| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 8.1-a1 |
8.1-a |
$2$ |
$3$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$3.96617$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1.067137437$ |
$24.75261030$ |
2.52490185 |
\( -382637522 a^{2} + \frac{12556080913}{8} a - \frac{2626438959}{2} \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - a - 4\) , \( 1\) , \( 5 a^{2} - a - 23\) , \( -5 a^{2} + 13 a + 45\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(5a^{2}-a-23\right){x}-5a^{2}+13a+45$ |
| 8.1-a2 |
8.1-a |
$2$ |
$3$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$3.96617$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.355712479$ |
$74.25783091$ |
2.52490185 |
\( -116 a^{2} + \frac{217}{2} a - \frac{931}{2} \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - a - 4\) , \( 1\) , \( -a + 2\) , \( -a\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a+2\right){x}-a$ |
| 8.1-b1 |
8.1-b |
$2$ |
$3$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$3.96617$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$7.301928065$ |
$2.971412678$ |
2.07397569 |
\( -382637522 a^{2} + \frac{12556080913}{8} a - \frac{2626438959}{2} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 5\) , \( a^{2} - a - 3\) , \( -29 a^{2} + 96 a - 26\) , \( -241 a^{2} + 750 a - 121\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-29a^{2}+96a-26\right){x}-241a^{2}+750a-121$ |
| 8.1-b2 |
8.1-b |
$2$ |
$3$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$3.96617$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$2.433976021$ |
$80.22814231$ |
2.07397569 |
\( -116 a^{2} + \frac{217}{2} a - \frac{931}{2} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 5\) , \( a^{2} - a - 3\) , \( a^{2} + a - 6\) , \( 3 a - 3\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(a^{2}+a-6\right){x}+3a-3$ |
| 17.1-a1 |
17.1-a |
$1$ |
$1$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( -17 \) |
$4.49709$ |
$(-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.264486329$ |
$120.5044270$ |
3.04655745 |
\( -\frac{3251}{17} a^{2} - \frac{3027}{17} a + \frac{7966}{17} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 3\) , \( a^{2} - a - 4\) , \( 2 a^{2} + a - 3\) , \( 3 a^{2} + a - 11\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(2a^{2}+a-3\right){x}+3a^{2}+a-11$ |
| 17.1-b1 |
17.1-b |
$1$ |
$1$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( -17 \) |
$4.49709$ |
$(-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.480111533$ |
$65.47733081$ |
3.00494305 |
\( -\frac{3251}{17} a^{2} - \frac{3027}{17} a + \frac{7966}{17} \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - 5\) , \( a^{2} - 3\) , \( -3 a^{2} + 3 a + 18\) , \( -12 a^{2} + 9 a + 71\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-3a^{2}+3a+18\right){x}-12a^{2}+9a+71$ |
| 25.1-a1 |
25.1-a |
$2$ |
$5$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{10} \) |
$4.79564$ |
$(-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$3.153618518$ |
$11.74726681$ |
3.54118919 |
\( -167568023749 a^{2} + 518415680623 a - 80031960509 \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} - 3\) , \( -5 a^{2} + 7 a - 19\) , \( -24 a^{2} + 88 a + 12\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a^{2}+7a-19\right){x}-24a^{2}+88a+12$ |
| 25.1-a2 |
25.1-a |
$2$ |
$5$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{2} \) |
$4.79564$ |
$(-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$0.630723703$ |
$58.73633409$ |
3.54118919 |
\( 71 a^{2} + 138 a - 24 \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} - 3\) , \( -3 a + 1\) , \( -2 a - 2\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+1\right){x}-2a-2$ |
| 25.1-b1 |
25.1-b |
$2$ |
$5$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{10} \) |
$4.79564$ |
$(-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$32.22597397$ |
$0.964671525$ |
2.97158838 |
\( -167568023749 a^{2} + 518415680623 a - 80031960509 \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - 4\) , \( a\) , \( -629 a^{2} + 1950 a - 304\) , \( -21246 a^{2} + 65732 a - 10149\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-629a^{2}+1950a-304\right){x}-21246a^{2}+65732a-10149$ |
| 25.1-b2 |
25.1-b |
$2$ |
$5$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{2} \) |
$4.79564$ |
$(-a+1)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$6.445194795$ |
$120.5839407$ |
2.97158838 |
\( 71 a^{2} + 138 a - 24 \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - 4\) , \( a\) , \( a^{2} + 1\) , \( -3 a^{2} + 12 a - 2\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(a^{2}+1\right){x}-3a^{2}+12a-2$ |
| 25.2-a1 |
25.2-a |
$1$ |
$1$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$68.15613145$ |
2.17163492 |
\( -739 a^{2} + \frac{6546}{5} a + \frac{11054}{5} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 4\) , \( -2 a + 4\) , \( a - 5\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-2a+4\right){x}+a-5$ |
| 25.2-b1 |
25.2-b |
$2$ |
$2$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{12} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$29.69826383$ |
1.89253074 |
\( -\frac{75930376906}{390625} a^{2} + \frac{63604103882}{390625} a + \frac{466557130139}{390625} \) |
\( \bigl[a^{2} - 4\) , \( -a\) , \( a^{2} - 4\) , \( -6 a - 3\) , \( -2 a - 3\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}-a{x}^{2}+\left(-6a-3\right){x}-2a-3$ |
| 25.2-b2 |
25.2-b |
$2$ |
$2$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$59.39652766$ |
1.89253074 |
\( \frac{243996}{625} a^{2} - \frac{290112}{625} a - \frac{284099}{625} \) |
\( \bigl[a^{2} - 4\) , \( -a\) , \( a^{2} - 4\) , \( -a - 3\) , \( -2\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}-a{x}^{2}+\left(-a-3\right){x}-2$ |
| 25.2-c1 |
25.2-c |
$4$ |
$4$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$3.870740921$ |
1.97331297 |
\( -\frac{109614468464784967498147891}{390625} a^{2} + \frac{91751491154081623221623177}{390625} a + \frac{672638804149286091641636229}{390625} \) |
\( \bigl[a^{2} - 4\) , \( a - 1\) , \( a\) , \( 2399 a^{2} - 1994 a - 14767\) , \( 116077 a^{2} - 97201 a - 712180\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2399a^{2}-1994a-14767\right){x}+116077a^{2}-97201a-712180$ |
| 25.2-c2 |
25.2-c |
$4$ |
$4$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{8} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$30.96592736$ |
1.97331297 |
\( -\frac{2259033269876}{625} a^{2} + \frac{7232665410147}{625} a + \frac{25047731142294}{625} \) |
\( \bigl[a^{2} - 4\) , \( a - 1\) , \( a\) , \( 144 a^{2} - 109 a - 922\) , \( 1954 a^{2} - 1690 a - 11833\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(144a^{2}-109a-922\right){x}+1954a^{2}-1690a-11833$ |
| 25.2-c3 |
25.2-c |
$4$ |
$4$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{10} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$15.48296368$ |
1.97331297 |
\( \frac{82885694499454622732003}{625} a^{2} + \frac{160035831570977414368103}{625} a - \frac{5656179148705836713857}{125} \) |
\( \bigl[a^{2} - 4\) , \( a - 1\) , \( a\) , \( 129 a^{2} - 144 a - 917\) , \( 2019 a^{2} - 1583 a - 11826\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(129a^{2}-144a-917\right){x}+2019a^{2}-1583a-11826$ |
| 25.2-c4 |
25.2-c |
$4$ |
$4$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{4} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$61.93185473$ |
1.97331297 |
\( \frac{5504045470089}{25} a^{2} - \frac{17028214764428}{25} a + \frac{2628775847884}{25} \) |
\( \bigl[a^{2} - 4\) , \( a - 1\) , \( a\) , \( 4 a^{2} + 11 a - 57\) , \( 62 a^{2} - 104 a - 218\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a^{2}+11a-57\right){x}+62a^{2}-104a-218$ |
| 25.2-d1 |
25.2-d |
$4$ |
$4$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{4} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.389103895$ |
$61.86746012$ |
3.53216084 |
\( \frac{5504045470089}{25} a^{2} - \frac{17028214764428}{25} a + \frac{2628775847884}{25} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( 1\) , \( -123 a^{2} - 230 a + 46\) , \( -1755 a^{2} - 3394 a + 602\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-123a^{2}-230a+46\right){x}-1755a^{2}-3394a+602$ |
| 25.2-d2 |
25.2-d |
$4$ |
$4$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.597275973$ |
$15.46686503$ |
3.53216084 |
\( -\frac{109614468464784967498147891}{390625} a^{2} + \frac{91751491154081623221623177}{390625} a + \frac{672638804149286091641636229}{390625} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( 1\) , \( -1943 a^{2} - 3765 a + 621\) , \( -120207 a^{2} - 232070 a + 41078\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-1943a^{2}-3765a+621\right){x}-120207a^{2}-232070a+41078$ |
| 25.2-d3 |
25.2-d |
$4$ |
$4$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{8} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.194551947$ |
$30.93373006$ |
3.53216084 |
\( -\frac{2259033269876}{625} a^{2} + \frac{7232665410147}{625} a + \frac{25047731142294}{625} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( 1\) , \( -1948 a^{2} - 3755 a + 666\) , \( -120499 a^{2} - 232666 a + 41116\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-1948a^{2}-3755a+666\right){x}-120499a^{2}-232666a+41116$ |
| 25.2-d4 |
25.2-d |
$4$ |
$4$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{10} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.389103895$ |
$3.866716257$ |
3.53216084 |
\( \frac{82885694499454622732003}{625} a^{2} + \frac{160035831570977414368103}{625} a - \frac{5656179148705836713857}{125} \) |
\( \bigl[1\) , \( -a^{2} + 4\) , \( 1\) , \( -31153 a^{2} - 60145 a + 10631\) , \( -7847187 a^{2} - 15151370 a + 2677490\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-31153a^{2}-60145a+10631\right){x}-7847187a^{2}-15151370a+2677490$ |
| 25.2-e1 |
25.2-e |
$2$ |
$2$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.154626682$ |
$121.0891647$ |
1.78975202 |
\( \frac{243996}{625} a^{2} - \frac{290112}{625} a - \frac{284099}{625} \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - 3\) , \( a^{2} - a - 4\) , \( 7 a^{2} + 10 a - 10\) , \( 6 a^{2} + 10 a - 6\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(7a^{2}+10a-10\right){x}+6a^{2}+10a-6$ |
| 25.2-e2 |
25.2-e |
$2$ |
$2$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{12} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.309253364$ |
$60.54458238$ |
1.78975202 |
\( -\frac{75930376906}{390625} a^{2} + \frac{63604103882}{390625} a + \frac{466557130139}{390625} \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - 3\) , \( a^{2} - a - 4\) , \( -18 a^{2} - 40 a - 5\) , \( -87 a^{2} - 169 a + 27\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-18a^{2}-40a-5\right){x}-87a^{2}-169a+27$ |
| 25.2-f1 |
25.2-f |
$1$ |
$1$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$4.79564$ |
$(-a-1), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.263467959$ |
$125.2196987$ |
3.15357819 |
\( -739 a^{2} + \frac{6546}{5} a + \frac{11054}{5} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 3\) , \( 0\) , \( 3 a^{2} + 4 a - 1\) , \( 3 a^{2} + 6 a - 1\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(3a^{2}+4a-1\right){x}+3a^{2}+6a-1$ |
| 29.3-a1 |
29.3-a |
$1$ |
$1$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
29.3 |
\( 29 \) |
\( - 29^{2} \) |
$4.91575$ |
$(a^2-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.268717909$ |
$73.97485410$ |
3.80026485 |
\( -\frac{11724341}{841} a^{2} + \frac{38888910}{841} a - \frac{13239425}{841} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3\) , \( a\) , \( -21 a^{2} + 62 a - 6\) , \( -110 a^{2} + 339 a - 51\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-21a^{2}+62a-6\right){x}-110a^{2}+339a-51$ |
| 29.3-b1 |
29.3-b |
$2$ |
$5$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
29.3 |
\( 29 \) |
\( - 29^{10} \) |
$4.91575$ |
$(a^2-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$5.163179455$ |
1.64512577 |
\( -\frac{4594685316282180182968}{420707233300201} a^{2} - \frac{8832530700030897032255}{420707233300201} a + \frac{1561843221500277203602}{420707233300201} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -310 a^{2} + 948 a - 117\) , \( -6862 a^{2} + 21249 a - 3335\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-310a^{2}+948a-117\right){x}-6862a^{2}+21249a-3335$ |
| 29.3-b2 |
29.3-b |
$2$ |
$5$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
29.3 |
\( 29 \) |
\( - 29^{2} \) |
$4.91575$ |
$(a^2-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$25.81589727$ |
1.64512577 |
\( \frac{18499880885}{841} a^{2} - \frac{15485040525}{841} a - \frac{113522068011}{841} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 5 a^{2} - 12 a - 7\) , \( 11 a^{2} - 31 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(5a^{2}-12a-7\right){x}+11a^{2}-31a-3$ |
| 29.3-c1 |
29.3-c |
$2$ |
$5$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
29.3 |
\( 29 \) |
\( - 29^{2} \) |
$4.91575$ |
$(a^2-7)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$3.553272733$ |
$128.4043349$ |
3.48900310 |
\( \frac{18499880885}{841} a^{2} - \frac{15485040525}{841} a - \frac{113522068011}{841} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( a^{2} - a - 4\) , \( 4 a^{2} - 4 a - 26\) , \( -a^{2} + a + 5\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(4a^{2}-4a-26\right){x}-a^{2}+a+5$ |
| 29.3-c2 |
29.3-c |
$2$ |
$5$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
29.3 |
\( 29 \) |
\( - 29^{10} \) |
$4.91575$ |
$(a^2-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2 \) |
$17.76636366$ |
$1.027234679$ |
3.48900310 |
\( -\frac{4594685316282180182968}{420707233300201} a^{2} - \frac{8832530700030897032255}{420707233300201} a + \frac{1561843221500277203602}{420707233300201} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( a^{2} - a - 4\) , \( -31 a^{2} + 21 a + 149\) , \( -155 a^{2} + 111 a + 849\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-31a^{2}+21a+149\right){x}-155a^{2}+111a+849$ |
| 29.3-d1 |
29.3-d |
$1$ |
$1$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
29.3 |
\( 29 \) |
\( - 29^{2} \) |
$4.91575$ |
$(a^2-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$16.31395113$ |
1.03961141 |
\( -\frac{11724341}{841} a^{2} + \frac{38888910}{841} a - \frac{13239425}{841} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( -2 a^{2} + 4 a + 22\) , \( -3 a^{2} + 4 a + 20\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-2a^{2}+4a+22\right){x}-3a^{2}+4a+20$ |
| 35.2-a1 |
35.2-a |
$2$ |
$2$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
35.2 |
\( 5 \cdot 7 \) |
\( 5^{4} \cdot 7^{2} \) |
$5.07226$ |
$(-a-1), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$50.23277565$ |
1.60054932 |
\( \frac{35168221089}{30625} a^{2} + \frac{72390685242}{30625} a - \frac{1511809016}{30625} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( 4 a - 12\) , \( 16 a^{2} - 35 a - 35\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(4a-12\right){x}+16a^{2}-35a-35$ |
| 35.2-a2 |
35.2-a |
$2$ |
$2$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
35.2 |
\( 5 \cdot 7 \) |
\( - 5^{2} \cdot 7 \) |
$5.07226$ |
$(-a-1), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$100.4655513$ |
1.60054932 |
\( -\frac{48911}{175} a^{2} - \frac{173133}{175} a + \frac{333509}{175} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( -a + 3\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-a+3\right){x}$ |
| 35.2-b1 |
35.2-b |
$2$ |
$2$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
35.2 |
\( 5 \cdot 7 \) |
\( 5^{4} \cdot 7^{2} \) |
$5.07226$ |
$(-a-1), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.135747887$ |
$271.1021920$ |
3.51778465 |
\( \frac{35168221089}{30625} a^{2} + \frac{72390685242}{30625} a - \frac{1511809016}{30625} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 4\) , \( 0\) , \( 12 a^{2} - 13 a - 70\) , \( -44 a^{2} + 36 a + 274\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(12a^{2}-13a-70\right){x}-44a^{2}+36a+274$ |
| 35.2-b2 |
35.2-b |
$2$ |
$2$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
35.2 |
\( 5 \cdot 7 \) |
\( - 5^{2} \cdot 7 \) |
$5.07226$ |
$(-a-1), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.271495775$ |
$271.1021920$ |
3.51778465 |
\( -\frac{48911}{175} a^{2} - \frac{173133}{175} a + \frac{333509}{175} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 4\) , \( 0\) , \( 2 a^{2} - 3 a - 5\) , \( -a + 4\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(2a^{2}-3a-5\right){x}-a+4$ |
| 49.2-a1 |
49.2-a |
$1$ |
$1$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{10} \) |
$5.36483$ |
$(-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$4$ |
\( 1 \) |
$1$ |
$18.96052639$ |
2.41653042 |
\( 12124909 a^{2} + 23419146 a - 4119521 \) |
\( \bigl[a + 1\) , \( -a^{2} + 4\) , \( 0\) , \( -6 a^{2} - 11 a + 7\) , \( -19 a^{2} - 29 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-6a^{2}-11a+7\right){x}-19a^{2}-29a+7$ |
| 49.2-b1 |
49.2-b |
$1$ |
$1$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{4} \) |
$5.36483$ |
$(-a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.885035674$ |
$32.14211800$ |
2.71918282 |
\( 12124909 a^{2} + 23419146 a - 4119521 \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 4\) , \( 4 a^{2} - 14 a - 3\) , \( -17 a^{2} + 51 a - 12\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(4a^{2}-14a-3\right){x}-17a^{2}+51a-12$ |
| 49.2-c1 |
49.2-c |
$1$ |
$1$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{10} \) |
$5.36483$ |
$(-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$36.62722921$ |
1.16704056 |
\( 12124909 a^{2} + 23419146 a - 4119521 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 37 a^{2} - 116 a + 18\) , \( -1629 a^{2} + 5039 a - 778\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(37a^{2}-116a+18\right){x}-1629a^{2}+5039a-778$ |
| 49.2-d1 |
49.2-d |
$1$ |
$1$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{4} \) |
$5.36483$ |
$(-a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.058315779$ |
$151.2439479$ |
2.52923094 |
\( 12124909 a^{2} + 23419146 a - 4119521 \) |
\( \bigl[a\) , \( -a^{2} + 4\) , \( 1\) , \( -7 a^{2} - 12 a + 7\) , \( 28 a^{2} + 55 a - 8\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-7a^{2}-12a+7\right){x}+28a^{2}+55a-8$ |
| 55.2-a1 |
55.2-a |
$4$ |
$6$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{3} \cdot 11^{12} \) |
$5.46912$ |
$(-a-1), (a^2-2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$12.84771906$ |
$6.634499430$ |
4.07387160 |
\( -\frac{88126318563617923433586}{392303547090125} a^{2} + \frac{73765000782016153928717}{392303547090125} a + \frac{540779761956845037439809}{392303547090125} \) |
\( \bigl[a^{2} - a - 4\) , \( 0\) , \( a^{2} - a - 4\) , \( 309 a^{2} - 259 a - 1906\) , \( 5697 a^{2} - 4767 a - 34965\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(309a^{2}-259a-1906\right){x}+5697a^{2}-4767a-34965$ |
| 55.2-a2 |
55.2-a |
$4$ |
$6$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{6} \) |
$5.46912$ |
$(-a-1), (a^2-2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$6.423859532$ |
$6.634499430$ |
4.07387160 |
\( \frac{10579229278741269}{27680640625} a^{2} - \frac{32345497963762218}{27680640625} a + \frac{3973705130591689}{27680640625} \) |
\( \bigl[a^{2} - a - 4\) , \( 0\) , \( a^{2} - a - 4\) , \( 19 a^{2} - 14 a - 121\) , \( 110 a^{2} - 90 a - 681\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(19a^{2}-14a-121\right){x}+110a^{2}-90a-681$ |
| 55.2-a3 |
55.2-a |
$4$ |
$6$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11^{4} \) |
$5.46912$ |
$(-a-1), (a^2-2a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$4.282573021$ |
$179.1314846$ |
4.07387160 |
\( \frac{1747148534369}{73205} a^{2} + \frac{3195734287557}{73205} a - \frac{567030464936}{73205} \) |
\( \bigl[a^{2} - a - 4\) , \( 0\) , \( a^{2} - a - 4\) , \( 4 a^{2} - 4 a - 31\) , \( 11 a^{2} - 8 a - 66\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(4a^{2}-4a-31\right){x}+11a^{2}-8a-66$ |
| 55.2-a4 |
55.2-a |
$4$ |
$6$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$5.46912$ |
$(-a-1), (a^2-2a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$2.141286510$ |
$179.1314846$ |
4.07387160 |
\( -\frac{3616326}{3025} a^{2} - \frac{9298503}{3025} a + \frac{5981869}{3025} \) |
\( \bigl[a^{2} - a - 4\) , \( 0\) , \( a^{2} - a - 4\) , \( -a^{2} + a + 4\) , \( -a^{2} + a + 5\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}-a^{2}+a+5$ |
| 55.2-b1 |
55.2-b |
$4$ |
$6$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{3} \cdot 11^{12} \) |
$5.46912$ |
$(-a-1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$21.38817362$ |
2.04445163 |
\( -\frac{88126318563617923433586}{392303547090125} a^{2} + \frac{73765000782016153928717}{392303547090125} a + \frac{540779761956845037439809}{392303547090125} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( 1\) , \( -6 a^{2} + 159 a - 417\) , \( -807 a^{2} + 1713 a + 1911\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-6a^{2}+159a-417\right){x}-807a^{2}+1713a+1911$ |
| 55.2-b2 |
55.2-b |
$4$ |
$6$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{6} \) |
$5.46912$ |
$(-a-1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$21.38817362$ |
2.04445163 |
\( \frac{10579229278741269}{27680640625} a^{2} - \frac{32345497963762218}{27680640625} a + \frac{3973705130591689}{27680640625} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( 1\) , \( -61 a^{2} + 189 a - 32\) , \( -615 a^{2} + 1902 a - 292\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-61a^{2}+189a-32\right){x}-615a^{2}+1902a-292$ |
| 55.2-b3 |
55.2-b |
$4$ |
$6$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5 \cdot 11^{4} \) |
$5.46912$ |
$(-a-1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$64.16452088$ |
2.04445163 |
\( \frac{1747148534369}{73205} a^{2} + \frac{3195734287557}{73205} a - \frac{567030464936}{73205} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( 1\) , \( -31 a^{2} + 89 a + 3\) , \( 196 a^{2} - 608 a + 98\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-31a^{2}+89a+3\right){x}+196a^{2}-608a+98$ |
| 55.2-b4 |
55.2-b |
$4$ |
$6$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$5.46912$ |
$(-a-1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$64.16452088$ |
2.04445163 |
\( -\frac{3616326}{3025} a^{2} - \frac{9298503}{3025} a + \frac{5981869}{3025} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( 1\) , \( -6 a^{2} + 9 a + 23\) , \( -a^{2} - 5 a + 23\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-6a^{2}+9a+23\right){x}-a^{2}-5a+23$ |
| 56.1-a1 |
56.1-a |
$1$ |
$1$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( - 2^{18} \cdot 7^{8} \) |
$5.48556$ |
$(-a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \cdot 3 \) |
$0.034610072$ |
$31.44003996$ |
4.99263688 |
\( \frac{977143394632247}{368947264} a^{2} - \frac{817750978067041}{368947264} a - \frac{1499021110396295}{92236816} \) |
\( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} - a - 3\) , \( -4 a^{2} + 33 a - 64\) , \( 99 a^{2} - 348 a + 167\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-4a^{2}+33a-64\right){x}+99a^{2}-348a+167$ |
| 56.1-b1 |
56.1-b |
$1$ |
$1$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( - 2^{18} \cdot 7^{8} \) |
$5.48556$ |
$(-a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.693789797$ |
2.55938253 |
\( \frac{977143394632247}{368947264} a^{2} - \frac{817750978067041}{368947264} a - \frac{1499021110396295}{92236816} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3\) , \( a^{2} - 3\) , \( 47 a^{2} - 40 a - 290\) , \( 374 a^{2} - 315 a - 2298\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(47a^{2}-40a-290\right){x}+374a^{2}-315a-2298$ |
| 56.1-c1 |
56.1-c |
$2$ |
$2$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{9} \cdot 7^{10} \) |
$5.48556$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.484293246$ |
$43.60964028$ |
4.03760707 |
\( -\frac{10131623595273050559}{2259801992} a^{2} + \frac{4240305089385957699}{1129900996} a + \frac{15542967850269814363}{564950498} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 5\) , \( 1\) , \( -126 a^{2} + 381 a - 58\) , \( -1482 a^{2} + 4593 a - 705\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-126a^{2}+381a-58\right){x}-1482a^{2}+4593a-705$ |
| 56.1-c2 |
56.1-c |
$2$ |
$2$ |
3.3.985.1 |
$3$ |
$[3, 0]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( - 2^{18} \cdot 7^{5} \) |
$5.48556$ |
$(-a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.968586492$ |
$87.21928057$ |
4.03760707 |
\( -\frac{26856825111}{1075648} a^{2} + \frac{17759645067}{1075648} a + \frac{178625712533}{1075648} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 5\) , \( 1\) , \( -46 a^{2} + 141 a - 18\) , \( 318 a^{2} - 983 a + 151\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-46a^{2}+141a-18\right){x}+318a^{2}-983a+151$ |
*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.
