| 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 |
| 2.1-a1 |
2.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{6} \) |
$1.47630$ |
$(9a+58)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.174484108$ |
$19.61204802$ |
2.955843377 |
\( \frac{8765}{64} a + \frac{46931}{64} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -997102094 a - 6427541423\) , \( 5396452882982 a + 34786733267797\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-997102094a-6427541423\right){x}+5396452882982a+34786733267797$ |
| 2.2-a1 |
2.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
2.2 |
\( 2 \) |
\( - 2^{6} \) |
$1.47630$ |
$(9a-67)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.174484108$ |
$19.61204802$ |
2.955843377 |
\( -\frac{8765}{64} a + \frac{3481}{4} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 997102094 a - 7424643565\) , \( -5397449985077 a + 40190610794296\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(997102094a-7424643565\right){x}-5397449985077a+40190610794296$ |
| 4.2-a1 |
4.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{8} \) |
$1.75563$ |
$(9a+58)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1.253442201$ |
$9.768128171$ |
1.762653726 |
\( 127760 a - 947728 \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -59 a - 380\) , \( 449 a + 2884\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-59a-380\right){x}+449a+2884$ |
| 4.2-a2 |
4.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{8} \) |
$1.75563$ |
$(9a+58)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.417814067$ |
$9.768128171$ |
1.762653726 |
\( 219920 a + 1417712 \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -12944719 a - 83444532\) , \( -66800788240 a - 430612710428\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-12944719a-83444532\right){x}-66800788240a-430612710428$ |
| 4.3-a1 |
4.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
4.3 |
\( 2^{2} \) |
\( - 2^{8} \) |
$1.75563$ |
$(9a-67)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1.253442201$ |
$9.768128171$ |
1.762653726 |
\( -127760 a - 819968 \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 59 a - 439\) , \( -450 a + 3333\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(59a-439\right){x}-450a+3333$ |
| 4.3-a2 |
4.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
4.3 |
\( 2^{2} \) |
\( - 2^{8} \) |
$1.75563$ |
$(9a-67)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.417814067$ |
$9.768128171$ |
1.762653726 |
\( -219920 a + 1637632 \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 12944719 a - 96389251\) , \( 66800788239 a - 497413498668\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(12944719a-96389251\right){x}+66800788239a-497413498668$ |
| 6.1-a1 |
6.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{2} \) |
$1.94292$ |
$(9a+58), (2a-15)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$0$ |
\( 2^{2} \) |
$1.936137913$ |
$54.86711879$ |
1.011123961 |
\( \frac{29620477}{36} a - \frac{217572205}{36} \) |
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 16091015449 a - 119817273067\) , \( -2928457927445299 a + 21805947829969921\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(16091015449a-119817273067\right){x}-2928457927445299a+21805947829969921$ |
| 6.1-b1 |
6.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{4} \cdot 3^{12} \) |
$1.94292$ |
$(9a+58), (2a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.116536241$ |
$6.304259119$ |
2.538385890 |
\( \frac{16608123325}{8503056} a + \frac{108939057107}{8503056} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -3362 a + 25136\) , \( 723821 a - 5389522\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-3362a+25136\right){x}+723821a-5389522$ |
| 6.1-b2 |
6.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{12} \cdot 3^{4} \) |
$1.94292$ |
$(9a+58), (2a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$0.349608724$ |
$6.304259119$ |
2.538385890 |
\( \frac{18088807909}{331776} a - \frac{97369373653}{331776} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 1360507364 a - 10130639756\) , \( 72092498259998 a - 536816746198054\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(1360507364a-10130639756\right){x}+72092498259998a-536816746198054$ |
| 6.4-a1 |
6.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{2} \) |
$1.94292$ |
$(9a-67), (2a+13)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.016001139$ |
$54.86711879$ |
1.011123961 |
\( -\frac{29620477}{36} a - \frac{15662644}{3} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -16091015449 a - 103726257618\) , \( 2928474018460748 a + 18877593628782240\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-16091015449a-103726257618\right){x}+2928474018460748a+18877593628782240$ |
| 6.4-b1 |
6.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( - 2^{12} \cdot 3^{4} \) |
$1.94292$ |
$(9a-67), (2a+13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$0.349608724$ |
$6.304259119$ |
2.538385890 |
\( -\frac{18088807909}{331776} a - \frac{1651678453}{6912} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1360507365 a - 8770132391\) , \( -72092498259998 a - 464724247938056\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1360507365a-8770132391\right){x}-72092498259998a-464724247938056$ |
| 6.4-b2 |
6.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( - 2^{4} \cdot 3^{12} \) |
$1.94292$ |
$(9a-67), (2a+13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.116536241$ |
$6.304259119$ |
2.538385890 |
\( -\frac{16608123325}{8503056} a + \frac{2615566259}{177147} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 3361 a + 21775\) , \( -723821 a - 4665701\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3361a+21775\right){x}-723821a-4665701$ |
| 7.1-a1 |
7.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$2.01926$ |
$(186a-1385)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.695579935$ |
$11.09844220$ |
1.111374459 |
\( -\frac{978944}{7} a - \frac{6295552}{7} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 40 a - 284\) , \( 62 a - 452\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(40a-284\right){x}+62a-452$ |
| 7.2-a1 |
7.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( -7 \) |
$2.01926$ |
$(-186a-1199)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.695579935$ |
$11.09844220$ |
1.111374459 |
\( \frac{978944}{7} a - \frac{7274496}{7} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -40 a - 244\) , \( -62 a - 390\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-40a-244\right){x}-62a-390$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{12} \) |
$2.08780$ |
$(9a+58), (9a-67)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$18.98778224$ |
5.467081892 |
\( -\frac{3645}{16} a + 2457 \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 76079034 a + 490422416\) , \( 1073733047729 a + 6921521588900\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(76079034a+490422416\right){x}+1073733047729a+6921521588900$ |
| 8.1-b1 |
8.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{18} \) |
$2.08780$ |
$(9a+58), (9a-67)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.567054283$ |
$27.08699714$ |
1.474163247 |
\( -\frac{5384765}{1024} a - \frac{100967}{64} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -73399 a - 473061\) , \( 28941427 a + 186563063\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-73399a-473061\right){x}+28941427a+186563063$ |
| 8.1-b2 |
8.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{38} \) |
$2.08780$ |
$(9a+58), (9a-67)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1.701162850$ |
$3.009666349$ |
1.474163247 |
\( -\frac{7077855903845}{1073741824} a + \frac{3387782773153}{67108864} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 316026 a + 2037259\) , \( 124583167 a + 803090951\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(316026a+2037259\right){x}+124583167a+803090951$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{12} \) |
$2.08780$ |
$(9a+58), (9a-67)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$18.98778224$ |
5.467081892 |
\( \frac{3645}{16} a + \frac{35667}{16} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -76079036 a + 566501450\) , \( -1073733047730 a + 7995254636629\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-76079036a+566501450\right){x}-1073733047730a+7995254636629$ |
| 8.2-b1 |
8.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{18} \) |
$2.08780$ |
$(9a+58), (9a-67)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.567054283$ |
$27.08699714$ |
1.474163247 |
\( \frac{5384765}{1024} a - \frac{7000237}{1024} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 73397 a - 546460\) , \( -28941428 a + 215504490\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(73397a-546460\right){x}-28941428a+215504490$ |
| 8.2-b2 |
8.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{38} \) |
$2.08780$ |
$(9a+58), (9a-67)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1.701162850$ |
$3.009666349$ |
1.474163247 |
\( \frac{7077855903845}{1073741824} a + \frac{47126668466603}{1073741824} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -316028 a + 2353285\) , \( -124583168 a + 927674118\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-316028a+2353285\right){x}-124583168a+927674118$ |
| 8.3-a1 |
8.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{10} \) |
$2.08780$ |
$(9a+58)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$29.91144035$ |
4.306145178 |
\( 305332 a + 1968524 \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -361059850 a - 2327471928\) , \( 9839737738550 a + 63429133832540\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-361059850a-2327471928\right){x}+9839737738550a+63429133832540$ |
| 8.4-a1 |
8.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{10} \) |
$2.08780$ |
$(9a-67)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$29.91144035$ |
4.306145178 |
\( -305332 a + 2273856 \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 361059850 a - 2688531778\) , \( -9839737738551 a + 73268871571090\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(361059850a-2688531778\right){x}-9839737738551a+73268871571090$ |
| 9.1-a1 |
9.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$2.15019$ |
$(2a-15), (2a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$4.877769064$ |
0.351109500 |
\( -\frac{262144}{27} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -1194764277440 a - 7701715763745\) , \( -2033430737977622730 a - 13107945947901041248\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-1194764277440a-7701715763745\right){x}-2033430737977622730a-13107945947901041248$ |
| 9.1-b1 |
9.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{5} \) |
$2.15019$ |
$(2a-15), (2a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.77806842$ |
1.639601242 |
\( -\frac{29596}{81} a + \frac{227473}{81} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 3645 a + 23496\) , \( -1365972 a - 8805359\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(3645a+23496\right){x}-1365972a-8805359$ |
| 9.1-b2 |
9.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{5} \) |
$2.15019$ |
$(2a-15), (2a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.77806842$ |
1.639601242 |
\( \frac{29596}{81} a + \frac{65959}{27} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -3645 a + 27141\) , \( 1365972 a - 10171331\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-3645a+27141\right){x}+1365972a-10171331$ |
| 9.1-b3 |
9.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$2.15019$ |
$(2a-15), (2a+13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$22.77806842$ |
1.639601242 |
\( \frac{117649}{9} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -914741399915 a - 5896626131618\) , \( -1169222979562069572 a - 7537070887590797737\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-914741399915a-5896626131618\right){x}-1169222979562069572a-7537070887590797737$ |
| 9.1-b4 |
9.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$2.15019$ |
$(2a-15), (2a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$5.694517106$ |
1.639601242 |
\( \frac{454756609}{3} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -14355839521115 a - 92540928473753\) , \( -78032921049237614610 a - 503017531980227308603\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-14355839521115a-92540928473753\right){x}-78032921049237614610a-503017531980227308603$ |
| 12.1-a1 |
12.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{25} \cdot 3^{9} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a-15)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$1.089613114$ |
5.647108910 |
\( -\frac{1179600739873172497}{2579890176} a - \frac{478964030264101379}{161243136} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -170462283 a - 1098837703\) , \( 3193269447819 a + 20584523749625\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-170462283a-1098837703\right){x}+3193269447819a+20584523749625$ |
| 12.1-b1 |
12.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3^{6} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$1$ |
$12.92015261$ |
0.930012935 |
\( -\frac{5689831}{46656} a + \frac{768431}{5832} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -10002481447 a + 74480697353\) , \( 1348252751477191 a - 10039389292497827\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-10002481447a+74480697353\right){x}+1348252751477191a-10039389292497827$ |
| 12.1-b2 |
12.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3^{3} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$25.84030522$ |
0.930012935 |
\( \frac{239839565}{1728} a + \frac{1551382603}{1728} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -17719623 a - 114224623\) , \( 106953450935 a + 689445687829\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-17719623a-114224623\right){x}+106953450935a+689445687829$ |
| 12.1-c1 |
12.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{5} \cdot 3^{3} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$28.22290706$ |
3.047293955 |
\( -\frac{30532205}{432} a + \frac{28484569}{54} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( a + 21\) , \( -3 a - 9\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(a+21\right){x}-3a-9$ |
| 12.1-c2 |
12.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{6} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a-15)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$28.22290706$ |
3.047293955 |
\( \frac{23600}{729} a + \frac{6313873}{2916} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 536841 a - 3997420\) , \( -191671979 a + 1427232092\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(536841a-3997420\right){x}-191671979a+1427232092$ |
| 12.1-c3 |
12.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{5} \cdot 3^{3} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$14.11145353$ |
3.047293955 |
\( -\frac{1420675}{432} a + \frac{31524571}{432} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -75752563129 a - 488317838584\) , \( -29373149835430081 a - 189345844523499520\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-75752563129a-488317838584\right){x}-29373149835430081a-189345844523499520$ |
| 12.1-c4 |
12.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3^{12} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$14.11145353$ |
3.047293955 |
\( \frac{88768547765}{531441} a + \frac{1146061856267}{1062882} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -2002859 a + 14913750\) , \( -1498092283 a + 11155127694\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-2002859a+14913750\right){x}-1498092283a+11155127694$ |
| 12.1-d1 |
12.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{27} \cdot 3^{3} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.111643759$ |
$6.436147815$ |
3.103366444 |
\( -\frac{38249833}{884736} a + \frac{36893783}{110592} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 330 a + 2131\) , \( 104628 a + 674445\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(330a+2131\right){x}+104628a+674445$ |
| 12.1-e1 |
12.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{15} \cdot 3^{2} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$12.92819349$ |
0.930591730 |
\( \frac{60421553}{147456} a - \frac{26798717}{9216} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 106 a - 793\) , \( -1797 a + 13367\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(106a-793\right){x}-1797a+13367$ |
| 12.1-e2 |
12.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3 \) |
$2.31053$ |
$(9a+58), (9a-67), (2a-15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$25.85638698$ |
0.930591730 |
\( -\frac{1083730391}{384} a + \frac{504605201}{24} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 27049582878 a - 201417198978\) , \( -6382173083123662 a + 47523077585696640\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(27049582878a-201417198978\right){x}-6382173083123662a+47523077585696640$ |
| 12.1-f1 |
12.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3^{7} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a-15)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$14.08939549$ |
8.113415035 |
\( -\frac{842890637}{559872} a - \frac{4473708931}{559872} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 19\) , \( 2 a - 13\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+19{x}+2a-13$ |
| 12.1-g1 |
12.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{11} \cdot 3^{5} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.123772114$ |
$11.92852476$ |
2.125498909 |
\( \frac{21325103}{31104} a - \frac{19816465}{3888} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 390968 a - 2911219\) , \( -382032235 a + 2844696830\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(390968a-2911219\right){x}-382032235a+2844696830$ |
| 12.2-a1 |
12.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{25} \cdot 3^{9} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$1.089613114$ |
5.647108910 |
\( \frac{1179600739873172497}{2579890176} a - \frac{2947675074699598187}{859963392} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 170462283 a - 1269299986\) , \( -3193269447819 a + 23777793197444\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(170462283a-1269299986\right){x}-3193269447819a+23777793197444$ |
| 12.2-b1 |
12.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3^{6} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \) |
$1$ |
$12.92015261$ |
0.930012935 |
\( \frac{5689831}{46656} a + \frac{152539}{15552} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 10002481447 a + 64478215906\) , \( -1348252751477191 a - 8691136541020636\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(10002481447a+64478215906\right){x}-1348252751477191a-8691136541020636$ |
| 12.2-b2 |
12.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3^{3} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$25.84030522$ |
0.930012935 |
\( -\frac{239839565}{1728} a + \frac{74634257}{72} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 17719623 a - 131944246\) , \( -106953450935 a + 796399138764\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(17719623a-131944246\right){x}-106953450935a+796399138764$ |
| 12.2-c1 |
12.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{2} \cdot 3^{12} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$14.11145353$ |
3.047293955 |
\( -\frac{88768547765}{531441} a + \frac{441199650599}{354294} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 2002859 a + 12910891\) , \( 1498092283 a + 9657035411\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2002859a+12910891\right){x}+1498092283a+9657035411$ |
| 12.2-c2 |
12.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{6} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a+13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$28.22290706$ |
3.047293955 |
\( -\frac{23600}{729} a + \frac{2136091}{972} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -536841 a - 3460579\) , \( 191671979 a + 1235560113\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-536841a-3460579\right){x}+191671979a+1235560113$ |
| 12.2-c3 |
12.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{5} \cdot 3^{3} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$14.11145353$ |
3.047293955 |
\( \frac{1420675}{432} a + \frac{1254329}{18} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 75752563129 a - 564070401713\) , \( 29373149835430081 a - 218718994358929601\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(75752563129a-564070401713\right){x}+29373149835430081a-218718994358929601$ |
| 12.2-c4 |
12.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{5} \cdot 3^{3} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$28.22290706$ |
3.047293955 |
\( \frac{30532205}{432} a + \frac{65781449}{144} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -a + 22\) , \( 3 a - 12\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+22\right){x}+3a-12$ |
| 12.2-d1 |
12.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{27} \cdot 3^{3} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a+13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.111643759$ |
$6.436147815$ |
3.103366444 |
\( \frac{38249833}{884736} a + \frac{85633477}{294912} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -331 a + 2461\) , \( -104629 a + 779073\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-331a+2461\right){x}-104629a+779073$ |
| 12.2-e1 |
12.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{15} \cdot 3^{2} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$12.92819349$ |
0.930591730 |
\( -\frac{60421553}{147456} a - \frac{122785973}{49152} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -107 a - 687\) , \( 1796 a + 11570\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-107a-687\right){x}+1796a+11570$ |
| 12.2-e2 |
12.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3 \) |
$2.31053$ |
$(9a+58), (9a-67), (2a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$25.85638698$ |
0.930591730 |
\( \frac{1083730391}{384} a + \frac{2329984275}{128} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -27049582879 a - 174367616100\) , \( 6382173083123661 a + 41140904502572978\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-27049582879a-174367616100\right){x}+6382173083123661a+41140904502572978$ |
| 12.2-f1 |
12.2-f |
$1$ |
$1$ |
\(\Q(\sqrt{193}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3^{7} \) |
$2.31053$ |
$(9a+58), (9a-67), (2a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$14.08939549$ |
8.113415035 |
\( \frac{842890637}{559872} a - \frac{110762491}{11664} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( a + 18\) , \( -4 a - 29\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+18\right){x}-4a-29$ |
*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.
