| 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 |
| 5.1-a1 |
5.1-a |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$11.63839$ |
$(-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1884.762848$ |
2.211992329 |
\( -\frac{499584}{25} a^{3} + \frac{96576}{5} a^{2} + \frac{2535296}{25} a + \frac{1268736}{25} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 3\) , \( 3 a^{3} - 3 a^{2} - 14 a - 4\) , \( -2 a^{3} + a^{2} + 10 a + 6\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(3a^{3}-3a^{2}-14a-4\right){x}-2a^{3}+a^{2}+10a+6$ |
| 5.1-a2 |
5.1-a |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$11.63839$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$942.3814240$ |
2.211992329 |
\( -\frac{18722242456}{5} a^{3} + 2665381856 a^{2} + \frac{92085411824}{5} a + \frac{43696705344}{5} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 4 a + 2\) , \( 1\) , \( -3 a^{3} + 7 a^{2} + 6 a - 7\) , \( -6 a^{3} + 19 a^{2} - 18\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+4a+2\right){x}^{2}+\left(-3a^{3}+7a^{2}+6a-7\right){x}-6a^{3}+19a^{2}-18$ |
| 5.1-a3 |
5.1-a |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$11.63839$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$942.3814240$ |
2.211992329 |
\( -\frac{45803904}{5} a^{3} + 32214080 a^{2} - \frac{61059584}{5} a - \frac{90599424}{5} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( 2 a^{3} - 4 a^{2} - 6 a + 5\) , \( a^{3} - 3 a^{2} - 2 a + 5\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(2a^{3}-4a^{2}-6a+5\right){x}+a^{3}-3a^{2}-2a+5$ |
| 5.1-a4 |
5.1-a |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{4} \) |
$11.63839$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$471.1907120$ |
2.211992329 |
\( \frac{77227804856}{625} a^{3} + \frac{12072038496}{125} a^{2} - \frac{140998166064}{625} a - \frac{83278003824}{625} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( -a^{2} + a + 3\) , \( a^{2} - 2\) , \( 3 a^{3} - 12 a^{2} + 2 a + 13\) , \( 4 a^{3} - 16 a^{2} + 7 a + 10\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(3a^{3}-12a^{2}+2a+13\right){x}+4a^{3}-16a^{2}+7a+10$ |
| 5.1-b1 |
5.1-b |
$1$ |
$1$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$11.63839$ |
$(-a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.051442652$ |
$473.2435769$ |
1.828584200 |
\( \frac{22668803}{25} a^{3} - \frac{15865097}{5} a^{2} + \frac{29347718}{25} a + \frac{44282013}{25} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 3\) , \( a^{2} - 3\) , \( 20 a^{3} - 51 a^{2} - 52 a + 107\) , \( -21 a^{3} + 53 a^{2} + 54 a - 113\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(20a^{3}-51a^{2}-52a+107\right){x}-21a^{3}+53a^{2}+54a-113$ |
| 5.1-c1 |
5.1-c |
$1$ |
$1$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$11.63839$ |
$(-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$82.46253814$ |
1.548472813 |
\( \frac{22668803}{25} a^{3} - \frac{15865097}{5} a^{2} + \frac{29347718}{25} a + \frac{44282013}{25} \) |
\( \bigl[1\) , \( -a^{3} + 3 a^{2} + 2 a - 4\) , \( a^{3} - a^{2} - 3 a - 1\) , \( 58 a^{3} - 148 a^{2} - 151 a + 319\) , \( -140 a^{3} + 358 a^{2} + 361 a - 764\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-4\right){x}^{2}+\left(58a^{3}-148a^{2}-151a+319\right){x}-140a^{3}+358a^{2}+361a-764$ |
| 5.1-d1 |
5.1-d |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$11.63839$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.229350336$ |
$553.1037775$ |
1.191030538 |
\( -\frac{45803904}{5} a^{3} + 32214080 a^{2} - \frac{61059584}{5} a - \frac{90599424}{5} \) |
\( \bigl[a^{2} - 3\) , \( a\) , \( a^{2} - 2\) , \( 3 a^{3} - a^{2} - 14 a - 8\) , \( 3 a^{3} - a^{2} - 13 a - 7\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+a{x}^{2}+\left(3a^{3}-a^{2}-14a-8\right){x}+3a^{3}-a^{2}-13a-7$ |
| 5.1-d2 |
5.1-d |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$11.63839$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.229350336$ |
$553.1037775$ |
1.191030538 |
\( -\frac{18722242456}{5} a^{3} + 2665381856 a^{2} + \frac{92085411824}{5} a + \frac{43696705344}{5} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{2} + 2 a + 3\) , \( a\) , \( -8 a^{3} + 13 a^{2} + 29 a - 11\) , \( -14 a^{3} + 29 a^{2} + 45 a - 50\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-8a^{3}+13a^{2}+29a-11\right){x}-14a^{3}+29a^{2}+45a-50$ |
| 5.1-d3 |
5.1-d |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{4} \) |
$11.63839$ |
$(-a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.057337584$ |
$2212.415110$ |
1.191030538 |
\( \frac{77227804856}{625} a^{3} + \frac{12072038496}{125} a^{2} - \frac{140998166064}{625} a - \frac{83278003824}{625} \) |
\( \bigl[a + 1\) , \( a^{3} - a^{2} - 3 a - 1\) , \( a\) , \( -a^{3} + 4 a^{2} + 4 a - 8\) , \( 2 a^{3} - 3 a^{2} - 6 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-3a-1\right){x}^{2}+\left(-a^{3}+4a^{2}+4a-8\right){x}+2a^{3}-3a^{2}-6a+7$ |
| 5.1-d4 |
5.1-d |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$11.63839$ |
$(-a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.114675168$ |
$2212.415110$ |
1.191030538 |
\( -\frac{499584}{25} a^{3} + \frac{96576}{5} a^{2} + \frac{2535296}{25} a + \frac{1268736}{25} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( -a - 1\) , \( a^{3} - a^{2} - 3 a\) , \( -a^{3} - 2 a^{2} - a - 1\) , \( 8 a^{3} + 6 a^{2} - 15 a - 9\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a^{3}-2a^{2}-a-1\right){x}+8a^{3}+6a^{2}-15a-9$ |
| 10.1-a1 |
10.1-a |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$12.69175$ |
$(a+1), (-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$1$ |
$47.40033653$ |
4.005353260 |
\( \frac{683585348240203}{250} a^{3} - \frac{481527817585077}{50} a^{2} + \frac{463311980608309}{125} a + \frac{669386004616744}{125} \) |
\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( a^{2} - a - 2\) , \( -122 a^{3} + 303 a^{2} + 342 a - 670\) , \( -1546 a^{3} + 3967 a^{2} + 3907 a - 8291\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+4\right){x}^{2}+\left(-122a^{3}+303a^{2}+342a-670\right){x}-1546a^{3}+3967a^{2}+3907a-8291$ |
| 10.1-a2 |
10.1-a |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$12.69175$ |
$(a+1), (-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$426.6030288$ |
4.005353260 |
\( -\frac{88747}{10} a^{3} - \frac{35635}{2} a^{2} + \frac{218803}{10} a + \frac{122123}{10} \) |
\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( a^{2} - a - 2\) , \( -2 a^{3} + 3 a^{2} + 7 a\) , \( -5 a^{3} + 10 a^{2} + 16 a - 17\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+4\right){x}^{2}+\left(-2a^{3}+3a^{2}+7a\right){x}-5a^{3}+10a^{2}+16a-17$ |
| 10.1-b1 |
10.1-b |
$1$ |
$1$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$12.69175$ |
$(a+1), (-a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.028976386$ |
$524.6348930$ |
2.283695856 |
\( -\frac{3670872}{25} a^{3} + \frac{8104397}{20} a^{2} + \frac{34193547}{100} a - \frac{92620073}{100} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( a^{2} - a - 3\) , \( -14 a^{3} + 37 a^{2} + 34 a - 79\) , \( 35 a^{3} - 90 a^{2} - 91 a + 190\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+4\right){x}^{2}+\left(-14a^{3}+37a^{2}+34a-79\right){x}+35a^{3}-90a^{2}-91a+190$ |
| 10.1-c1 |
10.1-c |
$1$ |
$1$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$12.69175$ |
$(a+1), (-a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \) |
$0.002354468$ |
$2030.141572$ |
2.872209124 |
\( -\frac{3670872}{25} a^{3} + \frac{8104397}{20} a^{2} + \frac{34193547}{100} a - \frac{92620073}{100} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( -6 a^{3} + 14 a^{2} + 19 a - 28\) , \( 15 a^{3} - 39 a^{2} - 37 a + 84\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(-6a^{3}+14a^{2}+19a-28\right){x}+15a^{3}-39a^{2}-37a+84$ |
| 10.1-d1 |
10.1-d |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$12.69175$ |
$(a+1), (-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$6.328646313$ |
0.534773927 |
\( \frac{683585348240203}{250} a^{3} - \frac{481527817585077}{50} a^{2} + \frac{463311980608309}{125} a + \frac{669386004616744}{125} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{2} - a - 3\) , \( -362 a^{3} + 931 a^{2} + 941 a - 1982\) , \( -7022 a^{3} + 17939 a^{2} + 18191 a - 38168\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+3\right){x}^{2}+\left(-362a^{3}+931a^{2}+941a-1982\right){x}-7022a^{3}+17939a^{2}+18191a-38168$ |
| 10.1-d2 |
10.1-d |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$12.69175$ |
$(a+1), (-a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$512.6203514$ |
0.534773927 |
\( -\frac{88747}{10} a^{3} - \frac{35635}{2} a^{2} + \frac{218803}{10} a + \frac{122123}{10} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{2} - a - 3\) , \( -2 a^{3} + 11 a^{2} + 6 a - 22\) , \( -13 a^{3} + 41 a^{2} + 35 a - 87\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+3\right){x}^{2}+\left(-2a^{3}+11a^{2}+6a-22\right){x}-13a^{3}+41a^{2}+35a-87$ |
| 15.1-a1 |
15.1-a |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5 \) |
$13.35159$ |
$(-a), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.170761763$ |
$652.8659256$ |
2.093444827 |
\( -\frac{1310848}{405} a^{3} + \frac{245824}{81} a^{2} + \frac{6564352}{405} a + \frac{3034112}{405} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - a^{2} - 3 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 2 a^{3} - a^{2} - 4 a + 5\) , \( a^{3} + 2 a^{2} - 2 a - 5\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a-1\right){x}^{2}+\left(2a^{3}-a^{2}-4a+5\right){x}+a^{3}+2a^{2}-2a-5$ |
| 15.1-a2 |
15.1-a |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$13.35159$ |
$(-a), (-a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.085380881$ |
$2611.463702$ |
2.093444827 |
\( \frac{973696}{225} a^{3} - \frac{451264}{45} a^{2} - \frac{2410624}{225} a + \frac{5487616}{225} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 2\) , \( a^{3} - a^{2} - 4 a - 1\) , \( 3 a^{3} - 3 a^{2} - 14 a - 4\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(3a^{3}-3a^{2}-14a-4\right){x}$ |
| 15.1-a3 |
15.1-a |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3 \cdot 5^{4} \) |
$13.35159$ |
$(-a), (-a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.170761763$ |
$1305.731851$ |
2.093444827 |
\( \frac{210481353608}{1875} a^{3} - \frac{107445585872}{375} a^{2} - \frac{545179981952}{1875} a + \frac{1143099186368}{1875} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( a\) , \( 7 a^{3} + 8 a^{2} - 3 a + 1\) , \( 172 a^{3} + 147 a^{2} - 289 a - 177\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(7a^{3}+8a^{2}-3a+1\right){x}+172a^{3}+147a^{2}-289a-177$ |
| 15.1-a4 |
15.1-a |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3 \cdot 5 \) |
$13.35159$ |
$(-a), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.170761763$ |
$1305.731851$ |
2.093444827 |
\( \frac{47186264}{15} a^{3} + \frac{13516624}{3} a^{2} - \frac{62546816}{15} a - \frac{47172496}{15} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - a^{2} - 4 a - 1\) , \( -142 a^{3} + 361 a^{2} + 371 a - 765\) , \( -1237 a^{3} + 3161 a^{2} + 3200 a - 6733\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{3}-a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a-1\right){x}^{2}+\left(-142a^{3}+361a^{2}+371a-765\right){x}-1237a^{3}+3161a^{2}+3200a-6733$ |
| 15.1-b1 |
15.1-b |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3 \cdot 5 \) |
$13.35159$ |
$(-a), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.255402891$ |
$1053.582186$ |
2.526452392 |
\( \frac{47186264}{15} a^{3} + \frac{13516624}{3} a^{2} - \frac{62546816}{15} a - \frac{47172496}{15} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( -50 a^{3} + 124 a^{2} + 139 a - 263\) , \( -244 a^{3} + 622 a^{2} + 629 a - 1306\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-50a^{3}+124a^{2}+139a-263\right){x}-244a^{3}+622a^{2}+629a-1306$ |
| 15.1-b2 |
15.1-b |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$13.35159$ |
$(-a), (-a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.127701445$ |
$2107.164372$ |
2.526452392 |
\( \frac{973696}{225} a^{3} - \frac{451264}{45} a^{2} - \frac{2410624}{225} a + \frac{5487616}{225} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( -a^{3} + 4 a^{2} + a - 11\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-a^{3}+4a^{2}+a-11\right){x}$ |
| 15.1-b3 |
15.1-b |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5 \) |
$13.35159$ |
$(-a), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.063850722$ |
$1053.582186$ |
2.526452392 |
\( -\frac{1310848}{405} a^{3} + \frac{245824}{81} a^{2} + \frac{6564352}{405} a + \frac{3034112}{405} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - 3 a^{2} - a + 6\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( -2 a^{3} - 10 a^{2} + 3 a + 20\) , \( 14 a^{3} + 2 a^{2} - 26 a + 2\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+6\right){x}^{2}+\left(-2a^{3}-10a^{2}+3a+20\right){x}+14a^{3}+2a^{2}-26a+2$ |
| 15.1-b4 |
15.1-b |
$4$ |
$4$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3 \cdot 5^{4} \) |
$13.35159$ |
$(-a), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.255402891$ |
$526.7910930$ |
2.526452392 |
\( \frac{210481353608}{1875} a^{3} - \frac{107445585872}{375} a^{2} - \frac{545179981952}{1875} a + \frac{1143099186368}{1875} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( a + 1\) , \( 1\) , \( -17 a^{3} + 13 a^{2} + 87 a + 43\) , \( -94 a^{3} + 67 a^{2} + 464 a + 221\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-17a^{3}+13a^{2}+87a+43\right){x}-94a^{3}+67a^{2}+464a+221$ |
| 16.1-a1 |
16.1-a |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{26} \) |
$13.45974$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$58.44780549$ |
1.097526705 |
\( -\frac{301955957}{16} a^{3} - \frac{118817153}{8} a^{2} + \frac{552469241}{16} a + \frac{81700927}{4} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( 0\) , \( -2 a^{3} + 9 a + 5\) , \( -10 a^{3} + 34 a + 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-2a^{3}+9a+5\right){x}-10a^{3}+34a+17$ |
| 16.1-a2 |
16.1-a |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{54} \) |
$13.45974$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$58.44780549$ |
1.097526705 |
\( \frac{77526197}{1024} a^{3} - \frac{110292741}{2048} a^{2} - \frac{381531341}{1024} a - \frac{361724209}{2048} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( -a^{2} + 2 a + 2\) , \( a + 1\) , \( 30 a^{3} - 23 a^{2} - 147 a - 63\) , \( -134 a^{3} + 76 a^{2} + 683 a + 393\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(30a^{3}-23a^{2}-147a-63\right){x}-134a^{3}+76a^{2}+683a+393$ |
| 16.1-b1 |
16.1-b |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{26} \) |
$13.45974$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$92.54555219$ |
1.737810583 |
\( -\frac{301955957}{16} a^{3} - \frac{118817153}{8} a^{2} + \frac{552469241}{16} a + \frac{81700927}{4} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 5 a\) , \( a^{3} - a^{2} - 3 a - 1\) , \( -43 a^{3} - 32 a^{2} + 80 a + 49\) , \( 455 a^{3} + 353 a^{2} - 835 a - 492\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(-43a^{3}-32a^{2}+80a+49\right){x}+455a^{3}+353a^{2}-835a-492$ |
| 16.1-b2 |
16.1-b |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{54} \) |
$13.45974$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$92.54555219$ |
1.737810583 |
\( \frac{77526197}{1024} a^{3} - \frac{110292741}{2048} a^{2} - \frac{381531341}{1024} a - \frac{361724209}{2048} \) |
\( \bigl[a + 1\) , \( -a\) , \( a^{2} - 3\) , \( 4 a^{3} - 7 a^{2} - 19 a + 2\) , \( 41 a^{3} - 113 a^{2} - 89 a + 268\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}-a{x}^{2}+\left(4a^{3}-7a^{2}-19a+2\right){x}+41a^{3}-113a^{2}-89a+268$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$13.45974$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.030759902$ |
$936.4544486$ |
2.163607576 |
\( -373 a^{3} - 642 a^{2} + 505 a + 412 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( 3 a^{3} - 12 a^{2} + 5 a + 11\) , \( 18 a^{3} - 65 a^{2} + 28 a + 35\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-2a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(3a^{3}-12a^{2}+5a+11\right){x}+18a^{3}-65a^{2}+28a+35$ |
| 16.1-d1 |
16.1-d |
$1$ |
$1$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$13.45974$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.060100272$ |
$699.9886807$ |
3.159907252 |
\( -373 a^{3} - 642 a^{2} + 505 a + 412 \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{2} - 3\) , \( -5 a^{3} + a^{2} + 25 a + 15\) , \( -8 a^{3} + 6 a^{2} + 34 a + 14\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-5a^{3}+a^{2}+25a+15\right){x}-8a^{3}+6a^{2}+34a+14$ |
| 18.1-a1 |
18.1-a |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{21} \) |
$13.65937$ |
$(a+1), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$15.92870694$ |
2.691968157 |
\( \frac{6166001994271}{28697814} a^{3} - \frac{4719181328729}{28697814} a^{2} - \frac{29584068994525}{28697814} a - \frac{13855850554757}{28697814} \) |
\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( a^{2} - 3\) , \( 25 a^{3} - 19 a^{2} - 120 a - 51\) , \( 311 a^{3} - 219 a^{2} - 1532 a - 735\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a-1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-1\right){x}^{2}+\left(25a^{3}-19a^{2}-120a-51\right){x}+311a^{3}-219a^{2}-1532a-735$ |
| 18.1-a2 |
18.1-a |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{3} \cdot 3^{11} \) |
$13.65937$ |
$(a+1), (-a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$430.0750875$ |
2.691968157 |
\( -\frac{209998}{243} a^{3} - \frac{3244}{243} a^{2} + \frac{621815}{486} a + \frac{139135}{486} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - 3 a^{2} - 3 a + 6\) , \( a^{3} - a^{2} - 3 a\) , \( 4 a^{3} - 15 a^{2} - 10 a + 33\) , \( 16 a^{3} - 18 a^{2} - 50 a + 21\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+6\right){x}^{2}+\left(4a^{3}-15a^{2}-10a+33\right){x}+16a^{3}-18a^{2}-50a+21$ |
| 18.1-b1 |
18.1-b |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{9} \) |
$13.65937$ |
$(a+1), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$184.9660639$ |
3.473273171 |
\( -\frac{97309}{54} a^{3} - \frac{90301}{54} a^{2} + \frac{60991}{54} a + \frac{41897}{54} \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 5 a\) , \( 1\) , \( -5 a^{3} + 14 a^{2} - 3\) , \( -6 a^{3} + 23 a^{2} - 13 a - 15\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(-5a^{3}+14a^{2}-3\right){x}-6a^{3}+23a^{2}-13a-15$ |
| 18.1-b2 |
18.1-b |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{3} \cdot 3^{15} \) |
$13.65937$ |
$(a+1), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$61.65535465$ |
3.473273171 |
\( -\frac{341092326653}{19683} a^{3} + \frac{1741103936819}{39366} a^{2} + \frac{1767320705443}{39366} a - \frac{1852554179036}{19683} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 4 a + 2\) , \( a^{2} - 3\) , \( 3 a^{3} - 24 a^{2} + 46 a - 9\) , \( -74 a^{3} + 235 a^{2} - 8 a - 209\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+2\right){x}^{2}+\left(3a^{3}-24a^{2}+46a-9\right){x}-74a^{3}+235a^{2}-8a-209$ |
| 18.1-c1 |
18.1-c |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{42} \cdot 3^{6} \) |
$13.65937$ |
$(a+1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1.557938591$ |
$20.24381648$ |
2.368915694 |
\( \frac{77526197}{1024} a^{3} - \frac{110292741}{2048} a^{2} - \frac{381531341}{1024} a - \frac{361724209}{2048} \) |
\( \bigl[1\) , \( -a^{3} + 3 a^{2} + 2 a - 4\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 4 a^{3} - 4 a^{2} - 25 a - 9\) , \( 21 a^{3} - 3 a^{2} - 89 a - 51\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-4\right){x}^{2}+\left(4a^{3}-4a^{2}-25a-9\right){x}+21a^{3}-3a^{2}-89a-51$ |
| 18.1-c2 |
18.1-c |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{6} \) |
$13.65937$ |
$(a+1), (-a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.519312863$ |
$546.5830451$ |
2.368915694 |
\( -\frac{301955957}{16} a^{3} - \frac{118817153}{8} a^{2} + \frac{552469241}{16} a + \frac{81700927}{4} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - 3 a^{2} - 3 a + 6\) , \( a^{2} - a - 2\) , \( 4 a^{3} - 14 a^{2} - 7 a + 36\) , \( 21 a^{3} - 39 a^{2} - 68 a + 59\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+6\right){x}^{2}+\left(4a^{3}-14a^{2}-7a+36\right){x}+21a^{3}-39a^{2}-68a+59$ |
| 18.1-d1 |
18.1-d |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{42} \cdot 3^{6} \) |
$13.65937$ |
$(a+1), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$1$ |
$7.249032697$ |
2.858552943 |
\( \frac{77526197}{1024} a^{3} - \frac{110292741}{2048} a^{2} - \frac{381531341}{1024} a - \frac{361724209}{2048} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 3\) , \( a\) , \( 44 a^{3} - 28 a^{2} - 224 a - 108\) , \( 317 a^{3} - 232 a^{2} - 1546 a - 730\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(44a^{3}-28a^{2}-224a-108\right){x}+317a^{3}-232a^{2}-1546a-730$ |
| 18.1-d2 |
18.1-d |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{6} \) |
$13.65937$ |
$(a+1), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$21.74709809$ |
2.858552943 |
\( -\frac{301955957}{16} a^{3} - \frac{118817153}{8} a^{2} + \frac{552469241}{16} a + \frac{81700927}{4} \) |
\( \bigl[a\) , \( a^{3} - 3 a^{2} - 2 a + 6\) , \( a^{3} - a^{2} - 4 a\) , \( -14 a^{3} + 6 a^{2} + 73 a + 48\) , \( 157 a^{3} - 117 a^{2} - 766 a - 345\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+6\right){x}^{2}+\left(-14a^{3}+6a^{2}+73a+48\right){x}+157a^{3}-117a^{2}-766a-345$ |
| 18.1-e1 |
18.1-e |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{3} \cdot 3^{15} \) |
$13.65937$ |
$(a+1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.551450570$ |
$21.32826304$ |
1.766847036 |
\( -\frac{341092326653}{19683} a^{3} + \frac{1741103936819}{39366} a^{2} + \frac{1767320705443}{39366} a - \frac{1852554179036}{19683} \) |
\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( -19 a^{3} + 50 a^{2} + 52 a - 116\) , \( -96 a^{3} + 245 a^{2} + 254 a - 530\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a-1\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a-1\right){x}^{2}+\left(-19a^{3}+50a^{2}+52a-116\right){x}-96a^{3}+245a^{2}+254a-530$ |
| 18.1-e2 |
18.1-e |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{9} \) |
$13.65937$ |
$(a+1), (-a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.183816856$ |
$575.8631021$ |
1.766847036 |
\( -\frac{97309}{54} a^{3} - \frac{90301}{54} a^{2} + \frac{60991}{54} a + \frac{41897}{54} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( -a^{2} + 2 a + 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( -4 a^{3} - a^{2} + 8 a + 6\) , \( 9 a^{3} + 5 a^{2} - 14 a - 6\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-4a^{3}-a^{2}+8a+6\right){x}+9a^{3}+5a^{2}-14a-6$ |
| 18.1-f1 |
18.1-f |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{21} \) |
$13.65937$ |
$(a+1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.298613192$ |
$53.33502333$ |
2.392535301 |
\( \frac{6166001994271}{28697814} a^{3} - \frac{4719181328729}{28697814} a^{2} - \frac{29584068994525}{28697814} a - \frac{13855850554757}{28697814} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - a - 4\) , \( a^{2} - 2\) , \( 9 a^{3} - 2 a^{2} - 27 a - 5\) , \( 11 a^{3} + 18 a^{2} - 27 a - 44\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(9a^{3}-2a^{2}-27a-5\right){x}+11a^{3}+18a^{2}-27a-44$ |
| 18.1-f2 |
18.1-f |
$2$ |
$3$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{3} \cdot 3^{11} \) |
$13.65937$ |
$(a+1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.099537730$ |
$160.0050700$ |
2.392535301 |
\( -\frac{209998}{243} a^{3} - \frac{3244}{243} a^{2} + \frac{621815}{486} a + \frac{139135}{486} \) |
\( \bigl[a\) , \( a^{3} - 3 a^{2} - 2 a + 6\) , \( a\) , \( -6 a^{3} + 34 a + 30\) , \( 118 a^{3} - 87 a^{2} - 577 a - 264\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{3}-3a^{2}-2a+6\right){x}^{2}+\left(-6a^{3}+34a+30\right){x}+118a^{3}-87a^{2}-577a-264$ |
| 24.1-a1 |
24.1-a |
$1$ |
$1$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{11} \cdot 3^{3} \) |
$14.15950$ |
$(a+1), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$63.08627965$ |
0.592313740 |
\( \frac{8394314}{27} a^{3} - \frac{29458249}{27} a^{2} + \frac{10901575}{27} a + \frac{16420580}{27} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{3} - a^{2} - 3 a - 1\) , \( -6 a^{3} - 2 a^{2} + 17 a + 9\) , \( 13 a^{3} + 7 a^{2} - 29 a - 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-6a^{3}-2a^{2}+17a+9\right){x}+13a^{3}+7a^{2}-29a-16$ |
| 24.1-b1 |
24.1-b |
$6$ |
$8$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$14.15950$ |
$(a+1), (-a)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.699470420$ |
$984.2610195$ |
3.231964151 |
\( -\frac{1202176}{81} a^{3} + \frac{739328}{81} a^{2} + \frac{6055936}{81} a + \frac{3307520}{81} \) |
\( \bigl[0\) , \( a^{3} - a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 4 a\) , \( -7 a^{3} + 17 a^{2} + 18 a - 27\) , \( 11 a^{3} - 25 a^{2} - 34 a + 51\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a-2\right){x}^{2}+\left(-7a^{3}+17a^{2}+18a-27\right){x}+11a^{3}-25a^{2}-34a+51$ |
| 24.1-b2 |
24.1-b |
$6$ |
$8$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$14.15950$ |
$(a+1), (-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.349735210$ |
$492.1305097$ |
3.231964151 |
\( \frac{49228768}{6561} a^{3} + \frac{8568832}{6561} a^{2} - \frac{112199488}{6561} a + \frac{37420432}{6561} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{3} - a^{2} - 3 a - 1\) , \( -28 a^{3} - 29 a^{2} + 48 a + 40\) , \( -336 a^{3} - 267 a^{2} + 611 a + 368\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+3\right){x}^{2}+\left(-28a^{3}-29a^{2}+48a+40\right){x}-336a^{3}-267a^{2}+611a+368$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{16} \) |
$14.15950$ |
$(a+1), (-a)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.699470420$ |
$246.0652548$ |
3.231964151 |
\( -\frac{219644035334144}{43046721} a^{3} + \frac{772387053104452}{43046721} a^{2} - \frac{292781441858056}{43046721} a - \frac{434456536743848}{43046721} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( -a^{3} + 3 a^{2} + 2 a - 5\) , \( 0\) , \( -15 a^{3} + 4 a^{2} + 58 a + 30\) , \( 4 a^{3} - 8 a^{2} - 32 a - 15\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-5\right){x}^{2}+\left(-15a^{3}+4a^{2}+58a+30\right){x}+4a^{3}-8a^{2}-32a-15$ |
| 24.1-b4 |
24.1-b |
$6$ |
$8$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$14.15950$ |
$(a+1), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1.398940841$ |
$3.844769607$ |
3.231964151 |
\( \frac{50925108998745224}{9} a^{3} - \frac{129982882586044090}{9} a^{2} - \frac{131895840843594974}{9} a + \frac{276566614510501910}{9} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{2} - 2 a - 2\) , \( a^{2} - a - 2\) , \( -105 a^{3} + 266 a^{2} + 244 a - 530\) , \( -926 a^{3} + 2297 a^{2} + 2537 a - 5098\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-105a^{3}+266a^{2}+244a-530\right){x}-926a^{3}+2297a^{2}+2537a-5098$ |
| 24.1-b5 |
24.1-b |
$6$ |
$8$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$14.15950$ |
$(a+1), (-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$0.699470420$ |
$61.51631371$ |
3.231964151 |
\( \frac{65431535104}{81} a^{3} + \frac{42803086972}{81} a^{2} - \frac{121350390136}{81} a - \frac{54249295880}{81} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{2} - 2 a - 2\) , \( a^{2} - a - 2\) , \( -5 a^{3} + a^{2} + 24 a - 20\) , \( -13 a^{3} - 11 a^{2} + 82 a - 61\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-5a^{3}+a^{2}+24a-20\right){x}-13a^{3}-11a^{2}+82a-61$ |
| 24.1-b6 |
24.1-b |
$6$ |
$8$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$14.15950$ |
$(a+1), (-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1.398940841$ |
$3.844769607$ |
3.231964151 |
\( \frac{116344852775823881080}{9} a^{3} + \frac{90941355856610478778}{9} a^{2} - \frac{212412074607426159394}{9} a - \frac{125477369587562062790}{9} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{2} - 2 a - 2\) , \( a^{2} - a - 2\) , \( 15 a^{3} - 224 a^{2} + 164 a + 130\) , \( 210 a^{3} - 2755 a^{2} + 1821 a + 1772\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(15a^{3}-224a^{2}+164a+130\right){x}+210a^{3}-2755a^{2}+1821a+1772$ |
| 24.1-c1 |
24.1-c |
$6$ |
$8$ |
4.4.11344.1 |
$4$ |
$[4, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$14.15950$ |
$(a+1), (-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.505187793$ |
$647.1292014$ |
3.069451230 |
\( \frac{49228768}{6561} a^{3} + \frac{8568832}{6561} a^{2} - \frac{112199488}{6561} a + \frac{37420432}{6561} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + a^{2} + 5 a + 2\) , \( a^{2} - 3\) , \( -3 a^{3} + 17 a + 6\) , \( -2 a^{3} - a^{2} + 14 a + 6\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+2\right){x}^{2}+\left(-3a^{3}+17a+6\right){x}-2a^{3}-a^{2}+14a+6$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
