| 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 |
$2$ |
$11$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3 \) |
$14.43250$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.2 |
|
\( 1 \) |
$1$ |
$0.021714933$ |
2.780221650 |
\( -17320935403935602154 a^{3} + \frac{70045782250784531003}{3} a^{2} + \frac{391326656179292150729}{3} a - 149319306081545580681 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( a\) , \( a^{2} - 4\) , \( \frac{20753}{3} a^{3} + \frac{2342}{3} a^{2} - 54658 a - 19596\) , \( \frac{2144189}{3} a^{3} + \frac{227318}{3} a^{2} - 5636519 a - 1948781\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+a{x}^{2}+\left(\frac{20753}{3}a^{3}+\frac{2342}{3}a^{2}-54658a-19596\right){x}+\frac{2144189}{3}a^{3}+\frac{227318}{3}a^{2}-5636519a-1948781$ |
| 3.1-a2 |
3.1-a |
$2$ |
$11$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{11} \) |
$14.43250$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
$0 \le r \le 1$ |
$\Z/11\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$11$ |
11B.1.1 |
|
\( 11 \) |
$1$ |
$317.9283472$ |
2.780221650 |
\( -\frac{73343}{729} a^{3} + \frac{24131}{729} a^{2} + \frac{615892}{729} a + \frac{18719}{27} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( a\) , \( a^{2} - 4\) , \( -\frac{7}{3} a^{3} + \frac{2}{3} a^{2} + 22 a + 9\) , \( -\frac{10}{3} a^{3} + \frac{5}{3} a^{2} + 32 a + 7\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+a{x}^{2}+\left(-\frac{7}{3}a^{3}+\frac{2}{3}a^{2}+22a+9\right){x}-\frac{10}{3}a^{3}+\frac{5}{3}a^{2}+32a+7$ |
| 9.1-a1 |
9.1-a |
$2$ |
$11$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{7} \) |
$16.55700$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$11$ |
11B.10.2 |
|
\( 2 \) |
$1$ |
$0.106055840$ |
3.742242954 |
\( -17320935403935602154 a^{3} + \frac{70045782250784531003}{3} a^{2} + \frac{391326656179292150729}{3} a - 149319306081545580681 \) |
\( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a\) , \( a^{2} - 4\) , \( 1899 a^{3} - 3107 a^{2} - 25597 a - 9911\) , \( 107727 a^{3} - 331234 a^{2} - 1894883 a - 638778\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-4a\right){x}^{2}+\left(1899a^{3}-3107a^{2}-25597a-9911\right){x}+107727a^{3}-331234a^{2}-1894883a-638778$ |
| 9.1-a2 |
9.1-a |
$2$ |
$11$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{17} \) |
$16.55700$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$11$ |
11B.10.1 |
|
\( 2 \) |
$1$ |
$141.1603238$ |
3.742242954 |
\( -\frac{73343}{729} a^{3} + \frac{24131}{729} a^{2} + \frac{615892}{729} a + \frac{18719}{27} \) |
\( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a\) , \( a^{2} - 4\) , \( -a^{3} + 3 a^{2} + 8 a + 4\) , \( 3 a^{3} + 8 a^{2} - 11 a - 3\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-4a\right){x}^{2}+\left(-a^{3}+3a^{2}+8a+4\right){x}+3a^{3}+8a^{2}-11a-3$ |
| 17.1-a1 |
17.1-a |
$2$ |
$2$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$17.92699$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1473.805653$ |
2.617082696 |
\( -\frac{30069856}{51} a^{3} - \frac{57403081}{51} a^{2} + \frac{24388892}{17} a + \frac{10411556}{17} \) |
\( \bigl[a^{2} - a - 4\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + 1\) , \( 0\) , \( 2 a^{3} - 17 a + 4\) , \( \frac{7}{3} a^{3} + \frac{1}{3} a^{2} - 20 a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-4a+1\right){x}^{2}+\left(2a^{3}-17a+4\right){x}+\frac{7}{3}a^{3}+\frac{1}{3}a^{2}-20a-1$ |
| 17.1-a2 |
17.1-a |
$2$ |
$2$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{2} \) |
$17.92699$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$736.9028267$ |
2.617082696 |
\( \frac{9878307305244158}{867} a^{3} + \frac{18933234918159542}{867} a^{2} - \frac{7934960729500279}{289} a - \frac{3386870152613548}{289} \) |
\( \bigl[a^{2} - a - 4\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + 1\) , \( 0\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - 2 a + 9\) , \( \frac{19}{3} a^{3} - \frac{2}{3} a^{2} - 48 a - 11\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-4a+1\right){x}^{2}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-2a+9\right){x}+\frac{19}{3}a^{3}-\frac{2}{3}a^{2}-48a-11$ |
| 21.1-a1 |
21.1-a |
$4$ |
$6$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7^{3} \) |
$18.40682$ |
$(-1/3a^3-1/3a^2+3a+2), (-1/3a^3-1/3a^2+2a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2775.234131$ |
3.285379908 |
\( -\frac{45668663}{343} a^{3} - \frac{10461181}{1029} a^{2} + \frac{362255132}{343} a + \frac{367286758}{1029} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( a^{2} - a - 3\) , \( -\frac{1}{3} a^{3} - \frac{4}{3} a^{2} + 1\) , \( \frac{2}{3} a^{3} + \frac{2}{3} a^{2} - 2 a - 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){x}^{2}+\left(-\frac{1}{3}a^{3}-\frac{4}{3}a^{2}+1\right){x}+\frac{2}{3}a^{3}+\frac{2}{3}a^{2}-2a-2$ |
| 21.1-a2 |
21.1-a |
$4$ |
$6$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{4} \cdot 7^{6} \) |
$18.40682$ |
$(-1/3a^3-1/3a^2+3a+2), (-1/3a^3-1/3a^2+2a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$693.8085328$ |
3.285379908 |
\( \frac{74079408535072}{1058841} a^{3} + \frac{42308209276609}{352947} a^{2} - \frac{67381326805957}{352947} a - \frac{31682015546507}{1058841} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( a^{2} - a - 3\) , \( -\frac{26}{3} a^{3} - \frac{44}{3} a^{2} + 25 a + 1\) , \( 47 a^{3} + 84 a^{2} - 120 a - 36\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){x}^{2}+\left(-\frac{26}{3}a^{3}-\frac{44}{3}a^{2}+25a+1\right){x}+47a^{3}+84a^{2}-120a-36$ |
| 21.1-a3 |
21.1-a |
$4$ |
$6$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{6} \cdot 7 \) |
$18.40682$ |
$(-1/3a^3-1/3a^2+3a+2), (-1/3a^3-1/3a^2+2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$308.3593479$ |
3.285379908 |
\( -\frac{3858185}{189} a^{3} + \frac{5279251}{63} a^{2} - \frac{2609822}{63} a - \frac{4497131}{189} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( \frac{28}{3} a^{3} + \frac{1}{3} a^{2} - 75 a - 21\) , \( 37 a^{3} + 4 a^{2} - 292 a - 103\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(\frac{28}{3}a^{3}+\frac{1}{3}a^{2}-75a-21\right){x}+37a^{3}+4a^{2}-292a-103$ |
| 21.1-a4 |
21.1-a |
$4$ |
$6$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{12} \cdot 7^{2} \) |
$18.40682$ |
$(-1/3a^3-1/3a^2+3a+2), (-1/3a^3-1/3a^2+2a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$77.08983698$ |
3.285379908 |
\( -\frac{841064654581664}{35721} a^{3} + \frac{1030023415263169}{11907} a^{2} - \frac{511441919731475}{11907} a - \frac{943603335173858}{35721} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( -19 a^{3} - 3 a^{2} + 150 a + 54\) , \( 148 a^{3} + 16 a^{2} - 1167 a - 407\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-19a^{3}-3a^{2}+150a+54\right){x}+148a^{3}+16a^{2}-1167a-407$ |
| 25.1-a1 |
25.1-a |
$2$ |
$2$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$18.81238$ |
$(1/3a^3+1/3a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1285.341688$ |
2.282421352 |
\( -\frac{3609194}{5} a^{3} + \frac{3497552}{5} a^{2} + 3698979 a + \frac{5853102}{5} \) |
\( \bigl[a^{2} - a - 4\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a + 1\) , \( a + 1\) , \( 3 a^{3} + a^{2} - 30 a + 3\) , \( -\frac{22}{3} a^{3} - \frac{1}{3} a^{2} + 53 a + 26\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-6a+1\right){x}^{2}+\left(3a^{3}+a^{2}-30a+3\right){x}-\frac{22}{3}a^{3}-\frac{1}{3}a^{2}+53a+26$ |
| 25.1-a2 |
25.1-a |
$2$ |
$2$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{4} \) |
$18.81238$ |
$(1/3a^3+1/3a^2-3a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$642.6708442$ |
2.282421352 |
\( -\frac{31023350936203}{15} a^{3} + \frac{569898787342063}{75} a^{2} - \frac{94324841361677}{25} a - \frac{58009213792802}{25} \) |
\( \bigl[a^{2} - a - 4\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a + 1\) , \( a + 1\) , \( \frac{14}{3} a^{3} - \frac{22}{3} a^{2} - 20 a + 3\) , \( -\frac{37}{3} a^{3} + \frac{32}{3} a^{2} + 67 a + 16\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-6a+1\right){x}^{2}+\left(\frac{14}{3}a^{3}-\frac{22}{3}a^{2}-20a+3\right){x}-\frac{37}{3}a^{3}+\frac{32}{3}a^{2}+67a+16$ |
| 27.2-a1 |
27.2-a |
$2$ |
$3$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{3} \) |
$18.99423$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$9$ |
\( 1 \) |
$0.205990629$ |
$89.20040611$ |
4.698443578 |
\( -\frac{2659993414}{3} a^{3} + \frac{3059637059}{3} a^{2} + 7384788197 a - 8211399121 \) |
\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 3 a + 1\) , \( 0\) , \( -\frac{14}{3} a^{3} - \frac{11}{3} a^{2} + 45 a + 19\) , \( -\frac{28}{3} a^{3} + \frac{20}{3} a^{2} + 54 a + 17\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+3a+1\right){x}^{2}+\left(-\frac{14}{3}a^{3}-\frac{11}{3}a^{2}+45a+19\right){x}-\frac{28}{3}a^{3}+\frac{20}{3}a^{2}+54a+17$ |
| 27.2-a2 |
27.2-a |
$2$ |
$3$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{9} \) |
$18.99423$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.068663543$ |
$802.8036549$ |
4.698443578 |
\( \frac{2272}{3} a^{3} + \frac{1171}{3} a^{2} - 5297 a - 3398 \) |
\( \bigl[a + 1\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a + 1\) , \( a^{2} - 3\) , \( -\frac{5}{3} a^{3} + \frac{1}{3} a^{2} + 10 a - 2\) , \( -\frac{7}{3} a^{3} + \frac{8}{3} a^{2} + 17 a - 22\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-6a+1\right){x}^{2}+\left(-\frac{5}{3}a^{3}+\frac{1}{3}a^{2}+10a-2\right){x}-\frac{7}{3}a^{3}+\frac{8}{3}a^{2}+17a-22$ |
| 27.2-b1 |
27.2-b |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{11} \) |
$18.99423$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.883293612$ |
$90.82575439$ |
4.859865586 |
\( \frac{6364868}{3} a^{3} + \frac{8738927}{3} a^{2} - 8598468 a - 3255814 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{2}{3} a^{3} + \frac{1}{3} a^{2} + 4 a - 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( \frac{10}{3} a^{3} - \frac{2}{3} a^{2} - 28 a - 4\) , \( \frac{28}{3} a^{3} + \frac{7}{3} a^{2} - 76 a - 33\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{1}{3}a^{2}+4a-3\right){x}^{2}+\left(\frac{10}{3}a^{3}-\frac{2}{3}a^{2}-28a-4\right){x}+\frac{28}{3}a^{3}+\frac{7}{3}a^{2}-76a-33$ |
| 27.2-c1 |
27.2-c |
$2$ |
$3$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{3} \) |
$18.99423$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$241.7504940$ |
1.717135589 |
\( \frac{18512}{3} a^{3} + \frac{1769}{3} a^{2} - 48583 a - 15892 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 2\) , \( a\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} - a + 2\) , \( a^{3} - 3 a^{2} + 2 a\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-2\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}-a+2\right){x}+a^{3}-3a^{2}+2a$ |
| 27.2-c2 |
27.2-c |
$2$ |
$3$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{9} \) |
$18.99423$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$2.984574000$ |
1.717135589 |
\( \frac{69390538551526}{3} a^{3} + \frac{7310207971123}{3} a^{2} - 182347992864521 a - 62777053162061 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 2\) , \( a\) , \( 18 a^{3} - 65 a^{2} + 34 a + 12\) , \( \frac{701}{3} a^{3} - \frac{2560}{3} a^{2} + 416 a + 253\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-2\right){x}^{2}+\left(18a^{3}-65a^{2}+34a+12\right){x}+\frac{701}{3}a^{3}-\frac{2560}{3}a^{2}+416a+253$ |
| 27.2-d1 |
27.2-d |
$2$ |
$3$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{3} \) |
$18.99423$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$21.79844721$ |
1.393494589 |
\( \frac{69390538551526}{3} a^{3} + \frac{7310207971123}{3} a^{2} - 182347992864521 a - 62777053162061 \) |
\( \bigl[a^{2} - 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( \frac{19}{3} a^{3} + \frac{1}{3} a^{2} - 63 a - 29\) , \( 7 a^{3} - 18 a^{2} - 128 a - 55\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-4a-2\right){x}^{2}+\left(\frac{19}{3}a^{3}+\frac{1}{3}a^{2}-63a-29\right){x}+7a^{3}-18a^{2}-128a-55$ |
| 27.2-d2 |
27.2-d |
$2$ |
$3$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{9} \) |
$18.99423$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$196.1860248$ |
1.393494589 |
\( \frac{18512}{3} a^{3} + \frac{1769}{3} a^{2} - 48583 a - 15892 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( -a^{2} + 5\) , \( a\) , \( -a^{2} - a + 9\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - 2 a + 5\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-a^{2}-a+9\right){x}+\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-2a+5$ |
| 27.2-e1 |
27.2-e |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{5} \) |
$18.99423$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.078952824$ |
$99.31703355$ |
3.044552071 |
\( \frac{6364868}{3} a^{3} + \frac{8738927}{3} a^{2} - 8598468 a - 3255814 \) |
\( \bigl[a^{2} - a - 4\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + a - 2\) , \( a^{2} - a - 4\) , \( -\frac{4}{3} a^{3} + \frac{20}{3} a^{2} - 2 a - 21\) , \( \frac{17}{3} a^{3} + \frac{8}{3} a^{2} - 66 a + 28\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+a-2\right){x}^{2}+\left(-\frac{4}{3}a^{3}+\frac{20}{3}a^{2}-2a-21\right){x}+\frac{17}{3}a^{3}+\frac{8}{3}a^{2}-66a+28$ |
| 27.2-f1 |
27.2-f |
$2$ |
$3$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{3} \) |
$18.99423$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.962322637$ |
$594.7379778$ |
3.684264377 |
\( \frac{2272}{3} a^{3} + \frac{1171}{3} a^{2} - 5297 a - 3398 \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( 0\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-2\right){x}^{2}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){x}$ |
| 27.2-f2 |
27.2-f |
$2$ |
$3$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{9} \) |
$18.99423$ |
$(-1/3a^3-1/3a^2+3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$5.886967913$ |
$7.342444170$ |
3.684264377 |
\( -\frac{2659993414}{3} a^{3} + \frac{3059637059}{3} a^{2} + 7384788197 a - 8211399121 \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{19}{3} a^{3} - \frac{19}{3} a^{2} + 33 a + 9\) , \( -\frac{67}{3} a^{3} - \frac{124}{3} a^{2} + 59 a + 22\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-2\right){x}^{2}+\left(-\frac{19}{3}a^{3}-\frac{19}{3}a^{2}+33a+9\right){x}-\frac{67}{3}a^{3}-\frac{124}{3}a^{2}+59a+22$ |
| 29.2-a1 |
29.2-a |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( -29 \) |
$19.16466$ |
$(-1/3a^3-1/3a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$173.3993546$ |
1.231642583 |
\( \frac{21593247109}{87} a^{3} - \frac{29360866361}{87} a^{2} - \frac{54354021521}{29} a + \frac{62317664466}{29} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 3 a + 2\) , \( 1\) , \( -\frac{23}{3} a^{3} - \frac{35}{3} a^{2} + 27 a + 7\) , \( -\frac{134}{3} a^{3} - \frac{248}{3} a^{2} + 113 a + 43\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+3a+2\right){x}^{2}+\left(-\frac{23}{3}a^{3}-\frac{35}{3}a^{2}+27a+7\right){x}-\frac{134}{3}a^{3}-\frac{248}{3}a^{2}+113a+43$ |
| 29.2-b1 |
29.2-b |
$2$ |
$3$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( - 29^{3} \) |
$19.16466$ |
$(-1/3a^3-1/3a^2+a-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.264195824$ |
$1021.907371$ |
2.556898197 |
\( -\frac{136474053}{24389} a^{3} + \frac{759835410}{24389} a^{2} - \frac{1394989701}{24389} a + \frac{985114313}{24389} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + 2\) , \( 0\) , \( \frac{2}{3} a^{3} - \frac{7}{3} a^{2} - 8 a + 10\) , \( -7 a^{3} - 15 a^{2} + 15 a + 13\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){x}{y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-4a+2\right){x}^{2}+\left(\frac{2}{3}a^{3}-\frac{7}{3}a^{2}-8a+10\right){x}-7a^{3}-15a^{2}+15a+13$ |
| 29.2-b2 |
29.2-b |
$2$ |
$3$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( -29 \) |
$19.16466$ |
$(-1/3a^3-1/3a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.792587473$ |
$113.5452634$ |
2.556898197 |
\( -\frac{391527369}{29} a^{3} - \frac{747299508}{29} a^{2} + \frac{953395335}{29} a + \frac{407098604}{29} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - 2 a + 4\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -2 a^{3} - a^{2} + 10 a - 5\) , \( -\frac{20}{3} a^{3} + \frac{1}{3} a^{2} + 37 a - 31\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-2a+4\right){x}^{2}+\left(-2a^{3}-a^{2}+10a-5\right){x}-\frac{20}{3}a^{3}+\frac{1}{3}a^{2}+37a-31$ |
| 39.1-a1 |
39.1-a |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{9} \cdot 13 \) |
$19.88769$ |
$(-1/3a^3-1/3a^2+3a+2), (-2/3a^3+1/3a^2+5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$165.0993253$ |
1.172688099 |
\( \frac{111853568}{3159} a^{3} + \frac{12132352}{3159} a^{2} - \frac{882774016}{3159} a - \frac{100966400}{1053} \) |
\( \bigl[0\) , \( -1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( \frac{4}{3} a^{3} - \frac{14}{3} a^{2} + 2 a + 2\) , \( -\frac{4}{3} a^{3} + \frac{14}{3} a^{2} - 3 a - 2\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){y}={x}^{3}-{x}^{2}+\left(\frac{4}{3}a^{3}-\frac{14}{3}a^{2}+2a+2\right){x}-\frac{4}{3}a^{3}+\frac{14}{3}a^{2}-3a-2$ |
| 39.1-b1 |
39.1-b |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{5} \cdot 13 \) |
$19.88769$ |
$(-1/3a^3-1/3a^2+3a+2), (-2/3a^3+1/3a^2+5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.257413700$ |
$156.3609513$ |
5.717776524 |
\( -\frac{3002368}{351} a^{3} + \frac{4784128}{351} a^{2} + \frac{610304}{351} a - \frac{966656}{117} \) |
\( \bigl[0\) , \( a^{2} - 5\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a\) , \( \frac{17}{3} a^{3} - \frac{61}{3} a^{2} + 8 a + 13\) , \( \frac{112}{3} a^{3} - \frac{410}{3} a^{2} + 68 a + 38\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(\frac{17}{3}a^{3}-\frac{61}{3}a^{2}+8a+13\right){x}+\frac{112}{3}a^{3}-\frac{410}{3}a^{2}+68a+38$ |
| 47.1-a1 |
47.1-a |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47 \) |
$20.35699$ |
$(-2/3a^3+1/3a^2+4a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.302657994$ |
$581.3716021$ |
4.999230649 |
\( -\frac{21742}{47} a^{3} + \frac{8397}{47} a^{2} + \frac{186762}{47} a + \frac{41657}{47} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 4 a + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-2\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+4a+1\right){x}+\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1$ |
| 48.1-a1 |
48.1-a |
$2$ |
$5$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{10} \) |
$20.41063$ |
$(-1/3a^3-1/3a^2+3a+2), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$796.9802678$ |
2.264356376 |
\( \frac{53998}{243} a^{3} - \frac{174017}{243} a^{2} - \frac{198685}{243} a + \frac{1780081}{486} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 3\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 5 a + 2\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 3\) , \( -\frac{8}{3} a^{3} + \frac{10}{3} a^{2} + 21 a - 21\) , \( -\frac{38}{3} a^{3} + \frac{52}{3} a^{2} + 96 a - 111\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-3\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-3\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-5a+2\right){x}^{2}+\left(-\frac{8}{3}a^{3}+\frac{10}{3}a^{2}+21a-21\right){x}-\frac{38}{3}a^{3}+\frac{52}{3}a^{2}+96a-111$ |
| 48.1-a2 |
48.1-a |
$2$ |
$5$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$20.41063$ |
$(-1/3a^3-1/3a^2+3a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 2 \cdot 5 \) |
$1$ |
$1.275168428$ |
2.264356376 |
\( \frac{188222875363696875}{8} a^{3} - \frac{1522351303597490689}{48} a^{2} - \frac{8504923474410890561}{48} a + \frac{19471549236222137689}{96} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - 2 a + 4\) , \( 0\) , \( \frac{119}{3} a^{3} - \frac{142}{3} a^{2} - 150 a - 126\) , \( 2041 a^{3} - 6773 a^{2} + 2003 a + 1146\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-2a+4\right){x}^{2}+\left(\frac{119}{3}a^{3}-\frac{142}{3}a^{2}-150a-126\right){x}+2041a^{3}-6773a^{2}+2003a+1146$ |
| 48.1-b1 |
48.1-b |
$2$ |
$3$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{6} \) |
$20.41063$ |
$(-1/3a^3-1/3a^2+3a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$32.82303819$ |
1.398837440 |
\( \frac{929865652521983315}{27} a^{3} - \frac{1138774984127055649}{9} a^{2} + \frac{1130881571253629065}{18} a + \frac{2086461174223332295}{54} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( -\frac{82}{3} a^{3} + \frac{113}{3} a^{2} + 211 a - 238\) , \( \frac{478}{3} a^{3} - \frac{626}{3} a^{2} - 1188 a + 1349\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-2\right){x}^{2}+\left(-\frac{82}{3}a^{3}+\frac{113}{3}a^{2}+211a-238\right){x}+\frac{478}{3}a^{3}-\frac{626}{3}a^{2}-1188a+1349$ |
| 48.1-b2 |
48.1-b |
$2$ |
$3$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$20.41063$ |
$(-1/3a^3-1/3a^2+3a+2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$295.4073437$ |
1.398837440 |
\( \frac{21224746042177}{24} a^{3} - \frac{9536989987379}{8} a^{2} - \frac{53280470046179}{8} a + \frac{182973377275723}{24} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a - 2\) , \( a^{2} - a - 4\) , \( 11 a^{3} - 7 a^{2} - 67 a - 24\) , \( -\frac{121}{3} a^{3} - \frac{160}{3} a^{2} + 444 a + 159\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-4a-2\right){x}^{2}+\left(11a^{3}-7a^{2}-67a-24\right){x}-\frac{121}{3}a^{3}-\frac{160}{3}a^{2}+444a+159$ |
| 48.1-c1 |
48.1-c |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$20.41063$ |
$(-1/3a^3-1/3a^2+3a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.046519900$ |
$1176.922004$ |
6.222195700 |
\( -\frac{2753009}{18} a^{3} - \frac{10565887}{36} a^{2} + \frac{26668097}{72} a + \frac{5985271}{36} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 4 a + 2\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 2\) , \( -3 a^{3} - a^{2} + 22 a + 6\) , \( -2 a^{3} + 18 a + 5\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+4a+2\right){x}^{2}+\left(-3a^{3}-a^{2}+22a+6\right){x}-2a^{3}+18a+5$ |
| 48.1-d1 |
48.1-d |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{8} \) |
$20.41063$ |
$(-1/3a^3-1/3a^2+3a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.100071083$ |
$251.1895626$ |
5.713436273 |
\( \frac{900817}{162} a^{3} - \frac{1470923}{162} a^{2} - \frac{3168587}{81} a + \frac{8660297}{162} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( -a^{2} + a + 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 2\) , \( 2 a^{3} + a^{2} - 19 a - 7\) , \( \frac{25}{3} a^{3} + \frac{1}{3} a^{2} - 64 a - 24\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(2a^{3}+a^{2}-19a-7\right){x}+\frac{25}{3}a^{3}+\frac{1}{3}a^{2}-64a-24$ |
| 48.1-e1 |
48.1-e |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{16} \cdot 3 \) |
$20.41063$ |
$(-1/3a^3-1/3a^2+3a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$125.7952267$ |
3.574056165 |
\( \frac{76926043}{48} a^{3} + \frac{1349417}{8} a^{2} - \frac{303233585}{24} a - \frac{8699767}{2} \) |
\( \bigl[a^{2} - a - 4\) , \( -\frac{2}{3} a^{3} + \frac{1}{3} a^{2} + 5 a - 2\) , \( a^{2} - a - 4\) , \( -\frac{2}{3} a^{3} + \frac{1}{3} a^{2} + 6 a - 5\) , \( \frac{7}{3} a^{3} - \frac{11}{3} a^{2} - 8 a - 4\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{1}{3}a^{2}+5a-2\right){x}^{2}+\left(-\frac{2}{3}a^{3}+\frac{1}{3}a^{2}+6a-5\right){x}+\frac{7}{3}a^{3}-\frac{11}{3}a^{2}-8a-4$ |
| 48.1-f1 |
48.1-f |
$3$ |
$9$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$20.41063$ |
$(-1/3a^3-1/3a^2+3a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 2 \) |
$1$ |
$2.732542865$ |
3.144265549 |
\( \frac{797557111969462491421}{3} a^{3} - \frac{1075105423836417293287}{3} a^{2} - \frac{4004214876876210459835}{2} a + \frac{13751062132018675906879}{6} \) |
\( \bigl[a\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 2 a\) , \( a^{2} - 3\) , \( \frac{325}{3} a^{3} + \frac{112}{3} a^{2} - 865 a - 498\) , \( \frac{5150}{3} a^{3} + \frac{941}{3} a^{2} - 13566 a - 5705\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+2a\right){x}^{2}+\left(\frac{325}{3}a^{3}+\frac{112}{3}a^{2}-865a-498\right){x}+\frac{5150}{3}a^{3}+\frac{941}{3}a^{2}-13566a-5705$ |
| 48.1-f2 |
48.1-f |
$3$ |
$9$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{12} \cdot 3^{6} \) |
$20.41063$ |
$(-1/3a^3-1/3a^2+3a+2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$221.3359721$ |
3.144265549 |
\( \frac{280173925}{216} a^{3} - \frac{125912675}{72} a^{2} - \frac{703303475}{72} a + \frac{2415702223}{216} \) |
\( \bigl[a\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 2 a\) , \( a^{2} - 3\) , \( \frac{5}{3} a^{3} + \frac{2}{3} a^{2} - 15 a - 8\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a - 5\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+2a\right){x}^{2}+\left(\frac{5}{3}a^{3}+\frac{2}{3}a^{2}-15a-8\right){x}+\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-6a-5$ |
| 48.1-f3 |
48.1-f |
$3$ |
$9$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$20.41063$ |
$(-1/3a^3-1/3a^2+3a+2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1992.023749$ |
3.144265549 |
\( \frac{165192620}{3} a^{3} - \frac{1676553739}{6} a^{2} + \frac{895634596}{3} a + \frac{420165101}{3} \) |
\( \bigl[a + 1\) , \( a^{2} - 3\) , \( 0\) , \( \frac{4}{3} a^{3} + \frac{1}{3} a^{2} - 3 a + 1\) , \( \frac{13}{3} a^{3} + \frac{28}{3} a^{2} - 11 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(\frac{4}{3}a^{3}+\frac{1}{3}a^{2}-3a+1\right){x}+\frac{13}{3}a^{3}+\frac{28}{3}a^{2}-11a-5$ |
| 48.1-g1 |
48.1-g |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$20.41063$ |
$(-1/3a^3-1/3a^2+3a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.352560036$ |
$351.6405927$ |
7.044647918 |
\( \frac{185538109}{6} a^{3} - \frac{83396763}{2} a^{2} - \frac{465693059}{2} a + \frac{1599654271}{6} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( -a^{2} + a + 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 2\) , \( -\frac{7}{3} a^{3} + \frac{11}{3} a^{2} + 14 a - 18\) , \( -\frac{31}{3} a^{3} + \frac{41}{3} a^{2} + 79 a - 96\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-\frac{7}{3}a^{3}+\frac{11}{3}a^{2}+14a-18\right){x}-\frac{31}{3}a^{3}+\frac{41}{3}a^{2}+79a-96$ |
| 48.1-h1 |
48.1-h |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$20.41063$ |
$(-1/3a^3-1/3a^2+3a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$146.4314743$ |
2.080183513 |
\( \frac{3428551}{24} a^{3} - \frac{4237589}{8} a^{2} + \frac{2169555}{8} a + \frac{499865}{3} \) |
\( \bigl[1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( a^{3} - 6 a^{2} + 8 a + 1\) , \( 8 a^{3} - 30 a^{2} + 14 a + 9\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){x}^{2}+\left(a^{3}-6a^{2}+8a+1\right){x}+8a^{3}-30a^{2}+14a+9$ |
| 49.1-a1 |
49.1-a |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{4} \) |
$20.46331$ |
$(-1/3a^3-1/3a^2+2a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$57.51697347$ |
1.225616219 |
\( 6360 a^{3} - 378485 a^{2} + 78352 a + 2833106 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( -a^{2} + a + 3\) , \( a + 1\) , \( -4 a^{3} - 4 a^{2} + 13 a + 1\) , \( -\frac{95}{3} a^{3} - \frac{176}{3} a^{2} + 82 a + 24\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-4a^{3}-4a^{2}+13a+1\right){x}-\frac{95}{3}a^{3}-\frac{176}{3}a^{2}+82a+24$ |
| 49.1-b1 |
49.1-b |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{10} \) |
$20.46331$ |
$(-1/3a^3-1/3a^2+2a)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
|
\( 1 \) |
$1$ |
$51.31204200$ |
6.311425977 |
\( 6360 a^{3} - 378485 a^{2} + 78352 a + 2833106 \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{2}{3} a^{3} + \frac{1}{3} a^{2} + 4 a - 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 2\) , \( \frac{46}{3} a^{3} + \frac{7}{3} a^{2} - 125 a - 54\) , \( 117 a^{3} + 7 a^{2} - 929 a - 296\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-2\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{1}{3}a^{2}+4a-1\right){x}^{2}+\left(\frac{46}{3}a^{3}+\frac{7}{3}a^{2}-125a-54\right){x}+117a^{3}+7a^{2}-929a-296$ |
| 51.1-a1 |
51.1-a |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{3} \cdot 17^{2} \) |
$20.56589$ |
$(-1/3a^3-1/3a^2+3a+2), (a+2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.019923622$ |
$1400.787218$ |
6.343481534 |
\( -\frac{27786899}{2601} a^{3} + \frac{37336988}{2601} a^{2} + \frac{209237104}{2601} a - \frac{79584637}{867} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 3\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - 3 a + 2\) , \( 0\) , \( \frac{4}{3} a^{3} - \frac{5}{3} a^{2} - 8 a + 10\) , \( -\frac{10}{3} a^{3} + \frac{41}{3} a^{2} - 13 a + 2\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-3\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-3a+2\right){x}^{2}+\left(\frac{4}{3}a^{3}-\frac{5}{3}a^{2}-8a+10\right){x}-\frac{10}{3}a^{3}+\frac{41}{3}a^{2}-13a+2$ |
| 57.1-a1 |
57.1-a |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
57.1 |
\( 3 \cdot 19 \) |
\( - 3^{2} \cdot 19 \) |
$20.85382$ |
$(-1/3a^3-1/3a^2+3a+2), (1/3a^3-2/3a^2-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.026666755$ |
$2988.763883$ |
4.528860944 |
\( \frac{764816735}{19} a^{3} - \frac{2749538048}{19} a^{2} + \frac{4046607218}{57} a + \frac{2502325034}{57} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 3\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 4 a\) , \( a^{2} - a - 3\) , \( -\frac{1}{3} a^{3} - \frac{7}{3} a^{2} - 2 a - 4\) , \( 2 a^{3} + 5 a^{2} - 3 a - 3\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+4a\right){x}^{2}+\left(-\frac{1}{3}a^{3}-\frac{7}{3}a^{2}-2a-4\right){x}+2a^{3}+5a^{2}-3a-3$ |
| 57.1-b1 |
57.1-b |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
57.1 |
\( 3 \cdot 19 \) |
\( - 3^{2} \cdot 19 \) |
$20.85382$ |
$(-1/3a^3-1/3a^2+3a+2), (1/3a^3-2/3a^2-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.254490339$ |
$181.8351186$ |
2.629518748 |
\( -\frac{43021}{57} a^{3} + \frac{85696}{57} a^{2} + \frac{369034}{57} a - \frac{454327}{57} \) |
\( \bigl[a + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( a\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( 2 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){x}+2a-3$ |
| 57.1-c1 |
57.1-c |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
57.1 |
\( 3 \cdot 19 \) |
\( - 3^{14} \cdot 19 \) |
$20.85382$ |
$(-1/3a^3-1/3a^2+3a+2), (1/3a^3-2/3a^2-2a+5)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
|
\( 2 \) |
$1$ |
$18.86826300$ |
3.895783893 |
\( -\frac{404963364612649}{4617} a^{3} + \frac{4913008494921869}{41553} a^{2} + \frac{27447645111084058}{41553} a - \frac{31419748638630586}{41553} \) |
\( \bigl[a^{2} - a - 4\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 3 a\) , \( a^{2} - a - 4\) , \( \frac{106}{3} a^{3} + \frac{10}{3} a^{2} - 278 a - 102\) , \( 883 a^{3} + 93 a^{2} - 6961 a - 2401\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+3a\right){x}^{2}+\left(\frac{106}{3}a^{3}+\frac{10}{3}a^{2}-278a-102\right){x}+883a^{3}+93a^{2}-6961a-2401$ |
| 57.1-d1 |
57.1-d |
$2$ |
$2$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
57.1 |
\( 3 \cdot 19 \) |
\( - 3^{34} \cdot 19^{2} \) |
$20.85382$ |
$(-1/3a^3-1/3a^2+3a+2), (1/3a^3-2/3a^2-2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.949888097$ |
$90.41503854$ |
5.008960080 |
\( \frac{4957694999417395}{46619598843} a^{3} + \frac{9593307021539665}{46619598843} a^{2} - \frac{11878525618289761}{46619598843} a - \frac{5175805466469244}{46619598843} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( 305 a^{3} + 31 a^{2} - 2403 a - 828\) , \( -3302 a^{3} - 350 a^{2} + 26036 a + 8964\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){x}^{2}+\left(305a^{3}+31a^{2}-2403a-828\right){x}-3302a^{3}-350a^{2}+26036a+8964$ |
| 57.1-d2 |
57.1-d |
$2$ |
$2$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
57.1 |
\( 3 \cdot 19 \) |
\( 3^{17} \cdot 19 \) |
$20.85382$ |
$(-1/3a^3-1/3a^2+3a+2), (1/3a^3-2/3a^2-2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$3.899776194$ |
$180.8300770$ |
5.008960080 |
\( -\frac{217217028070}{373977} a^{3} + \frac{1324842416596}{373977} a^{2} - \frac{2515509051217}{373977} a + \frac{161738260330}{41553} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{190}{3} a^{3} - \frac{22}{3} a^{2} + 502 a + 172\) , \( -\frac{1208}{3} a^{3} - \frac{134}{3} a^{2} + 3179 a + 1095\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){x}^{2}+\left(-\frac{190}{3}a^{3}-\frac{22}{3}a^{2}+502a+172\right){x}-\frac{1208}{3}a^{3}-\frac{134}{3}a^{2}+3179a+1095$ |
| 57.1-e1 |
57.1-e |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
57.1 |
\( 3 \cdot 19 \) |
\( - 3^{6} \cdot 19 \) |
$20.85382$ |
$(-1/3a^3-1/3a^2+3a+2), (1/3a^3-2/3a^2-2a+5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.199016654$ |
$115.2853003$ |
5.214954858 |
\( \frac{732466}{171} a^{3} + \frac{3616163}{513} a^{2} - \frac{6735095}{513} a - \frac{2042806}{513} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( a^{2} - 2 a - 5\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 6\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - 4 a - 5\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+6\right){x}+\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-4a-5$ |
| 57.1-f1 |
57.1-f |
$1$ |
$1$ |
4.4.19821.1 |
$4$ |
$[4, 0]$ |
57.1 |
\( 3 \cdot 19 \) |
\( - 3^{2} \cdot 19 \) |
$20.85382$ |
$(-1/3a^3-1/3a^2+3a+2), (1/3a^3-2/3a^2-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.241538489$ |
$306.1728257$ |
4.202233631 |
\( \frac{14227698499096}{57} a^{3} + \frac{9089735445467}{19} a^{2} - \frac{34285899745478}{57} a - \frac{14634193939504}{57} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 3\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a + 3\) , \( a^{2} - a - 3\) , \( 2 a^{3} - 5 a^{2} - 13 a + 16\) , \( \frac{4}{3} a^{3} - \frac{14}{3} a^{2} - 12 a + 22\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{1}{3}a^{2}-6a+3\right){x}^{2}+\left(2a^{3}-5a^{2}-13a+16\right){x}+\frac{4}{3}a^{3}-\frac{14}{3}a^{2}-12a+22$ |
*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.
