| 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 |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{2} \) |
$4.90915$ |
$(-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$228.5920046$ |
2.720562363 |
\( \frac{3844079}{25} a^{2} + \frac{7288942}{25} a - \frac{21167311}{25} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( -a^{2} - a + 8\) , \( 1\) , \( 19 a^{2} - 70 a + 70\) , \( 73 a^{2} - 305 a + 303\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+8\right){x}^{2}+\left(19a^{2}-70a+70\right){x}+73a^{2}-305a+303$ |
| 5.1-a2 |
5.1-a |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$4.90915$ |
$(-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$457.1840092$ |
2.720562363 |
\( -\frac{7034}{5} a^{2} - \frac{4157}{5} a + \frac{81121}{5} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -3 a^{2} + 9 a - 8\) , \( 3 a^{2} - 14 a + 13\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3a^{2}+9a-8\right){x}+3a^{2}-14a+13$ |
| 5.1-b1 |
5.1-b |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{2} \) |
$4.90915$ |
$(-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$138.5024266$ |
1.648371253 |
\( \frac{3844079}{25} a^{2} + \frac{7288942}{25} a - \frac{21167311}{25} \) |
\( \bigl[1\) , \( a^{2} + a - 9\) , \( 1\) , \( 132 a^{2} + 76 a - 1321\) , \( -1465 a^{2} - 866 a + 14744\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}+a-9\right){x}^{2}+\left(132a^{2}+76a-1321\right){x}-1465a^{2}-866a+14744$ |
| 5.1-b2 |
5.1-b |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$4.90915$ |
$(-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$277.0048532$ |
1.648371253 |
\( -\frac{7034}{5} a^{2} - \frac{4157}{5} a + \frac{81121}{5} \) |
\( \bigl[a + 1\) , \( a^{2} + 2 a - 7\) , \( 1\) , \( 5 a^{2} + 9 a - 30\) , \( 6 a^{2} + 11 a - 34\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}+2a-7\right){x}^{2}+\left(5a^{2}+9a-30\right){x}+6a^{2}+11a-34$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{8} \) |
$5.30916$ |
$(-a^2-2a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.472767921$ |
$23.82774685$ |
3.217657913 |
\( 1790471 a^{2} + 1047458 a - 18077536 \) |
\( \bigl[a\) , \( -a^{2} - a + 9\) , \( a^{2} + a - 8\) , \( -7 a^{2} + 10 a + 15\) , \( -17 a^{2} + 82 a - 85\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-8\right){y}={x}^{3}+\left(-a^{2}-a+9\right){x}^{2}+\left(-7a^{2}+10a+15\right){x}-17a^{2}+82a-85$ |
| 8.2-b1 |
8.2-b |
$1$ |
$1$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{8} \) |
$5.30916$ |
$(-a^2-2a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$34.00468640$ |
1.618811999 |
\( 1790471 a^{2} + 1047458 a - 18077536 \) |
\( \bigl[a^{2} + a - 8\) , \( a^{2} + a - 8\) , \( a^{2} + 2 a - 8\) , \( 33 a^{2} + 20 a - 332\) , \( -182 a^{2} - 107 a + 1828\bigr] \) |
${y}^2+\left(a^{2}+a-8\right){x}{y}+\left(a^{2}+2a-8\right){y}={x}^{3}+\left(a^{2}+a-8\right){x}^{2}+\left(33a^{2}+20a-332\right){x}-182a^{2}-107a+1828$ |
| 10.2-a1 |
10.2-a |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{6} \) |
$5.51033$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$33.09429439$ |
2.363208422 |
\( -\frac{302725786531}{64000000} a^{2} + \frac{65099296787}{64000000} a + \frac{4000612675729}{64000000} \) |
\( \bigl[1\) , \( a^{2} + 2 a - 9\) , \( 0\) , \( 235 a^{2} + 44 a - 2081\) , \( 2867 a^{2} + 1624 a - 28643\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}+2a-9\right){x}^{2}+\left(235a^{2}+44a-2081\right){x}+2867a^{2}+1624a-28643$ |
| 10.2-a2 |
10.2-a |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{3} \) |
$5.51033$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$66.18858878$ |
2.363208422 |
\( \frac{612085617101}{8000} a^{2} + \frac{1157177596323}{8000} a - \frac{3388050447359}{8000} \) |
\( \bigl[a + 1\) , \( a\) , \( a^{2} + 2 a - 7\) , \( -3 a^{2} + 11 a - 6\) , \( 3 a^{2} - 15 a + 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+a{x}^{2}+\left(-3a^{2}+11a-6\right){x}+3a^{2}-15a+16$ |
| 10.2-b1 |
10.2-b |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5^{2} \) |
$5.51033$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$87.72935632$ |
2.088202387 |
\( -\frac{5703018871}{100} a^{2} - \frac{3366119333}{100} a + \frac{57380322689}{100} \) |
\( \bigl[1\) , \( a^{2} + a - 7\) , \( 0\) , \( 51 a^{2} + 31 a - 509\) , \( 311 a^{2} + 184 a - 3127\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(51a^{2}+31a-509\right){x}+311a^{2}+184a-3127$ |
| 10.2-b2 |
10.2-b |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$5.51033$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$87.72935632$ |
2.088202387 |
\( \frac{455411}{10} a^{2} + \frac{607403}{10} a - \frac{2304169}{10} \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 7\) , \( a^{2} + a - 8\) , \( -7 a^{2} - 11 a + 47\) , \( -10 a^{2} - 19 a + 55\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-8\right){y}={x}^{3}+\left(-a^{2}-a+7\right){x}^{2}+\left(-7a^{2}-11a+47\right){x}-10a^{2}-19a+55$ |
| 10.2-c1 |
10.2-c |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{20} \cdot 5^{2} \) |
$5.51033$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$29.62352876$ |
0.705122277 |
\( \frac{15131101229}{26214400} a^{2} + \frac{258962195267}{26214400} a + \frac{88606429089}{26214400} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} + 2 a - 9\) , \( a^{2} + 2 a - 8\) , \( 21 a^{2} + 21 a - 181\) , \( -70 a^{2} - 46 a + 685\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-8\right){y}={x}^{3}+\left(a^{2}+2a-9\right){x}^{2}+\left(21a^{2}+21a-181\right){x}-70a^{2}-46a+685$ |
| 10.2-c2 |
10.2-c |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{10} \cdot 5 \) |
$5.51033$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$59.24705752$ |
0.705122277 |
\( \frac{97055570901}{5120} a^{2} - \frac{434889346277}{5120} a + \frac{446157236201}{5120} \) |
\( \bigl[1\) , \( a^{2} + a - 9\) , \( 0\) , \( -2244 a^{2} - 4241 a + 12426\) , \( 69028 a^{2} + 130500 a - 382092\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}+a-9\right){x}^{2}+\left(-2244a^{2}-4241a+12426\right){x}+69028a^{2}+130500a-382092$ |
| 10.2-d1 |
10.2-d |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$5.51033$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.517347607$ |
$556.8711836$ |
5.143113383 |
\( \frac{455411}{10} a^{2} + \frac{607403}{10} a - \frac{2304169}{10} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} + a - 7\) , \( a^{2} + 2 a - 7\) , \( 288 a^{2} + 181 a - 2859\) , \( -5041 a^{2} - 2949 a + 50811\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-7\right){y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(288a^{2}+181a-2859\right){x}-5041a^{2}-2949a+50811$ |
| 10.2-d2 |
10.2-d |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5^{2} \) |
$5.51033$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.258673803$ |
$278.4355918$ |
5.143113383 |
\( -\frac{5703018871}{100} a^{2} - \frac{3366119333}{100} a + \frac{57380322689}{100} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{2} + 2 a - 8\) , \( 634769 a^{2} + 374665 a - 6386656\) , \( -499499194 a^{2} - 294824121 a + 5025650188\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+2a-8\right){y}={x}^{3}+\left(634769a^{2}+374665a-6386656\right){x}-499499194a^{2}-294824121a+5025650188$ |
| 10.2-e1 |
10.2-e |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{20} \cdot 5^{2} \) |
$5.51033$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.164273007$ |
$31.41505017$ |
3.685130450 |
\( \frac{15131101229}{26214400} a^{2} + \frac{258962195267}{26214400} a + \frac{88606429089}{26214400} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} + 2 a - 7\) , \( a^{2} + a - 7\) , \( -38 a^{2} + 260 a - 319\) , \( -803 a^{2} + 3813 a - 4035\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a^{2}+2a-7\right){x}^{2}+\left(-38a^{2}+260a-319\right){x}-803a^{2}+3813a-4035$ |
| 10.2-e2 |
10.2-e |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{10} \cdot 5 \) |
$5.51033$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.328546015$ |
$62.83010034$ |
3.685130450 |
\( \frac{97055570901}{5120} a^{2} - \frac{434889346277}{5120} a + \frac{446157236201}{5120} \) |
\( \bigl[1\) , \( -a^{2} - 2 a + 8\) , \( 0\) , \( -132 a^{2} - 78 a + 460\) , \( -857 a^{2} + 508 a + 1360\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}-2a+8\right){x}^{2}+\left(-132a^{2}-78a+460\right){x}-857a^{2}+508a+1360$ |
| 10.2-f1 |
10.2-f |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{6} \) |
$5.51033$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.033165123$ |
$92.15088254$ |
3.928280776 |
\( -\frac{302725786531}{64000000} a^{2} + \frac{65099296787}{64000000} a + \frac{4000612675729}{64000000} \) |
\( \bigl[1\) , \( a^{2} - 7\) , \( a + 1\) , \( 685137 a^{2} + 404393 a - 6893418\) , \( -552115263 a^{2} - 325880200 a + 5555040351\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(685137a^{2}+404393a-6893418\right){x}-552115263a^{2}-325880200a+5555040351$ |
| 10.2-f2 |
10.2-f |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{3} \) |
$5.51033$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.066330246$ |
$184.3017650$ |
3.928280776 |
\( \frac{612085617101}{8000} a^{2} + \frac{1157177596323}{8000} a - \frac{3388050447359}{8000} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 639 a^{2} + 377 a - 6429\) , \( 8522 a^{2} + 5030 a - 85743\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(639a^{2}+377a-6429\right){x}+8522a^{2}+5030a-85743$ |
| 13.2-a1 |
13.2-a |
$1$ |
$1$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
13.2 |
\( 13 \) |
\( -13 \) |
$5.75663$ |
$(a^2-9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$104.7473845$ |
2.493278735 |
\( -\frac{3203}{13} a^{2} - \frac{1150}{13} a + \frac{29856}{13} \) |
\( \bigl[a^{2} + a - 8\) , \( a - 1\) , \( a + 1\) , \( -2 a^{2} - 2 a + 23\) , \( -a^{2} + 8\bigr] \) |
${y}^2+\left(a^{2}+a-8\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a^{2}-2a+23\right){x}-a^{2}+8$ |
| 13.2-b1 |
13.2-b |
$1$ |
$1$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
13.2 |
\( 13 \) |
\( -13 \) |
$5.75663$ |
$(a^2-9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$60.89440779$ |
1.449456066 |
\( -\frac{3203}{13} a^{2} - \frac{1150}{13} a + \frac{29856}{13} \) |
\( \bigl[a\) , \( a^{2} - 9\) , \( a^{2} + a - 7\) , \( -4 a^{2} + 3 a + 19\) , \( -14 a^{2} + 66 a - 79\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a^{2}-9\right){x}^{2}+\left(-4a^{2}+3a+19\right){x}-14a^{2}+66a-79$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{12} \) |
$5.95933$ |
$(-a^2-2a+6), (-a^2-a+11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$34.40933698$ |
1.638075614 |
\( -\frac{1285}{4} a^{2} + \frac{443}{4} a + 2364 \) |
\( \bigl[a^{2} + a - 8\) , \( a^{2} + 2 a - 9\) , \( 0\) , \( a^{2} + 3 a + 3\) , \( -3 a^{2} - 5 a + 17\bigr] \) |
${y}^2+\left(a^{2}+a-8\right){x}{y}={x}^{3}+\left(a^{2}+2a-9\right){x}^{2}+\left(a^{2}+3a+3\right){x}-3a^{2}-5a+17$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{12} \) |
$5.95933$ |
$(-a^2-2a+6), (-a^2-a+11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.172938633$ |
$59.90215931$ |
4.438483932 |
\( -\frac{1285}{4} a^{2} + \frac{443}{4} a + 2364 \) |
\( \bigl[a^{2} + a - 8\) , \( -a\) , \( a^{2} + 2 a - 8\) , \( -3 a^{2} + 8 a - 8\) , \( -15 a^{2} + 61 a - 60\bigr] \) |
${y}^2+\left(a^{2}+a-8\right){x}{y}+\left(a^{2}+2a-8\right){y}={x}^{3}-a{x}^{2}+\left(-3a^{2}+8a-8\right){x}-15a^{2}+61a-60$ |
| 17.1-a1 |
17.1-a |
$1$ |
$1$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$6.01985$ |
$(a^2+2a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.558153751$ |
$79.70943039$ |
3.176965173 |
\( -\frac{1849733}{4913} a^{2} - \frac{1346727}{4913} a + \frac{19256656}{4913} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 3 a^{2} + 2 a - 33\) , \( 3 a^{2} - 38\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a^{2}+2a-33\right){x}+3a^{2}-38$ |
| 17.1-b1 |
17.1-b |
$1$ |
$1$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$6.01985$ |
$(a^2+2a-7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.024650290$ |
$177.4613690$ |
2.811365316 |
\( -\frac{1849733}{4913} a^{2} - \frac{1346727}{4913} a + \frac{19256656}{4913} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{2} + a - 7\) , \( 2 a^{2} - 9 a + 15\) , \( 15 a^{2} - 64 a + 63\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a^{2}-9a+15\right){x}+15a^{2}-64a+63$ |
| 20.4-a1 |
20.4-a |
$4$ |
$6$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
20.4 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$6.18514$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$31.33727654$ |
1.118871352 |
\( \frac{43248306324339065829}{15625} a^{2} + \frac{81762963965643477942}{15625} a - \frac{239391663880746553136}{15625} \) |
\( \bigl[a\) , \( a^{2} + a - 8\) , \( a\) , \( 10204 a^{2} + 6022 a - 102671\) , \( 47025 a^{2} + 27756 a - 473138\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}+a-8\right){x}^{2}+\left(10204a^{2}+6022a-102671\right){x}+47025a^{2}+27756a-473138$ |
| 20.4-a2 |
20.4-a |
$4$ |
$6$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
20.4 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$6.18514$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$94.01182964$ |
1.118871352 |
\( -\frac{773943246}{25} a^{2} - \frac{455774283}{25} a + \frac{7791057664}{25} \) |
\( \bigl[a\) , \( a^{2} + a - 8\) , \( a\) , \( 7219 a^{2} + 4262 a - 72631\) , \( 598378 a^{2} + 353187 a - 6020506\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}+a-8\right){x}^{2}+\left(7219a^{2}+4262a-72631\right){x}+598378a^{2}+353187a-6020506$ |
| 20.4-a3 |
20.4-a |
$4$ |
$6$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
20.4 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{3} \) |
$6.18514$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$62.67455309$ |
1.118871352 |
\( \frac{100523797004}{125} a^{2} - \frac{435891372533}{125} a + \frac{438990695664}{125} \) |
\( \bigl[a\) , \( a^{2} + a - 8\) , \( a\) , \( 6804 a^{2} + 4017 a - 68456\) , \( -560045 a^{2} - 330560 a + 5634825\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}+a-8\right){x}^{2}+\left(6804a^{2}+4017a-68456\right){x}-560045a^{2}-330560a+5634825$ |
| 20.4-a4 |
20.4-a |
$4$ |
$6$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
20.4 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$6.18514$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$188.0236592$ |
1.118871352 |
\( -\frac{9791}{5} a^{2} - \frac{7368}{5} a + \frac{111744}{5} \) |
\( \bigl[a\) , \( a^{2} + a - 8\) , \( a\) , \( 459 a^{2} + 272 a - 4616\) , \( 8641 a^{2} + 5101 a - 86939\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}+a-8\right){x}^{2}+\left(459a^{2}+272a-4616\right){x}+8641a^{2}+5101a-86939$ |
| 20.4-b1 |
20.4-b |
$4$ |
$6$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
20.4 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$6.18514$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$286.5240688$ |
0.568339065 |
\( -\frac{9791}{5} a^{2} - \frac{7368}{5} a + \frac{111744}{5} \) |
\( \bigl[a^{2} + 2 a - 8\) , \( 0\) , \( a^{2} + 2 a - 8\) , \( a^{2} + 2 a - 8\) , \( a^{2} + 2 a - 7\bigr] \) |
${y}^2+\left(a^{2}+2a-8\right){x}{y}+\left(a^{2}+2a-8\right){y}={x}^{3}+\left(a^{2}+2a-8\right){x}+a^{2}+2a-7$ |
| 20.4-b2 |
20.4-b |
$4$ |
$6$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
20.4 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$6.18514$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$143.2620344$ |
0.568339065 |
\( -\frac{773943246}{25} a^{2} - \frac{455774283}{25} a + \frac{7791057664}{25} \) |
\( \bigl[a^{2} + 2 a - 8\) , \( 0\) , \( a^{2} + 2 a - 8\) , \( -4 a^{2} - 8 a + 17\) , \( -33 a^{2} - 62 a + 182\bigr] \) |
${y}^2+\left(a^{2}+2a-8\right){x}{y}+\left(a^{2}+2a-8\right){y}={x}^{3}+\left(-4a^{2}-8a+17\right){x}-33a^{2}-62a+182$ |
| 20.4-b3 |
20.4-b |
$4$ |
$6$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
20.4 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{3} \) |
$6.18514$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$10.61200254$ |
0.568339065 |
\( \frac{100523797004}{125} a^{2} - \frac{435891372533}{125} a + \frac{438990695664}{125} \) |
\( \bigl[a^{2} + 2 a - 8\) , \( 0\) , \( a^{2} + 2 a - 8\) , \( -29 a^{2} - 53 a + 152\) , \( -282 a^{2} - 529 a + 1549\bigr] \) |
${y}^2+\left(a^{2}+2a-8\right){x}{y}+\left(a^{2}+2a-8\right){y}={x}^{3}+\left(-29a^{2}-53a+152\right){x}-282a^{2}-529a+1549$ |
| 20.4-b4 |
20.4-b |
$4$ |
$6$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
20.4 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{6} \) |
$6.18514$ |
$(-a^2-2a+6), (-3a^2-6a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$5.306001274$ |
0.568339065 |
\( \frac{43248306324339065829}{15625} a^{2} + \frac{81762963965643477942}{15625} a - \frac{239391663880746553136}{15625} \) |
\( \bigl[a^{2} + 2 a - 8\) , \( 0\) , \( a^{2} + 2 a - 8\) , \( -489 a^{2} - 923 a + 2697\) , \( -13590 a^{2} - 25688 a + 75214\bigr] \) |
${y}^2+\left(a^{2}+2a-8\right){x}{y}+\left(a^{2}+2a-8\right){y}={x}^{3}+\left(-489a^{2}-923a+2697\right){x}-13590a^{2}-25688a+75214$ |
| 25.2-a1 |
25.2-a |
$6$ |
$8$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{10} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.111203990$ |
$3.650668451$ |
3.244216069 |
\( \frac{6489605573029919}{390625} a^{2} + \frac{12271735139565762}{390625} a - \frac{35911962693299821}{390625} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a - 1\) , \( a^{2} + a - 7\) , \( 200302 a^{2} + 118234 a - 2015281\) , \( 88663113 a^{2} + 52332483 a - 892073034\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(200302a^{2}+118234a-2015281\right){x}+88663113a^{2}+52332483a-892073034$ |
| 25.2-a2 |
25.2-a |
$6$ |
$8$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{8} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.555601995$ |
$29.20534761$ |
3.244216069 |
\( \frac{239789974}{625} a^{2} - \frac{899025973}{625} a + \frac{827544409}{625} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a - 1\) , \( a^{2} + a - 7\) , \( 13022 a^{2} + 7694 a - 130986\) , \( 1272960 a^{2} + 751369 a - 12807672\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(13022a^{2}+7694a-130986\right){x}+1272960a^{2}+751369a-12807672$ |
| 25.2-a3 |
25.2-a |
$6$ |
$8$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{4} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.111203990$ |
$233.6427808$ |
3.244216069 |
\( -\frac{27279}{25} a^{2} - \frac{25442}{25} a + \frac{344921}{25} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a - 1\) , \( a^{2} + a - 7\) , \( 3492 a^{2} + 2069 a - 35101\) , \( -182546 a^{2} - 107728 a + 1836724\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3492a^{2}+2069a-35101\right){x}-182546a^{2}-107728a+1836724$ |
| 25.2-a4 |
25.2-a |
$6$ |
$8$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.111203990$ |
$3.650668451$ |
3.244216069 |
\( \frac{2331591592209521}{625} a^{2} - \frac{10447364411116002}{625} a + \frac{10717538747470477}{625} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a - 1\) , \( a^{2} + a - 7\) , \( -21778 a^{2} - 12846 a + 219149\) , \( 6881691 a^{2} + 4061863 a - 69239234\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-21778a^{2}-12846a+219149\right){x}+6881691a^{2}+4061863a-69239234$ |
| 25.2-a5 |
25.2-a |
$6$ |
$8$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{2} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$6.222407980$ |
$116.8213904$ |
3.244216069 |
\( \frac{1004}{5} a^{2} + \frac{1441}{5} a - 793 \) |
\( \bigl[1\) , \( -a^{2} + 9\) , \( a + 1\) , \( -4 a^{2} - 3 a + 42\) , \( -15 a^{2} - 9 a + 148\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+9\right){x}^{2}+\left(-4a^{2}-3a+42\right){x}-15a^{2}-9a+148$ |
| 25.2-a6 |
25.2-a |
$6$ |
$8$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.555601995$ |
$467.2855617$ |
3.244216069 |
\( -\frac{56626004}{5} a^{2} - \frac{33261441}{5} a + 114077281 \) |
\( \bigl[a + 1\) , \( a^{2} + 2 a - 9\) , \( 1\) , \( 7600930 a^{2} + 4486372 a - 76475815\) , \( -20715700964 a^{2} - 12227223549 a + 208428497590\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}+2a-9\right){x}^{2}+\left(7600930a^{2}+4486372a-76475815\right){x}-20715700964a^{2}-12227223549a+208428497590$ |
| 25.2-b1 |
25.2-b |
$1$ |
$1$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{16} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \cdot 11 \) |
$0.024690472$ |
$20.61685205$ |
1.999232683 |
\( -\frac{18400188022}{48828125} a^{2} + \frac{19316353869}{48828125} a + \frac{97996616848}{48828125} \) |
\( \bigl[a^{2} + a - 8\) , \( -a\) , \( 1\) , \( -4 a^{2} - 3 a + 41\) , \( -2 a^{2} - 2 a + 18\bigr] \) |
${y}^2+\left(a^{2}+a-8\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4a^{2}-3a+41\right){x}-2a^{2}-2a+18$ |
| 25.2-c1 |
25.2-c |
$1$ |
$1$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{16} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \cdot 11 \) |
$0.066394325$ |
$35.80714767$ |
9.337105741 |
\( -\frac{18400188022}{48828125} a^{2} + \frac{19316353869}{48828125} a + \frac{97996616848}{48828125} \) |
\( \bigl[a\) , \( a^{2} + a - 9\) , \( a^{2} + a - 7\) , \( 18 a^{2} + 42 a - 104\) , \( 3068 a^{2} + 5785 a - 16963\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-7\right){y}={x}^{3}+\left(a^{2}+a-9\right){x}^{2}+\left(18a^{2}+42a-104\right){x}+3068a^{2}+5785a-16963$ |
| 25.2-d1 |
25.2-d |
$6$ |
$8$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.561902123$ |
$10.32845584$ |
4.607847568 |
\( \frac{2331591592209521}{625} a^{2} - \frac{10447364411116002}{625} a + \frac{10717538747470477}{625} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( -a^{2} - 2 a + 8\) , \( a + 1\) , \( -4689 a^{2} + 20973 a - 21445\) , \( -706644 a^{2} + 3166101 a - 3247561\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-2a+8\right){x}^{2}+\left(-4689a^{2}+20973a-21445\right){x}-706644a^{2}+3166101a-3247561$ |
| 25.2-d2 |
25.2-d |
$6$ |
$8$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{10} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.561902123$ |
$41.31382338$ |
4.607847568 |
\( \frac{6489605573029919}{390625} a^{2} + \frac{12271735139565762}{390625} a - \frac{35911962693299821}{390625} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( -a^{2} - 2 a + 8\) , \( a + 1\) , \( -209 a^{2} + 1253 a - 1875\) , \( -13370 a^{2} + 57699 a - 55065\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-2a+8\right){x}^{2}+\left(-209a^{2}+1253a-1875\right){x}-13370a^{2}+57699a-55065$ |
| 25.2-d3 |
25.2-d |
$6$ |
$8$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{8} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.780951061$ |
$82.62764676$ |
4.607847568 |
\( \frac{239789974}{625} a^{2} - \frac{899025973}{625} a + \frac{827544409}{625} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( -a^{2} - 2 a + 8\) , \( a + 1\) , \( -289 a^{2} + 1313 a - 1380\) , \( -11313 a^{2} + 50680 a - 51963\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-2a+8\right){x}^{2}+\left(-289a^{2}+1313a-1380\right){x}-11313a^{2}+50680a-51963$ |
| 25.2-d4 |
25.2-d |
$6$ |
$8$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{4} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.561902123$ |
$165.2552935$ |
4.607847568 |
\( -\frac{27279}{25} a^{2} - \frac{25442}{25} a + \frac{344921}{25} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( -a^{2} - 2 a + 8\) , \( a + 1\) , \( -19 a^{2} + 88 a - 95\) , \( -166 a^{2} + 760 a - 803\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-2a+8\right){x}^{2}+\left(-19a^{2}+88a-95\right){x}-166a^{2}+760a-803$ |
| 25.2-d5 |
25.2-d |
$6$ |
$8$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{2} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$3.123804246$ |
$82.62764676$ |
4.607847568 |
\( \frac{1004}{5} a^{2} + \frac{1441}{5} a - 793 \) |
\( \bigl[1\) , \( a^{2} + a - 7\) , \( a\) , \( 2 a^{2} - 6 a + 6\) , \( -4 a^{2} + 20 a - 23\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(2a^{2}-6a+6\right){x}-4a^{2}+20a-23$ |
| 25.2-d6 |
25.2-d |
$6$ |
$8$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$6.41950$ |
$(-3a^2-6a+17), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$3.123804246$ |
$82.62764676$ |
4.607847568 |
\( -\frac{56626004}{5} a^{2} - \frac{33261441}{5} a + 114077281 \) |
\( \bigl[a + 1\) , \( -a^{2} - 2 a + 9\) , \( a\) , \( 2178 a^{2} + 2346 a - 24984\) , \( 125275 a^{2} + 43898 a - 1173597\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-2a+9\right){x}^{2}+\left(2178a^{2}+2346a-24984\right){x}+125275a^{2}+43898a-1173597$ |
| 25.3-a1 |
25.3-a |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{8} \) |
$6.41950$ |
$(-3a^2-6a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.816804485$ |
$61.94016820$ |
3.612762348 |
\( \frac{3844079}{25} a^{2} + \frac{7288942}{25} a - \frac{21167311}{25} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a\) , \( a + 1\) , \( 27278 a^{2} + 16111 a - 274417\) , \( -3711155 a^{2} - 2190448 a + 37339407\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(27278a^{2}+16111a-274417\right){x}-3711155a^{2}-2190448a+37339407$ |
| 25.3-a2 |
25.3-a |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{7} \) |
$6.41950$ |
$(-3a^2-6a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.408402242$ |
$123.8803364$ |
3.612762348 |
\( -\frac{7034}{5} a^{2} - \frac{4157}{5} a + \frac{81121}{5} \) |
\( \bigl[1\) , \( a^{2} - 8\) , \( a + 1\) , \( 55 a^{2} + 31 a - 551\) , \( 286 a^{2} + 168 a - 2879\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(55a^{2}+31a-551\right){x}+286a^{2}+168a-2879$ |
| 25.3-b1 |
25.3-b |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{7} \) |
$6.41950$ |
$(-3a^2-6a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.064543148$ |
$204.4589046$ |
0.942334468 |
\( -\frac{7034}{5} a^{2} - \frac{4157}{5} a + \frac{81121}{5} \) |
\( \bigl[a^{2} + 2 a - 7\) , \( a^{2} - 8\) , \( a^{2} + 2 a - 8\) , \( 2 a^{2} + 5 a - 6\) , \( 5 a^{2} + 9 a - 33\bigr] \) |
${y}^2+\left(a^{2}+2a-7\right){x}{y}+\left(a^{2}+2a-8\right){y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(2a^{2}+5a-6\right){x}+5a^{2}+9a-33$ |
| 25.3-b2 |
25.3-b |
$2$ |
$2$ |
3.3.1765.1 |
$3$ |
$[3, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{8} \) |
$6.41950$ |
$(-3a^2-6a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.129086297$ |
$102.2294523$ |
0.942334468 |
\( \frac{3844079}{25} a^{2} + \frac{7288942}{25} a - \frac{21167311}{25} \) |
\( \bigl[a + 1\) , \( a^{2} - 8\) , \( a^{2} + a - 8\) , \( 2 a^{2} - 6 a\) , \( 4 a^{2} - 14 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-8\right){y}={x}^{3}+\left(a^{2}-8\right){x}^{2}+\left(2a^{2}-6a\right){x}+4a^{2}-14a+7$ |
*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.
