| 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 |
| 1.1-a1 |
1.1-a |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$3.37323$ |
$\textsf{none}$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.077910877$ |
$268.4797751$ |
1.662353930 |
\( 155 a^{2} - 374 a - 625 \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + a + 4\) , \( a^{2} - a - 4\) , \( -2 a^{2} + a + 8\) , \( -a^{2} + 2 a + 7\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-2a^{2}+a+8\right){x}-a^{2}+2a+7$ |
| 3.1-a1 |
3.1-a |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$4.05104$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$109.8229330$ |
2.909280566 |
\( \frac{14380364140544}{3} a^{2} - \frac{20183928528896}{3} a - \frac{106897171640320}{3} \) |
\( \bigl[0\) , \( -a^{2} + a + 4\) , \( a\) , \( -120 a^{2} + 373 a + 174\) , \( 2522 a^{2} - 7854 a - 3579\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-120a^{2}+373a+174\right){x}+2522a^{2}-7854a-3579$ |
| 3.1-b1 |
3.1-b |
$2$ |
$3$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{4} \) |
$4.05104$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$20.36079716$ |
2.157482773 |
\( \frac{784388}{81} a^{2} - \frac{882887}{81} a - \frac{6594601}{81} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - 3 a - 6\) , \( 0\) , \( 4 a^{2} - 11 a - 6\) , \( 4 a^{2} - 13 a - 6\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(4a^{2}-11a-6\right){x}+4a^{2}-13a-6$ |
| 3.1-b2 |
3.1-b |
$2$ |
$3$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{12} \) |
$4.05104$ |
$(-a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$61.08239150$ |
2.157482773 |
\( \frac{7034321}{531441} a^{2} - \frac{175125119}{531441} a + \frac{508034336}{531441} \) |
\( \bigl[a\) , \( 1\) , \( a^{2} - a - 5\) , \( -54 a^{2} + 75 a + 403\) , \( 287 a^{2} - 403 a - 2134\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+{x}^{2}+\left(-54a^{2}+75a+403\right){x}+287a^{2}-403a-2134$ |
| 3.2-a1 |
3.2-a |
$2$ |
$5$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{5} \) |
$4.05104$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4 |
$1$ |
\( 1 \) |
$0.142091374$ |
$190.5666650$ |
2.151931637 |
\( \frac{3328026115}{27} a^{2} - \frac{4710786470}{27} a - \frac{8274275080}{9} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 4\) , \( a + 1\) , \( 16 a^{2} - 53 a - 21\) , \( -83 a^{2} + 257 a + 118\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(16a^{2}-53a-21\right){x}-83a^{2}+257a+118$ |
| 3.2-a2 |
3.2-a |
$2$ |
$5$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( -3 \) |
$4.05104$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.3 |
$1$ |
\( 1 \) |
$0.710456870$ |
$38.11333300$ |
2.151931637 |
\( -\frac{44927975}{3} a^{2} + \frac{139885825}{3} a + 21257925 \) |
\( \bigl[a + 1\) , \( -a^{2} + 3 a + 6\) , \( a^{2} - a - 4\) , \( 2 a + 11\) , \( 5 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+3a+6\right){x}^{2}+\left(2a+11\right){x}+5a+7$ |
| 3.2-b1 |
3.2-b |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{8} \) |
$4.05104$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.126668633$ |
$57.76798451$ |
1.163054643 |
\( -\frac{106502}{9} a^{2} - \frac{2396909}{81} a - \frac{270406}{27} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -2 a^{2} + 6 a + 3\) , \( 6 a^{2} - 19 a - 8\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-2a^{2}+6a+3\right){x}+6a^{2}-19a-8$ |
| 8.1-a1 |
8.1-a |
$4$ |
$15$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$4.77047$ |
$(2)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.3 |
|
\( 1 \) |
$1$ |
$48.96703389$ |
3.458250612 |
\( -\frac{25}{2} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 2 a - 5\) , \( 2 a - 7\) , \( -35 a^{2} + 110 a + 46\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(2a-7\right){x}-35a^{2}+110a+46$ |
| 8.1-a2 |
8.1-a |
$4$ |
$15$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$4.77047$ |
$(2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B.1.2, 5B.1.3 |
|
\( 1 \) |
$1$ |
$1.813593847$ |
3.458250612 |
\( -\frac{349938025}{8} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 2 a - 5\) , \( -420 a^{2} + 1307 a + 588\) , \( -11184 a^{2} + 34820 a + 15870\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-420a^{2}+1307a+588\right){x}-11184a^{2}+34820a+15870$ |
| 8.1-a3 |
8.1-a |
$4$ |
$15$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{15} \) |
$4.77047$ |
$(2)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.1.4 |
|
\( 1 \) |
$1$ |
$244.8351694$ |
3.458250612 |
\( -\frac{121945}{32} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( 0\) , \( a^{2} - 2 a - 4\) , \( 2 a^{2} + 2 a - 32\) , \( -4 a^{2} + 2 a + 42\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(2a^{2}+2a-32\right){x}-4a^{2}+2a+42$ |
| 8.1-a4 |
8.1-a |
$4$ |
$15$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{45} \) |
$4.77047$ |
$(2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B.1.2, 5B.1.4 |
|
\( 1 \) |
$1$ |
$9.067969238$ |
3.458250612 |
\( \frac{46969655}{32768} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( 0\) , \( a^{2} - 2 a - 4\) , \( -18 a^{2} - 3 a + 233\) , \( 26 a^{2} - 4 a - 308\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-18a^{2}-3a+233\right){x}+26a^{2}-4a-308$ |
| 9.1-a1 |
9.1-a |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{14} \) |
$4.86504$ |
$(-a), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3^{2} \) |
$1$ |
$9.104735698$ |
2.170713066 |
\( \frac{24015583}{19683} a^{2} + \frac{31099475}{19683} a - \frac{404319071}{19683} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a\) , \( a^{2} - 2 a - 5\) , \( -4 a^{2} + 15 a + 3\) , \( -32 a^{2} + 97 a + 41\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}-a{x}^{2}+\left(-4a^{2}+15a+3\right){x}-32a^{2}+97a+41$ |
| 9.1-b1 |
9.1-b |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$4.86504$ |
$(-a), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$75.57044505$ |
2.001909994 |
\( -\frac{542}{9} a^{2} - \frac{1373}{9} a + 1280 \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - 3 a - 6\) , \( a^{2} - 2 a - 5\) , \( 2 a^{2} - 5 a - 7\) , \( 2 a^{2} - 5 a - 7\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(2a^{2}-5a-7\right){x}+2a^{2}-5a-7$ |
| 9.1-c1 |
9.1-c |
$2$ |
$5$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{15} \) |
$4.86504$ |
$(-a), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.4 |
$1$ |
\( 2 \) |
$0.173720602$ |
$68.97404900$ |
1.904499510 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 2 a - 4\) , \( -a^{2} - 2 a + 20\) , \( -6 a^{2} - 8 a + 102\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-a^{2}-2a+20\right){x}-6a^{2}-8a+102$ |
| 9.1-c2 |
9.1-c |
$2$ |
$5$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$4.86504$ |
$(-a), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.3 |
$1$ |
\( 2 \) |
$0.868603010$ |
$13.79480980$ |
1.904499510 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( -1\) , \( a^{2} - 2 a - 4\) , \( -28 a^{2} + 87 a + 40\) , \( -172 a^{2} + 536 a + 242\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){y}={x}^{3}-{x}^{2}+\left(-28a^{2}+87a+40\right){x}-172a^{2}+536a+242$ |
| 9.2-a1 |
9.2-a |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{14} \) |
$4.86504$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$19.11603439$ |
1.012792243 |
\( -\frac{106502}{9} a^{2} - \frac{2396909}{81} a - \frac{270406}{27} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a\) , \( 5 a^{2} - 4 a - 28\) , \( 3128 a^{2} - 4386 a - 23244\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(5a^{2}-4a-28\right){x}+3128a^{2}-4386a-23244$ |
| 9.2-b1 |
9.2-b |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{6} \) |
$4.86504$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Ns |
$1$ |
\( 2 \) |
$1$ |
$70.29840988$ |
3.724500741 |
\( 155 a^{2} - 374 a - 625 \) |
\( \bigl[a^{2} - 2 a - 5\) , \( -a + 1\) , \( a^{2} - 2 a - 5\) , \( 10 a^{2} - 15 a - 69\) , \( 81 a^{2} - 115 a - 598\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a^{2}-15a-69\right){x}+81a^{2}-115a-598$ |
| 9.2-c1 |
9.2-c |
$2$ |
$5$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{7} \) |
$4.86504$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$16.83174693$ |
1.783535475 |
\( -\frac{44927975}{3} a^{2} + \frac{139885825}{3} a + 21257925 \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a^{2} - a - 6\) , \( 1\) , \( -264 a^{2} + 372 a + 1969\) , \( 6260 a^{2} - 8785 a - 46529\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-264a^{2}+372a+1969\right){x}+6260a^{2}-8785a-46529$ |
| 9.2-c2 |
9.2-c |
$2$ |
$5$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{11} \) |
$4.86504$ |
$(a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$16.83174693$ |
1.783535475 |
\( \frac{3328026115}{27} a^{2} - \frac{4710786470}{27} a - \frac{8274275080}{9} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a + 1\) , \( 37 a^{2} - 64 a - 299\) , \( 292 a^{2} - 399 a - 2148\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(37a^{2}-64a-299\right){x}+292a^{2}-399a-2148$ |
| 9.3-a1 |
9.3-a |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{6} \) |
$4.86504$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Ns |
$1$ |
\( 2 \) |
$1$ |
$45.93855201$ |
2.433883943 |
\( 155 a^{2} - 374 a - 625 \) |
\( \bigl[a\) , \( -a^{2} + 3 a + 6\) , \( a\) , \( 4 a^{2} - 4 a - 24\) , \( 26 a^{2} - 34 a - 191\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+3a+6\right){x}^{2}+\left(4a^{2}-4a-24\right){x}+26a^{2}-34a-191$ |
| 9.3-b1 |
9.3-b |
$2$ |
$3$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{3} \) |
$4.86504$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Ns.2.1 |
$1$ |
\( 2 \) |
$0.113744175$ |
$148.8699425$ |
2.691410898 |
\( 0 \) |
\( \bigl[0\) , \( -a^{2} + 2 a + 6\) , \( a^{2} - 2 a - 4\) , \( -a^{2} + a + 9\) , \( 4549316 a^{2} - 6385308 a - 33817577\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-a^{2}+a+9\right){x}+4549316a^{2}-6385308a-33817577$ |
| 9.3-b2 |
9.3-b |
$2$ |
$3$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{9} \) |
$4.86504$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Ns.2.1 |
$1$ |
\( 2 \) |
$0.341232527$ |
$49.62331419$ |
2.691410898 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} - 2 a - 6\) , \( a^{2} - a - 4\) , \( -a^{2} + a + 9\) , \( -32 a^{2} + 44 a + 235\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-a^{2}+a+9\right){x}-32a^{2}+44a+235$ |
| 9.3-c1 |
9.3-c |
$2$ |
$3$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{18} \) |
$4.86504$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$22.33223613$ |
1.183190774 |
\( \frac{7034321}{531441} a^{2} - \frac{175125119}{531441} a + \frac{508034336}{531441} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a^{2} - 3 a - 4\) , \( a^{2} - a - 5\) , \( -3862 a^{2} + 5415 a + 28729\) , \( -184917 a^{2} + 259537 a + 1374614\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-3a-4\right){x}^{2}+\left(-3862a^{2}+5415a+28729\right){x}-184917a^{2}+259537a+1374614$ |
| 9.3-c2 |
9.3-c |
$2$ |
$3$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{10} \) |
$4.86504$ |
$(-a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$200.9901252$ |
1.183190774 |
\( \frac{784388}{81} a^{2} - \frac{882887}{81} a - \frac{6594601}{81} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( 0\) , \( 30 a^{2} - 38 a - 213\) , \( -141 a^{2} + 202 a + 1057\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(30a^{2}-38a-213\right){x}-141a^{2}+202a+1057$ |
| 9.3-d1 |
9.3-d |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{7} \) |
$4.86504$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$6.857196146$ |
0.363303127 |
\( \frac{14380364140544}{3} a^{2} - \frac{20183928528896}{3} a - \frac{106897171640320}{3} \) |
\( \bigl[0\) , \( -a\) , \( a^{2} - 2 a - 5\) , \( -5 a^{2} - 15 a - 9\) , \( 40 a^{2} + 99 a + 26\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){y}={x}^{3}-a{x}^{2}+\left(-5a^{2}-15a-9\right){x}+40a^{2}+99a+26$ |
| 11.1-a1 |
11.1-a |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{4} \) |
$5.03050$ |
$(-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.497693048$ |
$52.78562543$ |
4.175620920 |
\( -\frac{591109825}{14641} a^{2} + \frac{168169524}{1331} a + \frac{806004216}{14641} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a^{2} - a - 4\) , \( a\) , \( 140 a^{2} - 198 a - 1028\) , \( 2126 a^{2} - 2985 a - 15799\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(140a^{2}-198a-1028\right){x}+2126a^{2}-2985a-15799$ |
| 11.1-b1 |
11.1-b |
$2$ |
$3$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( 11^{3} \) |
$5.03050$ |
$(-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$38.55367602$ |
3.063935482 |
\( -\frac{71901176}{1331} a^{2} + \frac{21181945}{121} a + \frac{106117741}{1331} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 2 a - 5\) , \( -175 a^{2} + 246 a + 1302\) , \( -5301 a^{2} + 7441 a + 39404\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-175a^{2}+246a+1302\right){x}-5301a^{2}+7441a+39404$ |
| 11.1-b2 |
11.1-b |
$2$ |
$3$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$5.03050$ |
$(-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$115.6610280$ |
3.063935482 |
\( \frac{57289}{11} a^{2} + 12766 a + \frac{43849}{11} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a^{2} + 3 a + 6\) , \( a^{2} - a - 5\) , \( a^{2} - 8\) , \( 15 a^{2} - 21 a - 112\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+3a+6\right){x}^{2}+\left(a^{2}-8\right){x}+15a^{2}-21a-112$ |
| 13.1-a1 |
13.1-a |
$2$ |
$5$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$5.17253$ |
$(a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.3 |
$1$ |
\( 1 \) |
$2.794653852$ |
$19.03173937$ |
4.226883983 |
\( \frac{38809925}{13} a^{2} - \frac{54585550}{13} a - \frac{288215000}{13} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 6\) , \( a\) , \( 22 a^{2} - 32 a - 162\) , \( 73 a^{2} - 103 a - 544\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(22a^{2}-32a-162\right){x}+73a^{2}-103a-544$ |
| 13.1-a2 |
13.1-a |
$2$ |
$5$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13^{5} \) |
$5.17253$ |
$(a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.4 |
$1$ |
\( 1 \) |
$0.558930770$ |
$95.15869685$ |
4.226883983 |
\( \frac{4918797644590}{371293} a^{2} - \frac{15315014588555}{371293} a - \frac{6981306875720}{371293} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -82334 a^{2} + 115562 a + 612034\) , \( 6163405 a^{2} - 8650805 a - 45815986\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-82334a^{2}+115562a+612034\right){x}+6163405a^{2}-8650805a-45815986$ |
| 13.1-b1 |
13.1-b |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$5.17253$ |
$(a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.028458616$ |
$323.1768987$ |
0.730916762 |
\( -\frac{23497}{13} a^{2} - \frac{67943}{13} a - \frac{12738}{13} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 2 a - 4\) , \( 1\) , \( -a + 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-a+3\right){x}$ |
| 15.1-a1 |
15.1-a |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5^{2} \) |
$5.29738$ |
$(-a), (a^2-2a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$59.11014797$ |
3.131732144 |
\( \frac{385024}{15} a^{2} - \frac{544768}{15} a - \frac{569344}{3} \) |
\( \bigl[0\) , \( -1\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 2 a - 5\) , \( a - 4\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){y}={x}^{3}-{x}^{2}+\left(a^{2}-2a-5\right){x}+a-4$ |
| 15.2-a1 |
15.2-a |
$2$ |
$2$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5^{2} \) |
$5.29738$ |
$(a+1), (a^2-2a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.204576795$ |
$116.8370875$ |
1.899550815 |
\( -\frac{8047692611944}{15} a^{2} + \frac{3765181743514}{5} a + \frac{19940978134969}{5} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 6\) , \( a^{2} - a - 5\) , \( 1415 a^{2} - 1985 a - 10517\) , \( -53200 a^{2} + 74671 a + 395466\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(1415a^{2}-1985a-10517\right){x}-53200a^{2}+74671a+395466$ |
| 15.2-a2 |
15.2-a |
$2$ |
$2$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5 \) |
$5.29738$ |
$(a+1), (a^2-2a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.409153590$ |
$233.6741750$ |
1.899550815 |
\( \frac{4319116}{15} a^{2} - \frac{6182804}{15} a - \frac{10545267}{5} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 6\) , \( a^{2} - a - 5\) , \( 90 a^{2} - 125 a - 667\) , \( -842 a^{2} + 1183 a + 6261\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(90a^{2}-125a-667\right){x}-842a^{2}+1183a+6261$ |
| 15.2-b1 |
15.2-b |
$2$ |
$2$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{18} \cdot 5^{2} \) |
$5.29738$ |
$(a+1), (a^2-2a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.906991072$ |
$24.70165572$ |
1.780503778 |
\( \frac{281426225401277}{98415} a^{2} + \frac{26283320909279}{3645} a + \frac{26904815786374}{10935} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( -a\) , \( a^{2} - a - 4\) , \( 9079 a^{2} - 13001 a - 68029\) , \( 886009 a^{2} - 1239508 a - 6577581\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-a{x}^{2}+\left(9079a^{2}-13001a-68029\right){x}+886009a^{2}-1239508a-6577581$ |
| 15.2-b2 |
15.2-b |
$2$ |
$2$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{9} \cdot 5 \) |
$5.29738$ |
$(a+1), (a^2-2a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.813982145$ |
$49.40331145$ |
1.780503778 |
\( \frac{4465456564105576}{1215} a^{2} - \frac{13903366882920959}{1215} a - \frac{2112787830911287}{405} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( -a\) , \( a^{2} - a - 4\) , \( 534 a^{2} - 766 a - 3999\) , \( 16132 a^{2} - 22567 a - 119754\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-a{x}^{2}+\left(534a^{2}-766a-3999\right){x}+16132a^{2}-22567a-119754$ |
| 15.2-c1 |
15.2-c |
$2$ |
$2$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5^{3} \) |
$5.29738$ |
$(a+1), (a^2-2a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.129388465$ |
$351.8107162$ |
0.904395636 |
\( \frac{389512}{15} a^{2} + \frac{472372}{15} a + \frac{42009}{5} \) |
\( \bigl[1\) , \( -a\) , \( a^{2} - 2 a - 5\) , \( -183 a^{2} + 570 a + 262\) , \( 2764 a^{2} - 8605 a - 3927\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}-a{x}^{2}+\left(-183a^{2}+570a+262\right){x}+2764a^{2}-8605a-3927$ |
| 15.2-c2 |
15.2-c |
$2$ |
$2$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
15.2 |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5^{6} \) |
$5.29738$ |
$(a+1), (a^2-2a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.064694232$ |
$175.9053581$ |
0.904395636 |
\( \frac{8462925074}{25} a^{2} - \frac{79053985648}{75} a - \frac{2401300911}{5} \) |
\( \bigl[1\) , \( -a\) , \( a^{2} - 2 a - 5\) , \( -2913 a^{2} + 9070 a + 4137\) , \( 185461 a^{2} - 577439 a - 263251\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}-a{x}^{2}+\left(-2913a^{2}+9070a+4137\right){x}+185461a^{2}-577439a-263251$ |
| 17.1-a1 |
17.1-a |
$2$ |
$2$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{10} \) |
$5.40905$ |
$(a^2-2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$43.82708487$ |
2.902519601 |
\( -\frac{238533260515372309}{2015993900449} a^{2} + \frac{338955890703061771}{2015993900449} a + \frac{1768759962848715626}{2015993900449} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a + 1\) , \( 1\) , \( 1390 a^{2} - 1955 a - 10319\) , \( -49800 a^{2} + 69894 a + 370205\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1390a^{2}-1955a-10319\right){x}-49800a^{2}+69894a+370205$ |
| 17.1-a2 |
17.1-a |
$2$ |
$2$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{5} \) |
$5.40905$ |
$(a^2-2a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$1$ |
$87.65416974$ |
2.902519601 |
\( \frac{7755775528024}{1419857} a^{2} - \frac{24147602657377}{1419857} a - \frac{11009075233835}{1419857} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a + 1\) , \( 1\) , \( 65 a^{2} - 95 a - 469\) , \( -1165 a^{2} + 1631 a + 8674\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(65a^{2}-95a-469\right){x}-1165a^{2}+1631a+8674$ |
| 19.2-a1 |
19.2-a |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{4} \) |
$5.51025$ |
$(2a^2-4a-11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.449345427$ |
$20.85950334$ |
1.489800475 |
\( -\frac{3974454988}{361} a^{2} + \frac{12374843136}{361} a + \frac{5641246179}{361} \) |
\( \bigl[a^{2} - a - 5\) , \( a - 1\) , \( a\) , \( 37 a^{2} - 48 a - 263\) , \( -346 a^{2} + 494 a + 2588\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(37a^{2}-48a-263\right){x}-346a^{2}+494a+2588$ |
| 23.1-a1 |
23.1-a |
$2$ |
$2$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$5.68854$ |
$(a^2-2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.276249520$ |
$80.08672246$ |
3.621881350 |
\( -\frac{2259279}{23} a^{2} + \frac{17685405}{23} a + \frac{47465244}{23} \) |
\( \bigl[a\) , \( a\) , \( a^{2} - a - 5\) , \( -a^{2} + 6 a - 1\) , \( 12 a^{2} - 34 a - 22\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+a{x}^{2}+\left(-a^{2}+6a-1\right){x}+12a^{2}-34a-22$ |
| 23.1-a2 |
23.1-a |
$2$ |
$2$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{2} \) |
$5.68854$ |
$(a^2-2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.552499040$ |
$20.02168061$ |
3.621881350 |
\( -\frac{237972698674119}{529} a^{2} + \frac{334012621341096}{529} a + \frac{1768982415055911}{529} \) |
\( \bigl[a\) , \( a\) , \( a^{2} - a - 5\) , \( -41 a^{2} + 141 a + 19\) , \( 432 a^{2} - 1315 a - 712\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+a{x}^{2}+\left(-41a^{2}+141a+19\right){x}+432a^{2}-1315a-712$ |
| 24.1-a1 |
24.1-a |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{12} \cdot 3^{4} \) |
$5.72903$ |
$(-a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.059565852$ |
$99.40686050$ |
1.882294343 |
\( -\frac{275921}{648} a^{2} - \frac{219929}{1296} a + \frac{9295}{648} \) |
\( \bigl[a^{2} - a - 5\) , \( 1\) , \( a^{2} - a - 4\) , \( -a^{2} + a + 5\) , \( -a^{2} + a + 5\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+{x}^{2}+\left(-a^{2}+a+5\right){x}-a^{2}+a+5$ |
| 25.1-a1 |
25.1-a |
$1$ |
$1$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{6} \) |
$5.76814$ |
$(a^2-2a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.197649637$ |
$120.0678055$ |
1.885977113 |
\( 155 a^{2} - 374 a - 625 \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a\) , \( a^{2} - 2 a - 4\) , \( a - 3\) , \( a^{2} + 3 a - 1\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+a{x}^{2}+\left(a-3\right){x}+a^{2}+3a-1$ |
| 27.1-a1 |
27.1-a |
$2$ |
$3$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{6} \) |
$5.84261$ |
$(-a), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$23.84680507$ |
3.790303792 |
\( \frac{147564223}{27} a^{2} - \frac{209290999}{27} a - \frac{1101593750}{27} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a^{2} - a - 6\) , \( a\) , \( 25 a^{2} - 35 a - 184\) , \( 109 a^{2} - 150 a - 823\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(25a^{2}-35a-184\right){x}+109a^{2}-150a-823$ |
| 27.1-a2 |
27.1-a |
$2$ |
$3$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{10} \) |
$5.84261$ |
$(-a), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 2 \) |
$1$ |
$7.948935025$ |
3.790303792 |
\( -\frac{12515862845}{3} a^{2} + \frac{38968609946}{3} a + \frac{17765280589}{3} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a\) , \( 0\) , \( -24 a^{2} + 84 a + 39\) , \( -178 a^{2} + 604 a + 273\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}={x}^{3}+a{x}^{2}+\left(-24a^{2}+84a+39\right){x}-178a^{2}+604a+273$ |
| 27.1-b1 |
27.1-b |
$2$ |
$3$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{10} \) |
$5.84261$ |
$(-a), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$0.189788381$ |
$42.06139251$ |
5.075245769 |
\( \frac{784388}{81} a^{2} - \frac{882887}{81} a - \frac{6594601}{81} \) |
\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{2} - 2 a - 4\) , \( 64 a^{2} - 84 a - 470\) , \( -450 a^{2} + 638 a + 3353\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+a{x}^{2}+\left(64a^{2}-84a-470\right){x}-450a^{2}+638a+3353$ |
| 27.1-b2 |
27.1-b |
$2$ |
$3$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{18} \) |
$5.84261$ |
$(-a), (a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.063262793$ |
$42.06139251$ |
5.075245769 |
\( \frac{7034321}{531441} a^{2} - \frac{175125119}{531441} a + \frac{508034336}{531441} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 6\) , \( a^{2} - a - 4\) , \( -8446 a^{2} + 11854 a + 62786\) , \( -605315 a^{2} + 849606 a + 4499639\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-8446a^{2}+11854a+62786\right){x}-605315a^{2}+849606a+4499639$ |
| 27.1-c1 |
27.1-c |
$2$ |
$5$ |
3.3.1425.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$5.84261$ |
$(-a), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$26.51632159$ |
1.404869037 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( a^{2} - 3 a - 4\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 8 a - 6\) , \( -a^{2} - 5 a + 2\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(a^{2}-3a-4\right){x}^{2}+\left(a^{2}-8a-6\right){x}-a^{2}-5a+2$ |
*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.
