\frac{17}{2}a^{2}+\frac{23}{2}a+2\right){x}-9a^{3}+31a^{2}-15a-17$ |
| 3.1-b3 |
3.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$13.79056$ |
$(1/2a^3-1/2a^2-5/2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.229403419$ |
$344.7675090$ |
2.351705403 |
\( \frac{12420053}{162} a^{3} + \frac{3369131}{54} a^{2} - \frac{47076827}{162} a + \frac{6787868}{81} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( a^{2} - a - 3\) , \( a\) , \( -2 a^{3} + 4 a^{2} + 3 a - 3\) , \( -2 a^{3} + 6 a^{2} - 3 a - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-2a^{3}+4a^{2}+3a-3\right){x}-2a^{3}+6a^{2}-3a-5$ |
| 3.1-b4 |
3.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{32} \) |
$13.79056$ |
$(1/2a^3-1/2a^2-5/2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.458806839$ |
$21.54796931$ |
2.351705403 |
\( -\frac{102288071412608069844353}{3706040377703682} a^{3} + \frac{119389510916945748781441}{1235346792567894} a^{2} - \frac{179959387802949567169921}{3706040377703682} a - \frac{81780932195665608478625}{1853020188851841} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( a^{2} - 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( 2 a^{3} - 4 a^{2} - 12 a - 2\) , \( 68 a^{3} + 89 a^{2} - 210 a - 107\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(2a^{3}-4a^{2}-12a-2\right){x}+68a^{3}+89a^{2}-210a-107$ |
| 3.1-b5 |
3.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$13.79056$ |
$(1/2a^3-1/2a^2-5/2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.229403419$ |
$344.7675090$ |
2.351705403 |
\( -\frac{25637486733503}{86093442} a^{3} - \frac{4677525455849}{28697814} a^{2} + \frac{167554420555829}{86093442} a + \frac{54282517880836}{43046721} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( a^{2} - 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( -3 a^{3} - 9 a^{2} - 2 a + 3\) , \( 21 a^{3} + 28 a^{2} - 75 a - 38\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-3a^{3}-9a^{2}-2a+3\right){x}+21a^{3}+28a^{2}-75a-38$ |
| 3.1-b6 |
3.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$13.79056$ |
$(1/2a^3-1/2a^2-5/2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.114701709$ |
$1379.070036$ |
2.351705403 |
\( -\frac{1432433}{13122} a^{3} + \frac{341449}{4374} a^{2} + \frac{7045667}{13122} a + \frac{12831643}{6561} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( a^{2} - 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} + \frac{1}{2} a + 3\) , \( -\frac{3}{2} a^{3} - \frac{5}{2} a^{2} + \frac{9}{2} a + 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+\frac{1}{2}a+3\right){x}-\frac{3}{2}a^{3}-\frac{5}{2}a^{2}+\frac{9}{2}a+2$ |
| 4.1-a1 |
4.1-a |
$2$ |
$5$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{10} \) |
$14.29550$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 5 \) |
$1.494323611$ |
$13.87623719$ |
3.082783857 |
\( \frac{53826719946875}{64} a^{3} - \frac{185108694165561}{64} a^{2} + \frac{87531672190689}{64} a + \frac{20537254296311}{16} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a + 1\) , \( a^{3} - 4 a\) , \( 2 a^{3} - a^{2} - 14 a - 48\) , \( 38 a^{3} - 31 a^{2} - 170 a - 4\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a^{3}-a^{2}-14a-48\right){x}+38a^{3}-31a^{2}-170a-4$ |
| 4.1-a2 |
4.1-a |
$2$ |
$5$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{2} \) |
$14.29550$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$0.298864722$ |
$346.9059298$ |
3.082783857 |
\( \frac{25621}{4} a^{3} + \frac{38575}{4} a^{2} - \frac{77051}{4} a - \frac{16681}{2} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a + 1\) , \( a^{3} - 4 a\) , \( 2 a^{3} + 4 a^{2} - 9 a - 3\) , \( 4 a^{3} + 8 a^{2} - 15 a - 7\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a^{3}+4a^{2}-9a-3\right){x}+4a^{3}+8a^{2}-15a-7$ |
| 4.1-b1 |
4.1-b |
$2$ |
$5$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{10} \) |
$14.29550$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$1.030730532$ |
0.191549867 |
\( \frac{53826719946875}{64} a^{3} - \frac{185108694165561}{64} a^{2} + \frac{87531672190689}{64} a + \frac{20537254296311}{16} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( -\frac{1131}{2} a^{3} + \frac{1881}{2} a^{2} + \frac{7159}{2} a - 5779\) , \( -\frac{39037}{2} a^{3} + \frac{58751}{2} a^{2} + \frac{247527}{2} a - 179770\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}^{2}+\left(-\frac{1131}{2}a^{3}+\frac{1881}{2}a^{2}+\frac{7159}{2}a-5779\right){x}-\frac{39037}{2}a^{3}+\frac{58751}{2}a^{2}+\frac{247527}{2}a-179770$ |
| 4.1-b2 |
4.1-b |
$2$ |
$5$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{2} \) |
$14.29550$ |
$(a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$644.2065829$ |
0.191549867 |
\( \frac{25621}{4} a^{3} + \frac{38575}{4} a^{2} - \frac{77051}{4} a - \frac{16681}{2} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -a^{2} - a + 3\) , \( a^{3} - 4 a\) , \( -2 a^{2} + 5\) , \( \frac{11}{2} a^{3} - \frac{5}{2} a^{2} - \frac{61}{2} a - 12\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-2a^{2}+5\right){x}+\frac{11}{2}a^{3}-\frac{5}{2}a^{2}-\frac{61}{2}a-12$ |
| 12.1-a1 |
12.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3 \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.774113237$ |
$631.1283610$ |
3.631774688 |
\( -\frac{1307703981005}{12} a^{3} - \frac{162976069959}{4} a^{2} + \frac{8482197737297}{12} a + \frac{951830717234}{3} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( a^{2} + a - 4\) , \( a\) , \( \frac{7}{2} a^{3} - \frac{23}{2} a^{2} - \frac{57}{2} a + 53\) , \( -\frac{43}{2} a^{3} - \frac{195}{2} a^{2} - \frac{17}{2} a + 251\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(\frac{7}{2}a^{3}-\frac{23}{2}a^{2}-\frac{57}{2}a+53\right){x}-\frac{43}{2}a^{3}-\frac{195}{2}a^{2}-\frac{17}{2}a+251$ |
| 12.1-a2 |
12.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3 \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.774113237$ |
$157.7820902$ |
3.631774688 |
\( \frac{758955402069437}{12} a^{3} + \frac{399496746369175}{4} a^{2} - \frac{2222290335704369}{12} a - \frac{294307880630930}{3} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( 53 a^{3} - 144 a^{2} + 10 a + 21\) , \( -\frac{1561}{2} a^{3} + \frac{4685}{2} a^{2} - \frac{1035}{2} a - 858\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a+3\right){x}^{2}+\left(53a^{3}-144a^{2}+10a+21\right){x}-\frac{1561}{2}a^{3}+\frac{4685}{2}a^{2}-\frac{1035}{2}a-858$ |
| 12.1-a3 |
12.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.387056618$ |
$1262.256722$ |
3.631774688 |
\( \frac{124305619}{72} a^{3} + \frac{69552727}{24} a^{2} - \frac{337560937}{72} a - \frac{91498457}{36} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( a^{3} - 6 a + 1\) , \( a^{3} - 4 a\) , \( 4 a^{3} - 8 a^{2} - 5 a + 8\) , \( -5 a^{3} + 23 a^{2} - 18 a - 8\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-6a+1\right){x}^{2}+\left(4a^{3}-8a^{2}-5a+8\right){x}-5a^{3}+23a^{2}-18a-8$ |
| 12.1-a4 |
12.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{16} \cdot 3^{2} \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.096764154$ |
$315.5641805$ |
3.631774688 |
\( -\frac{53554909}{4608} a^{3} - \frac{5340673}{1536} a^{2} + \frac{345786775}{4608} a + \frac{67436831}{2304} \) |
\( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{3} - 4 a\) , \( -a^{3} + 2 a^{2} + 7 a - 10\) , \( 4 a^{3} - 5 a^{2} - 24 a + 28\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{3}+2a^{2}+7a-10\right){x}+4a^{3}-5a^{2}-24a+28$ |
| 12.1-a5 |
12.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.193528309$ |
$1262.256722$ |
3.631774688 |
\( \frac{5580005647}{2592} a^{3} - \frac{2698752947}{864} a^{2} - \frac{35403039655}{2592} a + \frac{3091018997}{162} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 3\) , \( -\frac{3}{2} a^{3} - \frac{1}{2} a^{2} + \frac{13}{2} a - 2\) , \( -4 a^{3} - 5 a^{2} + 12 a + 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}^{2}+\left(-\frac{3}{2}a^{3}-\frac{1}{2}a^{2}+\frac{13}{2}a-2\right){x}-4a^{3}-5a^{2}+12a+3$ |
| 12.1-a6 |
12.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{8} \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.387056618$ |
$315.5641805$ |
3.631774688 |
\( \frac{2757970737714201205}{52488} a^{3} - \frac{1334205989042635679}{17496} a^{2} - \frac{17499449907519419455}{52488} a + \frac{12222583887443291953}{26244} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 3\) , \( -\frac{13}{2} a^{3} - \frac{11}{2} a^{2} + \frac{53}{2} a - 2\) , \( 7 a^{3} + 8 a^{2} - 24 a - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}^{2}+\left(-\frac{13}{2}a^{3}-\frac{11}{2}a^{2}+\frac{53}{2}a-2\right){x}+7a^{3}+8a^{2}-24a-5$ |
| 12.1-b1 |
12.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{16} \cdot 3^{2} \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.721488939$ |
$160.9251966$ |
3.452315071 |
\( -\frac{53554909}{4608} a^{3} - \frac{5340673}{1536} a^{2} + \frac{345786775}{4608} a + \frac{67436831}{2304} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{3}{2} a - 1\) , \( \frac{7}{2} a^{3} + \frac{11}{2} a^{2} - \frac{23}{2} a - 6\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-2\right){x}^{2}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{3}{2}a-1\right){x}+\frac{7}{2}a^{3}+\frac{11}{2}a^{2}-\frac{23}{2}a-6$ |
| 12.1-b2 |
12.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.360744469$ |
$643.7007867$ |
3.452315071 |
\( \frac{5580005647}{2592} a^{3} - \frac{2698752947}{864} a^{2} - \frac{35403039655}{2592} a + \frac{3091018997}{162} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 1\) , \( 1\) , \( \frac{29}{2} a^{3} + \frac{5}{2} a^{2} - \frac{173}{2} a - 37\) , \( -\frac{47}{2} a^{3} - \frac{9}{2} a^{2} + \frac{289}{2} a + 64\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-1\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+1\right){x}^{2}+\left(\frac{29}{2}a^{3}+\frac{5}{2}a^{2}-\frac{173}{2}a-37\right){x}-\frac{47}{2}a^{3}-\frac{9}{2}a^{2}+\frac{289}{2}a+64$ |
| 12.1-b3 |
12.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{8} \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.721488939$ |
$40.23129917$ |
3.452315071 |
\( \frac{2757970737714201205}{52488} a^{3} - \frac{1334205989042635679}{17496} a^{2} - \frac{17499449907519419455}{52488} a + \frac{12222583887443291953}{26244} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 1\) , \( 1\) , \( -\frac{81}{2} a^{3} - \frac{105}{2} a^{2} + \frac{687}{2} a + 163\) , \( -\frac{135}{2} a^{3} - \frac{537}{2} a^{2} + \frac{1913}{2} a + 480\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-1\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+1\right){x}^{2}+\left(-\frac{81}{2}a^{3}-\frac{105}{2}a^{2}+\frac{687}{2}a+163\right){x}-\frac{135}{2}a^{3}-\frac{537}{2}a^{2}+\frac{1913}{2}a+480$ |
| 12.1-b4 |
12.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3 \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.360744469$ |
$1287.401573$ |
3.452315071 |
\( \frac{758955402069437}{12} a^{3} + \frac{399496746369175}{4} a^{2} - \frac{2222290335704369}{12} a - \frac{294307880630930}{3} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -103 a^{3} + 149 a^{2} + 651 a - 908\) , \( 1247 a^{3} - 1810 a^{2} - 7914 a + 11056\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{5}{2}a-1\right){x}^{2}+\left(-103a^{3}+149a^{2}+651a-908\right){x}+1247a^{3}-1810a^{2}-7914a+11056$ |
| 12.1-b5 |
12.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.180372234$ |
$2574.803147$ |
3.452315071 |
\( \frac{124305619}{72} a^{3} + \frac{69552727}{24} a^{2} - \frac{337560937}{72} a - \frac{91498457}{36} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -23 a^{3} + 34 a^{2} + 141 a - 198\) , \( -110 a^{3} + 161 a^{2} + 691 a - 968\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{5}{2}a-1\right){x}^{2}+\left(-23a^{3}+34a^{2}+141a-198\right){x}-110a^{3}+161a^{2}+691a-968$ |
| 12.1-b6 |
12.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3 \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.360744469$ |
$1287.401573$ |
3.452315071 |
\( -\frac{1307703981005}{12} a^{3} - \frac{162976069959}{4} a^{2} + \frac{8482197737297}{12} a + \frac{951830717234}{3} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( a^{3} - 4 a + 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a - 1\) , \( -\frac{3}{2} a^{3} - \frac{3}{2} a^{2} + \frac{15}{2} a + 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+3\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}^{2}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{7}{2}a-1\right){x}-\frac{3}{2}a^{3}-\frac{3}{2}a^{2}+\frac{15}{2}a+2$ |
| 12.1-c1 |
12.1-c |
$1$ |
$1$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{13} \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.556411627$ |
$171.9128978$ |
2.844208018 |
\( \frac{1049416907}{6377292} a^{3} + \frac{395116529}{2125764} a^{2} - \frac{4876120775}{6377292} a - \frac{743685596}{1594323} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{3}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 3\) , \( -\frac{3}{2} a^{3} + \frac{3}{2} a^{2} + \frac{13}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - 3\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{3}{2}a-1\right){x}^{2}+\left(-\frac{3}{2}a^{3}+\frac{3}{2}a^{2}+\frac{13}{2}a-3\right){x}-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-3$ |
| 12.1-d1 |
12.1-d |
$1$ |
$1$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3^{13} \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 13 \) |
$0.018723521$ |
$369.2609900$ |
2.672520377 |
\( \frac{1049416907}{6377292} a^{3} + \frac{395116529}{2125764} a^{2} - \frac{4876120775}{6377292} a - \frac{743685596}{1594323} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{5}{2} a - 3\) , \( a\) , \( 4 a^{3} + 6 a^{2} - 14 a - 2\) , \( 13 a^{3} + 14 a^{2} - 31 a - 18\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-1\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{5}{2}a-3\right){x}^{2}+\left(4a^{3}+6a^{2}-14a-2\right){x}+13a^{3}+14a^{2}-31a-18$ |
| 12.2-a1 |
12.2-a |
$2$ |
$2$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (-1/2a^3+1/2a^2+7/2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$271.1186909$ |
2.015376386 |
\( -\frac{5026151635}{36} a^{3} + \frac{2933210821}{6} a^{2} - \frac{2210604581}{9} a - \frac{2009202809}{9} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( -8 a^{3} - 10 a^{2} + 28 a + 8\) , \( -46 a^{3} - 75 a^{2} + 133 a + 82\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{5}{2}a+3\right){x}^{2}+\left(-8a^{3}-10a^{2}+28a+8\right){x}-46a^{3}-75a^{2}+133a+82$ |
| 12.2-a2 |
12.2-a |
$2$ |
$2$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3 \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (-1/2a^3+1/2a^2+7/2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1084.474763$ |
2.015376386 |
\( -\frac{805445}{6} a^{3} - 32672 a^{2} + \frac{4411588}{3} a + \frac{5572375}{3} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{3}{2} a - 3\) , \( a^{3} - 4 a\) , \( a^{3} + 2 a^{2} - 14 a - 8\) , \( -7 a^{3} + 36 a + 15\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{3}{2}a-3\right){x}^{2}+\left(a^{3}+2a^{2}-14a-8\right){x}-7a^{3}+36a+15$ |
| 12.2-b1 |
12.2-b |
$2$ |
$2$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (-1/2a^3+1/2a^2+7/2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$289.7043352$ |
2.153533842 |
\( -\frac{5026151635}{36} a^{3} + \frac{2933210821}{6} a^{2} - \frac{2210604581}{9} a - \frac{2009202809}{9} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( 0\) , \( 6 a^{3} + 3 a^{2} - 38 a - 16\) , \( -14 a^{3} - 5 a^{2} + 92 a + 41\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}^{2}+\left(6a^{3}+3a^{2}-38a-16\right){x}-14a^{3}-5a^{2}+92a+41$ |
| 12.2-b2 |
12.2-b |
$2$ |
$2$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{2} \cdot 3 \) |
$16.39984$ |
$(1/2a^3-1/2a^2-5/2a+1), (-1/2a^3+1/2a^2+7/2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1158.817340$ |
2.153533842 |
\( -\frac{805445}{6} a^{3} - 32672 a^{2} + \frac{4411588}{3} a + \frac{5572375}{3} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{7}{2} a - 1\) , \( a + 1\) , \( -43 a^{3} - 62 a^{2} + 133 a + 49\) , \( \frac{781}{2} a^{3} + \frac{1245}{2} a^{2} - \frac{2273}{2} a - 626\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{7}{2}a-1\right){x}^{2}+\left(-43a^{3}-62a^{2}+133a+49\right){x}+\frac{781}{2}a^{3}+\frac{1245}{2}a^{2}-\frac{2273}{2}a-626$ |
| 17.1-a1 |
17.1-a |
$4$ |
$6$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$17.12963$ |
$(-1/2a^3+1/2a^2+5/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$2.623619348$ |
$110.5856630$ |
6.470198622 |
\( -\frac{4417791485045697}{9826} a^{3} + \frac{15496172499429131}{9826} a^{2} - \frac{7797203413682701}{9826} a - \frac{3540429105928813}{4913} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( -a^{3} + 5 a\) , \( a + 1\) , \( 56 a^{3} - 90 a^{2} - 360 a + 543\) , \( \frac{911}{2} a^{3} - \frac{1333}{2} a^{2} - \frac{5773}{2} a + 4081\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(56a^{3}-90a^{2}-360a+543\right){x}+\frac{911}{2}a^{3}-\frac{1333}{2}a^{2}-\frac{5773}{2}a+4081$ |
| 17.1-a2 |
17.1-a |
$4$ |
$6$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$17.12963$ |
$(-1/2a^3+1/2a^2+5/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.437269891$ |
$995.2709676$ |
6.470198622 |
\( -\frac{770619148263}{578} a^{3} - \frac{288508273607}{578} a^{2} + \frac{4999048655765}{578} a + \frac{1123723467545}{289} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 3\) , \( \frac{159}{2} a^{3} + \frac{51}{2} a^{2} - \frac{1009}{2} a - 232\) , \( -\frac{1405}{2} a^{3} - \frac{513}{2} a^{2} + \frac{9087}{2} a + 2035\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{7}{2}a-1\right){x}^{2}+\left(\frac{159}{2}a^{3}+\frac{51}{2}a^{2}-\frac{1009}{2}a-232\right){x}-\frac{1405}{2}a^{3}-\frac{513}{2}a^{2}+\frac{9087}{2}a+2035$ |
| 17.1-a3 |
17.1-a |
$4$ |
$6$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$17.12963$ |
$(-1/2a^3+1/2a^2+5/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1.311809674$ |
$110.5856630$ |
6.470198622 |
\( \frac{263007023042890885564830375}{48275138} a^{3} + \frac{415277184041257311049103851}{48275138} a^{2} - \frac{770066522743120132155985881}{48275138} a - \frac{203963746899704786799431376}{24137569} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 3\) , \( 127 a^{3} - 112 a^{2} - 487 a - 192\) , \( \frac{321}{2} a^{3} - \frac{5083}{2} a^{2} + \frac{8991}{2} a + 2558\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{7}{2}a-1\right){x}^{2}+\left(127a^{3}-112a^{2}-487a-192\right){x}+\frac{321}{2}a^{3}-\frac{5083}{2}a^{2}+\frac{8991}{2}a+2558$ |
| 17.1-a4 |
17.1-a |
$4$ |
$6$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$17.12963$ |
$(-1/2a^3+1/2a^2+5/2a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.874539782$ |
$995.2709676$ |
6.470198622 |
\( \frac{399737}{34} a^{3} + \frac{254141}{34} a^{2} - \frac{2761835}{34} a - \frac{661140}{17} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 3\) , \( \frac{9}{2} a^{3} + \frac{1}{2} a^{2} - \frac{49}{2} a - 17\) , \( -6 a^{3} - 7 a^{2} + 49 a + 20\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{7}{2}a-1\right){x}^{2}+\left(\frac{9}{2}a^{3}+\frac{1}{2}a^{2}-\frac{49}{2}a-17\right){x}-6a^{3}-7a^{2}+49a+20$ |
| 17.1-b1 |
17.1-b |
$4$ |
$6$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$17.12963$ |
$(-1/2a^3+1/2a^2+5/2a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1012.112779$ |
0.417977698 |
\( -\frac{770619148263}{578} a^{3} - \frac{288508273607}{578} a^{2} + \frac{4999048655765}{578} a + \frac{1123723467545}{289} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( 0\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( -2 a^{3} - 2 a^{2} + 6 a - 7\) , \( -\frac{27}{2} a^{3} - \frac{47}{2} a^{2} + \frac{77}{2} a + 30\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){y}={x}^{3}+\left(-2a^{3}-2a^{2}+6a-7\right){x}-\frac{27}{2}a^{3}-\frac{47}{2}a^{2}+\frac{77}{2}a+30$ |
| 17.1-b2 |
17.1-b |
$4$ |
$6$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$17.12963$ |
$(-1/2a^3+1/2a^2+5/2a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2024.225558$ |
0.417977698 |
\( \frac{399737}{34} a^{3} + \frac{254141}{34} a^{2} - \frac{2761835}{34} a - \frac{661140}{17} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( 0\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){x}+\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-1$ |
| 17.1-b3 |
17.1-b |
$4$ |
$6$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$17.12963$ |
$(-1/2a^3+1/2a^2+5/2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$24.99043899$ |
0.417977698 |
\( -\frac{4417791485045697}{9826} a^{3} + \frac{15496172499429131}{9826} a^{2} - \frac{7797203413682701}{9826} a - \frac{3540429105928813}{4913} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( 0\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( -12 a^{3} - 22 a^{2} + 36 a + 23\) , \( -\frac{237}{2} a^{3} - \frac{381}{2} a^{2} + \frac{703}{2} a + 184\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){y}={x}^{3}+\left(-12a^{3}-22a^{2}+36a+23\right){x}-\frac{237}{2}a^{3}-\frac{381}{2}a^{2}+\frac{703}{2}a+184$ |
| 17.1-b4 |
17.1-b |
$4$ |
$6$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$17.12963$ |
$(-1/2a^3+1/2a^2+5/2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$12.49521949$ |
0.417977698 |
\( \frac{263007023042890885564830375}{48275138} a^{3} + \frac{415277184041257311049103851}{48275138} a^{2} - \frac{770066522743120132155985881}{48275138} a - \frac{203963746899704786799431376}{24137569} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( 0\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( -212 a^{3} - 332 a^{2} + 626 a + 308\) , \( -5758 a^{3} - 9088 a^{2} + 16872 a + 8908\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){y}={x}^{3}+\left(-212a^{3}-332a^{2}+626a+308\right){x}-5758a^{3}-9088a^{2}+16872a+8908$ |
| 21.1-a1 |
21.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3 \cdot 7 \) |
$17.58811$ |
$(1/2a^3-1/2a^2-5/2a+1), (1/2a^3-1/2a^2-5/2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$3167.233147$ |
5.885952451 |
\( -\frac{1100449474}{21} a^{3} - \frac{134828966}{7} a^{2} + \frac{7158414610}{21} a + \frac{3211752181}{21} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 1\) , \( 0\) , \( -2 a^{3} - 3 a^{2} + 7 a + 3\) , \( \frac{3}{2} a^{3} + \frac{5}{2} a^{2} - \frac{9}{2} a - 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-1\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{5}{2}a+1\right){x}^{2}+\left(-2a^{3}-3a^{2}+7a+3\right){x}+\frac{3}{2}a^{3}+\frac{5}{2}a^{2}-\frac{9}{2}a-2$ |
| 21.1-a2 |
21.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3 \cdot 7 \) |
$17.58811$ |
$(1/2a^3-1/2a^2-5/2a+1), (1/2a^3-1/2a^2-5/2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$791.8082868$ |
5.885952451 |
\( -\frac{5421515538098}{21} a^{3} + \frac{8152783650822}{7} a^{2} - \frac{31178487892402}{21} a + \frac{10728627059387}{21} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( -a^{3} + 4 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 2\) , \( 79 a^{3} + 131 a^{2} - 225 a - 130\) , \( 1186 a^{3} + 1876 a^{2} - 3469 a - 1839\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+2\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(79a^{3}+131a^{2}-225a-130\right){x}+1186a^{3}+1876a^{2}-3469a-1839$ |
| 21.1-a3 |
21.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{2} \) |
$17.58811$ |
$(1/2a^3-1/2a^2-5/2a+1), (1/2a^3-1/2a^2-5/2a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$3167.233147$ |
5.885952451 |
\( \frac{2572412}{441} a^{3} + \frac{27590204}{147} a^{2} - \frac{365156660}{441} a + \frac{348454489}{441} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( -a^{3} + 4 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 2\) , \( -31 a^{3} - 44 a^{2} + 95 a + 45\) , \( \frac{315}{2} a^{3} + \frac{505}{2} a^{2} - \frac{917}{2} a - 246\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+2\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-31a^{3}-44a^{2}+95a+45\right){x}+\frac{315}{2}a^{3}+\frac{505}{2}a^{2}-\frac{917}{2}a-246$ |
| 21.1-a4 |
21.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{8} \cdot 7^{2} \) |
$17.58811$ |
$(1/2a^3-1/2a^2-5/2a+1), (1/2a^3-1/2a^2-5/2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$197.9520717$ |
5.885952451 |
\( -\frac{254226640}{321489} a^{3} + \frac{288122270}{107163} a^{2} - \frac{546360212}{321489} a + \frac{23103481}{321489} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( -a^{3} - a^{2} + 7 a + 5\) , \( \frac{3}{2} a^{3} - \frac{1}{2} a^{2} - \frac{17}{2} a - 4\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}^{2}+\left(-a^{3}-a^{2}+7a+5\right){x}+\frac{3}{2}a^{3}-\frac{1}{2}a^{2}-\frac{17}{2}a-4$ |
| 21.1-a5 |
21.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7^{8} \) |
$17.58811$ |
$(1/2a^3-1/2a^2-5/2a+1), (1/2a^3-1/2a^2-5/2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$49.48801792$ |
5.885952451 |
\( \frac{2080892160245020}{51883209} a^{3} + \frac{1113600007794790}{17294403} a^{2} - \frac{5927838335012392}{51883209} a - \frac{3160168767016753}{51883209} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( 5 a^{3} + 2 a^{2} - 64 a - 9\) , \( 9 a^{3} + 13 a^{2} - 155 a - 57\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a+2\right){x}^{2}+\left(5a^{3}+2a^{2}-64a-9\right){x}+9a^{3}+13a^{2}-155a-57$ |
| 21.1-a6 |
21.1-a |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{4} \) |
$17.58811$ |
$(1/2a^3-1/2a^2-5/2a+1), (1/2a^3-1/2a^2-5/2a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$791.8082868$ |
5.885952451 |
\( \frac{236438396}{194481} a^{3} + \frac{145140344}{64827} a^{2} - \frac{584482280}{194481} a + \frac{65640385}{194481} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{7}{2} a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{5}{2} a^{3} - \frac{11}{2} a^{2} - \frac{23}{2} a + 16\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{21}{2} a + 10\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{7}{2}a+2\right){x}^{2}+\left(\frac{5}{2}a^{3}-\frac{11}{2}a^{2}-\frac{23}{2}a+16\right){x}+\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{21}{2}a+10$ |
| 21.1-b1 |
21.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7^{2} \) |
$17.58811$ |
$(1/2a^3-1/2a^2-5/2a+1), (1/2a^3-1/2a^2-5/2a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.322061707$ |
$537.8458622$ |
5.150550162 |
\( -\frac{15014837309}{642978} a^{3} - \frac{1045743809}{214326} a^{2} + \frac{92490665681}{642978} a + \frac{20230532953}{321489} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 1\) , \( a^{3} - 4 a\) , \( 5 a^{3} + 5 a^{2} - 17 a - 9\) , \( 7 a^{3} + 12 a^{2} - 17 a - 12\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-1\right){x}^{2}+\left(5a^{3}+5a^{2}-17a-9\right){x}+7a^{3}+12a^{2}-17a-12$ |
| 21.1-b2 |
21.1-b |
$6$ |
$8$ |
4.4.18097.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{2} \) |
$17.58811$ |
$(1/2a^3-1/2a^2-5/2a+1), (1/2a^3-1/2a^2-5/2a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.288246830$ |
$537.8458622$ |
5.150550162 |
\( \frac{133558645}{882} a^{3} + \frac{209234905}{294} a^{2} - \frac{564364501}{882} a - \frac{184094597}{441} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( a^{2} - a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 1\) , \( -\frac{241}{2} a^{3} - \frac{375}{2} a^{2} + \frac{705}{2} a + 180\) , \( 1939 a^{3} + 3062 a^{2} - 5679 a - 3007\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-\frac{241}{2}a^{3}-\frac{375}{2}a^{2}+\frac{705}{2}a+180\right){x}+1939a^{3}+3062a^{2}-5679a-3007$ |
*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.
