| 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 |
$2$ |
$2$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{10} \) |
$12.93108$ |
$(a^3+a^2-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$269.5324910$ |
1.015579165 |
\( \frac{13902918145}{1024} a^{3} + \frac{8433777799}{512} a^{2} - \frac{59975003189}{1024} a + \frac{6307656687}{1024} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -a^{3} + 6 a - 3\) , \( 2 a^{3} + a^{2} - 11 a + 3\) , \( -7 a^{3} + 8 a^{2} + 50 a - 69\) , \( -17 a^{3} + 19 a^{2} + 123 a - 173\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}+\left(2a^{3}+a^{2}-11a+3\right){y}={x}^{3}+\left(-a^{3}+6a-3\right){x}^{2}+\left(-7a^{3}+8a^{2}+50a-69\right){x}-17a^{3}+19a^{2}+123a-173$ |
| 2.1-a2 |
2.1-a |
$2$ |
$2$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$12.93108$ |
$(a^3+a^2-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$539.0649820$ |
1.015579165 |
\( -\frac{50247}{32} a^{3} - \frac{5985}{16} a^{2} + \frac{92659}{32} a + \frac{94679}{32} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( -a^{3} + 7 a - 3\) , \( a^{3} - 6 a + 3\) , \( -12 a^{3} - 14 a^{2} + 54 a - 4\) , \( -83 a^{3} - 100 a^{2} + 360 a - 39\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a^{3}-6a+3\right){y}={x}^{3}+\left(-a^{3}+7a-3\right){x}^{2}+\left(-12a^{3}-14a^{2}+54a-4\right){x}-83a^{3}-100a^{2}+360a-39$ |
| 2.1-b1 |
2.1-b |
$2$ |
$2$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{10} \) |
$12.93108$ |
$(a^3+a^2-5a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.095999855$ |
$376.9609313$ |
2.727090641 |
\( \frac{13902918145}{1024} a^{3} + \frac{8433777799}{512} a^{2} - \frac{59975003189}{1024} a + \frac{6307656687}{1024} \) |
\( \bigl[a\) , \( -a^{2} - 2 a + 5\) , \( a^{3} + a^{2} - 5 a - 1\) , \( 15 a^{3} + 6 a^{2} - 97 a + 18\) , \( 26 a^{3} + 12 a^{2} - 165 a + 21\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(-a^{2}-2a+5\right){x}^{2}+\left(15a^{3}+6a^{2}-97a+18\right){x}+26a^{3}+12a^{2}-165a+21$ |
| 2.1-b2 |
2.1-b |
$2$ |
$2$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$12.93108$ |
$(a^3+a^2-5a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.191999710$ |
$376.9609313$ |
2.727090641 |
\( -\frac{50247}{32} a^{3} - \frac{5985}{16} a^{2} + \frac{92659}{32} a + \frac{94679}{32} \) |
\( \bigl[a^{3} - 6 a + 4\) , \( a^{3} + a^{2} - 5 a\) , \( a^{3} - 5 a + 3\) , \( -8 a^{3} + 9 a^{2} + 60 a - 83\) , \( -26 a^{3} + 24 a^{2} + 187 a - 246\bigr] \) |
${y}^2+\left(a^{3}-6a+4\right){x}{y}+\left(a^{3}-5a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a\right){x}^{2}+\left(-8a^{3}+9a^{2}+60a-83\right){x}-26a^{3}+24a^{2}+187a-246$ |
| 4.1-a1 |
4.1-a |
$1$ |
$1$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$14.10144$ |
$(a^3+a^2-5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.029885437$ |
$2740.170709$ |
2.468481570 |
\( -29438 a^{3} - 15943 a^{2} + 153398 a - 95265 \) |
\( \bigl[a + 1\) , \( -a^{3} - a^{2} + 4 a\) , \( 2 a^{3} + a^{2} - 10 a + 3\) , \( -6 a^{3} - 6 a^{2} + 29 a - 4\) , \( 11 a^{3} + 13 a^{2} - 47 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(2a^{3}+a^{2}-10a+3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a\right){x}^{2}+\left(-6a^{3}-6a^{2}+29a-4\right){x}+11a^{3}+13a^{2}-47a+4$ |
| 4.1-b1 |
4.1-b |
$1$ |
$1$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$14.10144$ |
$(a^3+a^2-5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.038427825$ |
$623.0610233$ |
2.165161489 |
\( -29438 a^{3} - 15943 a^{2} + 153398 a - 95265 \) |
\( \bigl[a^{3} - 5 a + 4\) , \( -2 a^{3} - a^{2} + 12 a - 2\) , \( 0\) , \( -13 a^{3} - 5 a^{2} + 81 a - 13\) , \( -6 a^{3} - a^{2} + 38 a - 14\bigr] \) |
${y}^2+\left(a^{3}-5a+4\right){x}{y}={x}^{3}+\left(-2a^{3}-a^{2}+12a-2\right){x}^{2}+\left(-13a^{3}-5a^{2}+81a-13\right){x}-6a^{3}-a^{2}+38a-14$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{15} \) |
$15.37773$ |
$(-a^3+7a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$707.6226806$ |
5.332543387 |
\( \frac{4720379}{32} a^{3} - \frac{9119687}{16} a^{2} + \frac{9019057}{16} a - \frac{1754885}{32} \) |
\( \bigl[2 a^{3} + a^{2} - 10 a + 3\) , \( -a^{3} + 7 a - 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 37 a^{3} + 23 a^{2} - 217 a + 25\) , \( -44 a^{3} - 9 a^{2} + 310 a - 34\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-10a+3\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{3}+7a-3\right){x}^{2}+\left(37a^{3}+23a^{2}-217a+25\right){x}-44a^{3}-9a^{2}+310a-34$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{15} \) |
$15.37773$ |
$(-a^3+7a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.009921534$ |
$1061.582859$ |
1.587432980 |
\( \frac{4720379}{32} a^{3} - \frac{9119687}{16} a^{2} + \frac{9019057}{16} a - \frac{1754885}{32} \) |
\( \bigl[a^{3} - 6 a + 3\) , \( a^{2} + 2 a - 5\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 3 a^{3} - 3 a^{2} - 21 a + 27\bigr] \) |
${y}^2+\left(a^{3}-6a+3\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a^{2}+2a-5\right){x}^{2}+\left(a^{3}+a^{2}-4a-1\right){x}+3a^{3}-3a^{2}-21a+27$ |
| 14.1-a1 |
14.1-a |
$1$ |
$1$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$16.49195$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.056313965$ |
$441.2877219$ |
2.996336534 |
\( -\frac{3112729}{784} a^{3} + \frac{825441}{392} a^{2} + \frac{26502365}{784} a - \frac{32146199}{784} \) |
\( \bigl[2 a^{3} + a^{2} - 11 a + 3\) , \( -a^{2} - a + 4\) , \( 1\) , \( -3 a^{3} - 2 a^{2} + 19 a + 4\) , \( -4 a^{3} - 2 a^{2} + 26 a\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-11a+3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-3a^{3}-2a^{2}+19a+4\right){x}-4a^{3}-2a^{2}+26a$ |
| 14.1-b1 |
14.1-b |
$2$ |
$2$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{34} \cdot 7^{2} \) |
$16.49195$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 17 \) |
$0.054533573$ |
$179.5662673$ |
5.017995604 |
\( -\frac{1402574522628382639}{841813590016} a^{3} - \frac{348633256698689353}{420906795008} a^{2} + \frac{8799534999868774715}{841813590016} a - \frac{844138674551993185}{841813590016} \) |
\( \bigl[a\) , \( -a^{2} - a + 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( -4 a^{3} + 30 a - 32\) , \( 5 a^{3} - 7 a^{2} - 28 a + 41\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-4a^{3}+30a-32\right){x}+5a^{3}-7a^{2}-28a+41$ |
| 14.1-b2 |
14.1-b |
$2$ |
$2$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{17} \cdot 7^{4} \) |
$16.49195$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 17 \) |
$0.109067146$ |
$179.5662673$ |
5.017995604 |
\( -\frac{705345550725079}{314703872} a^{3} + \frac{1343251625907103}{157351936} a^{2} - \frac{2604379864571517}{314703872} a + \frac{252085497925447}{314703872} \) |
\( \bigl[a^{3} - 6 a + 4\) , \( -a^{3} - a^{2} + 6 a + 2\) , \( 2 a^{3} + a^{2} - 11 a + 2\) , \( 106 a^{3} + 127 a^{2} - 455 a + 56\) , \( 1513 a^{3} + 1834 a^{2} - 6526 a + 689\bigr] \) |
${y}^2+\left(a^{3}-6a+4\right){x}{y}+\left(2a^{3}+a^{2}-11a+2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+6a+2\right){x}^{2}+\left(106a^{3}+127a^{2}-455a+56\right){x}+1513a^{3}+1834a^{2}-6526a+689$ |
| 14.1-c1 |
14.1-c |
$1$ |
$1$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$16.49195$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.018230905$ |
$1191.147189$ |
5.236683102 |
\( -\frac{3112729}{784} a^{3} + \frac{825441}{392} a^{2} + \frac{26502365}{784} a - \frac{32146199}{784} \) |
\( \bigl[2 a^{3} + a^{2} - 10 a + 2\) , \( a^{3} + a^{2} - 6 a - 1\) , \( 2 a^{3} + a^{2} - 11 a + 3\) , \( 8 a^{3} + 9 a^{2} - 40 a + 4\) , \( 19 a^{3} + 23 a^{2} - 85 a + 8\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-10a+2\right){x}{y}+\left(2a^{3}+a^{2}-11a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-1\right){x}^{2}+\left(8a^{3}+9a^{2}-40a+4\right){x}+19a^{3}+23a^{2}-85a+8$ |
| 14.1-d1 |
14.1-d |
$2$ |
$2$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{17} \cdot 7^{4} \) |
$16.49195$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.810611253$ |
$76.91955795$ |
1.879498800 |
\( -\frac{705345550725079}{314703872} a^{3} + \frac{1343251625907103}{157351936} a^{2} - \frac{2604379864571517}{314703872} a + \frac{252085497925447}{314703872} \) |
\( \bigl[1\) , \( -2 a^{3} - a^{2} + 12 a - 2\) , \( 2 a^{3} + a^{2} - 11 a + 2\) , \( -7 a^{3} + 47 a - 29\) , \( 2 a^{3} - 3 a^{2} - 13 a + 17\bigr] \) |
${y}^2+{x}{y}+\left(2a^{3}+a^{2}-11a+2\right){y}={x}^{3}+\left(-2a^{3}-a^{2}+12a-2\right){x}^{2}+\left(-7a^{3}+47a-29\right){x}+2a^{3}-3a^{2}-13a+17$ |
| 14.1-d2 |
14.1-d |
$2$ |
$2$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{34} \cdot 7^{2} \) |
$16.49195$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.621222506$ |
$38.45977897$ |
1.879498800 |
\( -\frac{1402574522628382639}{841813590016} a^{3} - \frac{348633256698689353}{420906795008} a^{2} + \frac{8799534999868774715}{841813590016} a - \frac{844138674551993185}{841813590016} \) |
\( \bigl[2 a^{3} + a^{2} - 11 a + 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 6 a + 3\) , \( 986 a^{3} + 480 a^{2} - 6186 a + 662\) , \( 25024 a^{3} + 12147 a^{2} - 157124 a + 16845\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-11a+3\right){x}{y}+\left(a^{3}-6a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(986a^{3}+480a^{2}-6186a+662\right){x}+25024a^{3}+12147a^{2}-157124a+16845$ |
| 16.2-a1 |
16.2-a |
$1$ |
$1$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.76953$ |
$(a^3+a^2-5a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$174.4631331$ |
1.314729237 |
\( 284127 a^{3} - 1081423 a^{2} + 1047747 a - 100847 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 1\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 5 a - 1\) , \( 2 a^{3} + 3 a^{2} - 9 a + 3\) , \( -6 a^{3} - 7 a^{2} + 26 a - 2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-1\right){x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(2a^{3}+3a^{2}-9a+3\right){x}-6a^{3}-7a^{2}+26a-2$ |
| 16.2-b1 |
16.2-b |
$1$ |
$1$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.76953$ |
$(a^3+a^2-5a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$163.9793903$ |
1.235725249 |
\( 284127 a^{3} - 1081423 a^{2} + 1047747 a - 100847 \) |
\( \bigl[2 a^{3} + a^{2} - 10 a + 3\) , \( -2 a^{3} - a^{2} + 12 a - 3\) , \( 0\) , \( 3 a^{3} + a^{2} - 14 a + 33\) , \( -17 a^{3} + 21 a^{2} + 132 a - 163\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-10a+3\right){x}{y}={x}^{3}+\left(-2a^{3}-a^{2}+12a-3\right){x}^{2}+\left(3a^{3}+a^{2}-14a+33\right){x}-17a^{3}+21a^{2}+132a-163$ |
| 20.1-a1 |
20.1-a |
$2$ |
$3$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$17.24387$ |
$(a^3+a^2-5a+1), (-a^3-a^2+4a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.096979135$ |
$555.1780208$ |
3.245885640 |
\( \frac{577683}{625} a^{3} + \frac{150876}{625} a^{2} - \frac{3697308}{625} a + \frac{1213771}{625} \) |
\( \bigl[a^{3} + a^{2} - 4 a\) , \( -a^{2} - 2 a + 3\) , \( 2 a^{3} + a^{2} - 11 a + 2\) , \( -a^{2} - a + 3\) , \( 2 a^{3} + a^{2} - 12 a + 2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a\right){x}{y}+\left(2a^{3}+a^{2}-11a+2\right){y}={x}^{3}+\left(-a^{2}-2a+3\right){x}^{2}+\left(-a^{2}-a+3\right){x}+2a^{3}+a^{2}-12a+2$ |
| 20.1-a2 |
20.1-a |
$2$ |
$3$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \) |
$17.24387$ |
$(a^3+a^2-5a+1), (-a^3-a^2+4a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.290937407$ |
$61.68644675$ |
3.245885640 |
\( \frac{3572627025204800007}{244140625} a^{3} + \frac{1734078654053521929}{244140625} a^{2} - \frac{22432655728011652257}{244140625} a + \frac{2405188399233704509}{244140625} \) |
\( \bigl[a^{3} + a^{2} - 4 a\) , \( -a^{2} - 2 a + 3\) , \( 2 a^{3} + a^{2} - 11 a + 2\) , \( 15 a^{3} + 4 a^{2} - 101 a + 13\) , \( -85 a^{3} - 52 a^{2} + 517 a - 55\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a\right){x}{y}+\left(2a^{3}+a^{2}-11a+2\right){y}={x}^{3}+\left(-a^{2}-2a+3\right){x}^{2}+\left(15a^{3}+4a^{2}-101a+13\right){x}-85a^{3}-52a^{2}+517a-55$ |
| 20.1-b1 |
20.1-b |
$2$ |
$3$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{12} \) |
$17.24387$ |
$(a^3+a^2-5a+1), (-a^3-a^2+4a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$2.260030634$ |
$2.983678530$ |
3.658739634 |
\( \frac{3572627025204800007}{244140625} a^{3} + \frac{1734078654053521929}{244140625} a^{2} - \frac{22432655728011652257}{244140625} a + \frac{2405188399233704509}{244140625} \) |
\( \bigl[a^{3} - 6 a + 3\) , \( a^{3} - 6 a + 4\) , \( a^{3} + a^{2} - 5 a - 1\) , \( -53 a^{3} + 45 a^{2} + 376 a - 488\) , \( -630 a^{3} + 514 a^{2} + 4622 a - 5937\bigr] \) |
${y}^2+\left(a^{3}-6a+3\right){x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a+4\right){x}^{2}+\left(-53a^{3}+45a^{2}+376a-488\right){x}-630a^{3}+514a^{2}+4622a-5937$ |
| 20.1-b2 |
20.1-b |
$2$ |
$3$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$17.24387$ |
$(a^3+a^2-5a+1), (-a^3-a^2+4a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.753343544$ |
$241.6779609$ |
3.658739634 |
\( \frac{577683}{625} a^{3} + \frac{150876}{625} a^{2} - \frac{3697308}{625} a + \frac{1213771}{625} \) |
\( \bigl[a^{3} - 6 a + 3\) , \( a^{3} - 6 a + 4\) , \( a^{3} + a^{2} - 5 a - 1\) , \( 7 a^{3} - 5 a^{2} - 49 a + 57\) , \( 15 a^{3} - 12 a^{2} - 113 a + 143\bigr] \) |
${y}^2+\left(a^{3}-6a+3\right){x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a+4\right){x}^{2}+\left(7a^{3}-5a^{2}-49a+57\right){x}+15a^{3}-12a^{2}-113a+143$ |
| 22.1-a1 |
22.1-a |
$2$ |
$5$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{5} \cdot 11^{15} \) |
$17.45053$ |
$(a^3+a^2-5a+1), (a^3-6a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$5.922091815$ |
1.115700938 |
\( \frac{9490847137992359103500120676591}{133671941421300832} a^{3} + \frac{2303385139035408331944609147369}{66835970710650416} a^{2} - \frac{59593076224960684051570256631707}{133671941421300832} a + \frac{6389461144447085830854130185345}{133671941421300832} \) |
\( \bigl[2 a^{3} + a^{2} - 11 a + 3\) , \( -a^{3} + 7 a - 2\) , \( a^{3} - 5 a + 3\) , \( -84 a^{3} + 13 a^{2} + 660 a - 743\) , \( 2047 a^{3} - 2450 a^{2} - 13835 a + 19248\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-11a+3\right){x}{y}+\left(a^{3}-5a+3\right){y}={x}^{3}+\left(-a^{3}+7a-2\right){x}^{2}+\left(-84a^{3}+13a^{2}+660a-743\right){x}+2047a^{3}-2450a^{2}-13835a+19248$ |
| 22.1-a2 |
22.1-a |
$2$ |
$5$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{25} \cdot 11^{3} \) |
$17.45053$ |
$(a^3+a^2-5a+1), (a^3-6a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$148.0522953$ |
1.115700938 |
\( -\frac{224434265826801}{44660948992} a^{3} + \frac{446665945759721}{22330474496} a^{2} - \frac{868050440285979}{44660948992} a + \frac{42220806083329}{44660948992} \) |
\( \bigl[2 a^{3} + a^{2} - 11 a + 3\) , \( -a^{3} + 7 a - 2\) , \( a^{3} - 5 a + 3\) , \( -9 a^{3} + 3 a^{2} + 70 a - 48\) , \( -23 a^{3} + 17 a^{2} + 166 a - 168\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-11a+3\right){x}{y}+\left(a^{3}-5a+3\right){y}={x}^{3}+\left(-a^{3}+7a-2\right){x}^{2}+\left(-9a^{3}+3a^{2}+70a-48\right){x}-23a^{3}+17a^{2}+166a-168$ |
| 22.1-b1 |
22.1-b |
$2$ |
$5$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{25} \cdot 11^{3} \) |
$17.45053$ |
$(a^3+a^2-5a+1), (a^3-6a+4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 3 \cdot 5^{2} \) |
$1$ |
$163.1554231$ |
3.688547851 |
\( -\frac{224434265826801}{44660948992} a^{3} + \frac{446665945759721}{22330474496} a^{2} - \frac{868050440285979}{44660948992} a + \frac{42220806083329}{44660948992} \) |
\( \bigl[2 a^{3} + a^{2} - 10 a + 2\) , \( a^{3} - 5 a + 2\) , \( 0\) , \( 35 a^{3} + 22 a^{2} - 207 a + 23\) , \( 364 a^{3} + 184 a^{2} - 2266 a + 243\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-10a+2\right){x}{y}={x}^{3}+\left(a^{3}-5a+2\right){x}^{2}+\left(35a^{3}+22a^{2}-207a+23\right){x}+364a^{3}+184a^{2}-2266a+243$ |
| 22.1-b2 |
22.1-b |
$2$ |
$5$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{5} \cdot 11^{15} \) |
$17.45053$ |
$(a^3+a^2-5a+1), (a^3-6a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 3 \cdot 5^{2} \) |
$1$ |
$0.261048677$ |
3.688547851 |
\( \frac{9490847137992359103500120676591}{133671941421300832} a^{3} + \frac{2303385139035408331944609147369}{66835970710650416} a^{2} - \frac{59593076224960684051570256631707}{133671941421300832} a + \frac{6389461144447085830854130185345}{133671941421300832} \) |
\( \bigl[2 a^{3} + a^{2} - 10 a + 2\) , \( a^{3} - 5 a + 2\) , \( 0\) , \( 25415 a^{3} + 12302 a^{2} - 159652 a + 17118\) , \( 3260309 a^{3} + 1582114 a^{2} - 20472503 a + 2195029\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-10a+2\right){x}{y}={x}^{3}+\left(a^{3}-5a+2\right){x}^{2}+\left(25415a^{3}+12302a^{2}-159652a+17118\right){x}+3260309a^{3}+1582114a^{2}-20472503a+2195029$ |
| 25.1-a1 |
25.1-a |
$1$ |
$1$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{7} \) |
$17.73162$ |
$(-a^3-a^2+4a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$60.50848234$ |
0.911966550 |
\( \frac{70511858}{5} a^{3} + \frac{20855046}{5} a^{2} - \frac{478832313}{5} a + \frac{51535651}{5} \) |
\( \bigl[a^{3} + a^{2} - 4 a\) , \( a + 1\) , \( a^{3} + a^{2} - 5 a\) , \( 14 a^{3} + 12 a^{2} - 74 a + 7\) , \( a^{3} + 9 a^{2} + 16 a - 4\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a\right){x}{y}+\left(a^{3}+a^{2}-5a\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(14a^{3}+12a^{2}-74a+7\right){x}+a^{3}+9a^{2}+16a-4$ |
| 25.1-b1 |
25.1-b |
$4$ |
$4$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{7} \) |
$17.73162$ |
$(-a^3-a^2+4a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$361.5960395$ |
2.724936074 |
\( -\frac{29421}{5} a^{3} + \frac{71663}{5} a^{2} + \frac{29111}{5} a - \frac{98662}{5} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -2 a^{3} - a^{2} + 11 a - 3\) , \( a^{3} + a^{2} - 5 a - 1\) , \( -15 a^{3} - 8 a^{2} + 77 a - 41\) , \( 41 a^{3} + 66 a^{2} - 157 a - 44\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(-2a^{3}-a^{2}+11a-3\right){x}^{2}+\left(-15a^{3}-8a^{2}+77a-41\right){x}+41a^{3}+66a^{2}-157a-44$ |
| 25.1-b2 |
25.1-b |
$4$ |
$4$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{10} \) |
$17.73162$ |
$(-a^3-a^2+4a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$361.5960395$ |
2.724936074 |
\( \frac{84129534731394}{625} a^{3} + \frac{102106440533343}{625} a^{2} - \frac{362875625915269}{625} a + \frac{38004369760703}{625} \) |
\( \bigl[a\) , \( a^{3} - 6 a + 3\) , \( a^{3} + a^{2} - 5 a\) , \( -7 a^{3} + 13 a^{2} + 17 a - 30\) , \( -9 a^{3} + a^{2} + 81 a - 92\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-6a+3\right){x}^{2}+\left(-7a^{3}+13a^{2}+17a-30\right){x}-9a^{3}+a^{2}+81a-92$ |
| 25.1-b3 |
25.1-b |
$4$ |
$4$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{7} \) |
$17.73162$ |
$(-a^3-a^2+4a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$22.59975247$ |
2.724936074 |
\( \frac{88635127010427516}{5} a^{3} - \frac{79033479804681463}{5} a^{2} - \frac{629007411085314741}{5} a + \frac{818212288924880927}{5} \) |
\( \bigl[a^{3} - 6 a + 4\) , \( -2 a^{3} - a^{2} + 12 a - 1\) , \( 1\) , \( -10 a^{3} - 19 a^{2} + 87 a - 31\) , \( 14 a^{3} - 66 a^{2} + 131 a - 80\bigr] \) |
${y}^2+\left(a^{3}-6a+4\right){x}{y}+{y}={x}^{3}+\left(-2a^{3}-a^{2}+12a-1\right){x}^{2}+\left(-10a^{3}-19a^{2}+87a-31\right){x}+14a^{3}-66a^{2}+131a-80$ |
| 25.1-b4 |
25.1-b |
$4$ |
$4$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.73162$ |
$(-a^3-a^2+4a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$361.5960395$ |
2.724936074 |
\( \frac{1148136599}{25} a^{3} - \frac{1016813522}{25} a^{2} - \frac{8138669224}{25} a + \frac{10569806338}{25} \) |
\( \bigl[a^{3} - 6 a + 4\) , \( -2 a^{3} - a^{2} + 12 a - 1\) , \( 1\) , \( -10 a^{3} - 9 a^{2} + 57 a - 6\) , \( 4 a^{3} + 8 a^{2} - 4 a - 1\bigr] \) |
${y}^2+\left(a^{3}-6a+4\right){x}{y}+{y}={x}^{3}+\left(-2a^{3}-a^{2}+12a-1\right){x}^{2}+\left(-10a^{3}-9a^{2}+57a-6\right){x}+4a^{3}+8a^{2}-4a-1$ |
| 25.1-c1 |
25.1-c |
$4$ |
$4$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{7} \) |
$17.73162$ |
$(-a^3-a^2+4a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.080678829$ |
$329.7990932$ |
3.208201838 |
\( \frac{88635127010427516}{5} a^{3} - \frac{79033479804681463}{5} a^{2} - \frac{629007411085314741}{5} a + \frac{818212288924880927}{5} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( -a^{2} - a + 5\) , \( a^{3} + a^{2} - 5 a\) , \( 302 a^{3} + 186 a^{2} - 1875 a - 48\) , \( -4460 a^{3} - 2355 a^{2} + 27890 a - 1825\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a^{3}+a^{2}-5a\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(302a^{3}+186a^{2}-1875a-48\right){x}-4460a^{3}-2355a^{2}+27890a-1825$ |
| 25.1-c2 |
25.1-c |
$4$ |
$4$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$17.73162$ |
$(-a^3-a^2+4a-1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.080678829$ |
$1319.196373$ |
3.208201838 |
\( \frac{1148136599}{25} a^{3} - \frac{1016813522}{25} a^{2} - \frac{8138669224}{25} a + \frac{10569806338}{25} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( -a^{2} - a + 5\) , \( a^{3} + a^{2} - 5 a\) , \( 22 a^{3} + 11 a^{2} - 140 a + 7\) , \( -31 a^{3} - 16 a^{2} + 193 a - 18\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a^{3}+a^{2}-5a\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(22a^{3}+11a^{2}-140a+7\right){x}-31a^{3}-16a^{2}+193a-18$ |
| 25.1-c3 |
25.1-c |
$4$ |
$4$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{7} \) |
$17.73162$ |
$(-a^3-a^2+4a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.020169707$ |
$1319.196373$ |
3.208201838 |
\( -\frac{29421}{5} a^{3} + \frac{71663}{5} a^{2} + \frac{29111}{5} a - \frac{98662}{5} \) |
\( \bigl[2 a^{3} + a^{2} - 10 a + 2\) , \( -a - 1\) , \( a^{3} - 6 a + 3\) , \( 2 a^{3} + 5 a^{2} - 14 a\) , \( a^{3} + 5 a^{2} - 10 a\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-10a+2\right){x}{y}+\left(a^{3}-6a+3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a^{3}+5a^{2}-14a\right){x}+a^{3}+5a^{2}-10a$ |
| 25.1-c4 |
25.1-c |
$4$ |
$4$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{10} \) |
$17.73162$ |
$(-a^3-a^2+4a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.080678829$ |
$329.7990932$ |
3.208201838 |
\( \frac{84129534731394}{625} a^{3} + \frac{102106440533343}{625} a^{2} - \frac{362875625915269}{625} a + \frac{38004369760703}{625} \) |
\( \bigl[2 a^{3} + a^{2} - 11 a + 3\) , \( 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 1137 a^{3} + 553 a^{2} - 7141 a + 768\) , \( 32538 a^{3} + 15795 a^{2} - 204306 a + 21905\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-11a+3\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+{x}^{2}+\left(1137a^{3}+553a^{2}-7141a+768\right){x}+32538a^{3}+15795a^{2}-204306a+21905$ |
| 25.1-d1 |
25.1-d |
$1$ |
$1$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{7} \) |
$17.73162$ |
$(-a^3-a^2+4a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$9$ |
\( 2 \) |
$1$ |
$21.62055716$ |
2.932729718 |
\( \frac{70511858}{5} a^{3} + \frac{20855046}{5} a^{2} - \frac{478832313}{5} a + \frac{51535651}{5} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 1\) , \( -a^{2} - a + 5\) , \( 2 a^{3} + a^{2} - 11 a + 3\) , \( -5 a^{3} - 19 a^{2} + 32 a + 8\) , \( -9 a^{3} - 96 a^{2} + 168 a - 12\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-1\right){x}{y}+\left(2a^{3}+a^{2}-11a+3\right){y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-5a^{3}-19a^{2}+32a+8\right){x}-9a^{3}-96a^{2}+168a-12$ |
| 28.1-a1 |
28.1-a |
$4$ |
$6$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$17.98459$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$4.372512176$ |
$43.83495528$ |
4.333167762 |
\( \frac{24039395414608477}{343} a^{3} + \frac{29176248520407432}{343} a^{2} - \frac{103688812477624586}{343} a + \frac{10859439730169291}{343} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 1\) , \( -2 a^{3} - a^{2} + 11 a - 3\) , \( a^{3} + a^{2} - 4 a\) , \( 152 a^{3} - 144 a^{2} - 1092 a + 1456\) , \( -820 a^{3} + 699 a^{2} + 5903 a - 7612\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-1\right){x}{y}+\left(a^{3}+a^{2}-4a\right){y}={x}^{3}+\left(-2a^{3}-a^{2}+11a-3\right){x}^{2}+\left(152a^{3}-144a^{2}-1092a+1456\right){x}-820a^{3}+699a^{2}+5903a-7612$ |
| 28.1-a2 |
28.1-a |
$4$ |
$6$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$17.98459$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1.457504058$ |
$394.5145975$ |
4.333167762 |
\( \frac{47713}{7} a^{3} + \frac{110085}{7} a^{2} - \frac{133429}{7} a - \frac{186569}{7} \) |
\( \bigl[a^{3} - 6 a + 3\) , \( a^{3} - 7 a + 4\) , \( a^{3} + a^{2} - 4 a\) , \( -7 a^{3} - 5 a^{2} + 35 a - 18\) , \( -21 a^{3} - 8 a^{2} + 114 a - 83\bigr] \) |
${y}^2+\left(a^{3}-6a+3\right){x}{y}+\left(a^{3}+a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-7a+4\right){x}^{2}+\left(-7a^{3}-5a^{2}+35a-18\right){x}-21a^{3}-8a^{2}+114a-83$ |
| 28.1-a3 |
28.1-a |
$4$ |
$6$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{4} \cdot 7^{2} \) |
$17.98459$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.728752029$ |
$394.5145975$ |
4.333167762 |
\( \frac{4948470311}{49} a^{3} - \frac{4432416146}{49} a^{2} - \frac{35130292108}{49} a + \frac{45807353181}{49} \) |
\( \bigl[a^{3} - 5 a + 4\) , \( -2 a^{3} - a^{2} + 11 a - 1\) , \( a^{3} + a^{2} - 5 a - 1\) , \( -3 a^{3} - 4 a^{2} + 19 a + 3\) , \( -2 a^{3} - a^{2} + 11 a - 2\bigr] \) |
${y}^2+\left(a^{3}-5a+4\right){x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(-2a^{3}-a^{2}+11a-1\right){x}^{2}+\left(-3a^{3}-4a^{2}+19a+3\right){x}-2a^{3}-a^{2}+11a-2$ |
| 28.1-a4 |
28.1-a |
$4$ |
$6$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{4} \cdot 7^{6} \) |
$17.98459$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$2.186256088$ |
$43.83495528$ |
4.333167762 |
\( -\frac{58991001474401370845134}{117649} a^{3} - \frac{28633695056137501631935}{117649} a^{2} + \frac{370404780368043596995741}{117649} a - \frac{39714126185228454891650}{117649} \) |
\( \bigl[a^{3} - 5 a + 4\) , \( -2 a^{3} - a^{2} + 11 a - 1\) , \( a^{3} + a^{2} - 5 a - 1\) , \( 22 a^{3} - 14 a^{2} - 121 a + 18\) , \( -69 a^{3} - 215 a^{2} + 736 a - 78\bigr] \) |
${y}^2+\left(a^{3}-5a+4\right){x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(-2a^{3}-a^{2}+11a-1\right){x}^{2}+\left(22a^{3}-14a^{2}-121a+18\right){x}-69a^{3}-215a^{2}+736a-78$ |
| 28.1-b1 |
28.1-b |
$4$ |
$6$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{4} \cdot 7^{6} \) |
$17.98459$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3 \) |
$1$ |
$7.118938551$ |
0.724238596 |
\( -\frac{58991001474401370845134}{117649} a^{3} - \frac{28633695056137501631935}{117649} a^{2} + \frac{370404780368043596995741}{117649} a - \frac{39714126185228454891650}{117649} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 1\) , \( a^{3} - 6 a + 2\) , \( a^{3} + a^{2} - 5 a - 1\) , \( -1895 a^{3} - 2285 a^{2} + 8193 a - 922\) , \( -89471 a^{3} - 108595 a^{2} + 385907 a - 40395\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-1\right){x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a+2\right){x}^{2}+\left(-1895a^{3}-2285a^{2}+8193a-922\right){x}-89471a^{3}-108595a^{2}+385907a-40395$ |
| 28.1-b2 |
28.1-b |
$4$ |
$6$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{4} \cdot 7^{2} \) |
$17.98459$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$576.6340226$ |
0.724238596 |
\( \frac{4948470311}{49} a^{3} - \frac{4432416146}{49} a^{2} - \frac{35130292108}{49} a + \frac{45807353181}{49} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 1\) , \( a^{3} - 6 a + 2\) , \( a^{3} + a^{2} - 5 a - 1\) , \( -10 a^{3} + 58 a - 57\) , \( -300 a^{3} - 391 a^{2} + 1258 a - 25\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-1\right){x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a+2\right){x}^{2}+\left(-10a^{3}+58a-57\right){x}-300a^{3}-391a^{2}+1258a-25$ |
| 28.1-b3 |
28.1-b |
$4$ |
$6$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7 \) |
$17.98459$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$1153.268045$ |
0.724238596 |
\( \frac{47713}{7} a^{3} + \frac{110085}{7} a^{2} - \frac{133429}{7} a - \frac{186569}{7} \) |
\( \bigl[2 a^{3} + a^{2} - 10 a + 3\) , \( -a + 1\) , \( 2 a^{3} + a^{2} - 11 a + 2\) , \( 7 a^{3} + 9 a^{2} - 39 a + 4\) , \( 11 a^{3} + 15 a^{2} - 58 a + 6\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-10a+3\right){x}{y}+\left(2a^{3}+a^{2}-11a+2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7a^{3}+9a^{2}-39a+4\right){x}+11a^{3}+15a^{2}-58a+6$ |
| 28.1-b4 |
28.1-b |
$4$ |
$6$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{3} \) |
$17.98459$ |
$(a^3+a^2-5a+1), (-a^3+6a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$14.23787710$ |
0.724238596 |
\( \frac{24039395414608477}{343} a^{3} + \frac{29176248520407432}{343} a^{2} - \frac{103688812477624586}{343} a + \frac{10859439730169291}{343} \) |
\( \bigl[2 a^{3} + a^{2} - 10 a + 3\) , \( -a + 1\) , \( 2 a^{3} + a^{2} - 11 a + 2\) , \( 62 a^{3} + 34 a^{2} - 389 a + 44\) , \( 385 a^{3} + 187 a^{2} - 2428 a + 262\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-10a+3\right){x}{y}+\left(2a^{3}+a^{2}-11a+2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(62a^{3}+34a^{2}-389a+44\right){x}+385a^{3}+187a^{2}-2428a+262$ |
| 34.2-a1 |
34.2-a |
$4$ |
$6$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( 2^{3} \cdot 17^{2} \) |
$18.42641$ |
$(a^3+a^2-5a+1), (a^3+a^2-6a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$687.2982082$ |
1.150973570 |
\( \frac{49443369}{2312} a^{3} - \frac{21426461}{1156} a^{2} - \frac{350284029}{2312} a + \frac{452824007}{2312} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a + 1\) , \( 2 a^{2} + 4 a - 4\) , \( 6 a^{3} + 3 a^{2} - 34 a + 13\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(2a^{2}+4a-4\right){x}+6a^{3}+3a^{2}-34a+13$ |
| 34.2-a2 |
34.2-a |
$4$ |
$6$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( 2^{9} \cdot 17^{6} \) |
$18.42641$ |
$(a^3+a^2-5a+1), (a^3+a^2-6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 2 \) |
$1$ |
$8.485163065$ |
1.150973570 |
\( -\frac{153836126769733519}{12358435328} a^{3} + \frac{327321339768455831}{6179217664} a^{2} - \frac{727775098824073061}{12358435328} a + \frac{71582561224715903}{12358435328} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a + 1\) , \( 60 a^{3} + 32 a^{2} - 361 a + 6\) , \( 330 a^{3} + 161 a^{2} - 2043 a + 171\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(60a^{3}+32a^{2}-361a+6\right){x}+330a^{3}+161a^{2}-2043a+171$ |
| 34.2-a3 |
34.2-a |
$4$ |
$6$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( - 2^{18} \cdot 17^{3} \) |
$18.42641$ |
$(a^3+a^2-5a+1), (a^3+a^2-6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 2 \) |
$1$ |
$8.485163065$ |
1.150973570 |
\( -\frac{9389265120751297298783}{1287913472} a^{3} - \frac{2278699510952573295385}{643956736} a^{2} + \frac{58955415474218212553387}{1287913472} a - \frac{6321093261012038686385}{1287913472} \) |
\( \bigl[2 a^{3} + a^{2} - 10 a + 2\) , \( -a^{3} + 7 a - 3\) , \( 2 a^{3} + a^{2} - 10 a + 3\) , \( -286 a^{3} - 158 a^{2} + 1485 a - 904\) , \( -2991 a^{3} - 5220 a^{2} + 10800 a + 5294\bigr] \) |
${y}^2+\left(2a^{3}+a^{2}-10a+2\right){x}{y}+\left(2a^{3}+a^{2}-10a+3\right){y}={x}^{3}+\left(-a^{3}+7a-3\right){x}^{2}+\left(-286a^{3}-158a^{2}+1485a-904\right){x}-2991a^{3}-5220a^{2}+10800a+5294$ |
| 34.2-a4 |
34.2-a |
$4$ |
$6$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( - 2^{6} \cdot 17 \) |
$18.42641$ |
$(a^3+a^2-5a+1), (a^3+a^2-6a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$687.2982082$ |
1.150973570 |
\( \frac{4101368543425}{1088} a^{3} - \frac{1828543489337}{544} a^{2} - \frac{29105749036085}{1088} a + \frac{37860792539951}{1088} \) |
\( \bigl[a^{3} - 6 a + 4\) , \( -a^{3} + 6 a - 2\) , \( a^{3} + a^{2} - 4 a\) , \( -78 a^{3} - 93 a^{2} + 337 a - 34\) , \( -197 a^{3} - 238 a^{2} + 850 a - 89\bigr] \) |
${y}^2+\left(a^{3}-6a+4\right){x}{y}+\left(a^{3}+a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+6a-2\right){x}^{2}+\left(-78a^{3}-93a^{2}+337a-34\right){x}-197a^{3}-238a^{2}+850a-89$ |
| 34.2-b1 |
34.2-b |
$4$ |
$4$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( 2^{2} \cdot 17^{12} \) |
$18.42641$ |
$(a^3+a^2-5a+1), (a^3+a^2-6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$18.24722372$ |
3.300203282 |
\( \frac{123962436462182934673995}{2330488948919044} a^{3} - \frac{55462372861231411578175}{1165244474459522} a^{2} - \frac{879926343910341618302855}{2330488948919044} a + \frac{1148411264851197779607169}{2330488948919044} \) |
\( \bigl[a^{3} + a^{2} - 5 a\) , \( a^{3} - 6 a + 2\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 151 a^{3} - 38 a^{2} - 1248 a + 134\) , \( -6766 a^{3} - 4929 a^{2} + 38045 a - 4057\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a^{3}-6a+2\right){x}^{2}+\left(151a^{3}-38a^{2}-1248a+134\right){x}-6766a^{3}-4929a^{2}+38045a-4057$ |
| 34.2-b2 |
34.2-b |
$4$ |
$4$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( 2^{8} \cdot 17^{3} \) |
$18.42641$ |
$(a^3+a^2-5a+1), (a^3+a^2-6a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$291.9555796$ |
3.300203282 |
\( \frac{363533551329}{1257728} a^{3} + \frac{88390907559}{628864} a^{2} - \frac{2282438453909}{1257728} a + \frac{244740353551}{1257728} \) |
\( \bigl[1\) , \( 2 a^{3} + a^{2} - 10 a + 2\) , \( a\) , \( a^{3} + 7 a^{2} - 15 a + 2\) , \( 2 a^{3} - 11 a^{2} + 20 a - 2\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(2a^{3}+a^{2}-10a+2\right){x}^{2}+\left(a^{3}+7a^{2}-15a+2\right){x}+2a^{3}-11a^{2}+20a-2$ |
| 34.2-b3 |
34.2-b |
$4$ |
$4$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( 2^{4} \cdot 17^{6} \) |
$18.42641$ |
$(a^3+a^2-5a+1), (a^3+a^2-6a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$291.9555796$ |
3.300203282 |
\( -\frac{138895984621769542975}{386201104} a^{3} - \frac{33709423840206756025}{193100552} a^{2} + \frac{872128550926888937675}{386201104} a - \frac{93508026905139541313}{386201104} \) |
\( \bigl[1\) , \( 2 a^{3} + a^{2} - 10 a + 2\) , \( a\) , \( 26 a^{3} - 3 a^{2} - 120 a + 12\) , \( -106 a^{3} - 43 a^{2} + 651 a - 71\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(2a^{3}+a^{2}-10a+2\right){x}^{2}+\left(26a^{3}-3a^{2}-120a+12\right){x}-106a^{3}-43a^{2}+651a-71$ |
| 34.2-b4 |
34.2-b |
$4$ |
$4$ |
4.4.17609.1 |
$4$ |
$[4, 0]$ |
34.2 |
\( 2 \cdot 17 \) |
\( 2^{2} \cdot 17^{3} \) |
$18.42641$ |
$(a^3+a^2-5a+1), (a^3+a^2-6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$291.9555796$ |
3.300203282 |
\( -\frac{10943525261002917880395673371}{19652} a^{3} - \frac{2655943765388057072395455281}{9826} a^{2} + \frac{68714447448744532152283205271}{19652} a - \frac{7367437952653927889071308721}{19652} \) |
\( \bigl[1\) , \( 2 a^{3} + a^{2} - 10 a + 2\) , \( a\) , \( 381 a^{3} + 17 a^{2} - 1995 a + 212\) , \( -6310 a^{3} + 539 a^{2} + 31260 a - 3384\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(2a^{3}+a^{2}-10a+2\right){x}^{2}+\left(381a^{3}+17a^{2}-1995a+212\right){x}-6310a^{3}+539a^{2}+31260a-3384$ |
*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.
