| 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 |
| 7.1-a1 |
7.1-a |
$1$ |
$1$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$13.57920$ |
$(-a^3+6a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$79.29395121$ |
1.330980717 |
\( \frac{12424402469369}{49} a^{3} + \frac{2847594258273}{49} a^{2} - \frac{73893764301934}{49} a - \frac{54209189647314}{49} \) |
\( \bigl[a + 1\) , \( a^{3} - a^{2} - 5 a\) , \( a^{3} - 5 a - 2\) , \( -2 a^{3} + 2 a^{2} + 9 a - 6\) , \( 5 a^{3} - 3 a^{2} - 28 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(-2a^{3}+2a^{2}+9a-6\right){x}+5a^{3}-3a^{2}-28a$ |
| 7.1-b1 |
7.1-b |
$4$ |
$4$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$13.57920$ |
$(-a^3+6a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$94.62873772$ |
1.588381248 |
\( \frac{23917904519087604710389}{49} a^{3} + \frac{63242615342045880483181}{49} a^{2} + \frac{23715767212974947739240}{49} a - \frac{9045580317799654704024}{49} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( a^{2} - 4\) , \( 1\) , \( -396 a^{3} + 309 a^{2} + 2126 a - 497\) , \( -6084 a^{3} + 4826 a^{2} + 32692 a - 7673\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-396a^{3}+309a^{2}+2126a-497\right){x}-6084a^{3}+4826a^{2}+32692a-7673$ |
| 7.1-b2 |
7.1-b |
$4$ |
$4$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$13.57920$ |
$(-a^3+6a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$378.5149509$ |
1.588381248 |
\( \frac{8467122384327}{2401} a^{3} + \frac{22405155329415}{2401} a^{2} + \frac{8405048898123}{2401} a - \frac{3205235424655}{2401} \) |
\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( a^{3} - 7 a - 1\) , \( 1\) , \( 27 a^{3} + 2 a^{2} - 162 a - 95\) , \( 79 a^{3} + 16 a^{2} - 466 a - 325\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a-1\right){x}{y}+{y}={x}^{3}+\left(a^{3}-7a-1\right){x}^{2}+\left(27a^{3}+2a^{2}-162a-95\right){x}+79a^{3}+16a^{2}-466a-325$ |
| 7.1-b3 |
7.1-b |
$4$ |
$4$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$13.57920$ |
$(-a^3+6a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1514.059803$ |
1.588381248 |
\( -\frac{150393}{49} a^{3} - \frac{1452302}{49} a^{2} - \frac{2211513}{49} a + \frac{591904}{49} \) |
\( \bigl[-a^{3} + a^{2} + 6 a - 1\) , \( a^{3} - 6 a - 1\) , \( a\) , \( 4 a^{3} - 6 a^{2} - 26 a + 8\) , \( 6 a^{3} - 3 a^{2} - 28 a + 6\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+6a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-6a-1\right){x}^{2}+\left(4a^{3}-6a^{2}-26a+8\right){x}+6a^{3}-3a^{2}-28a+6$ |
| 7.1-b4 |
7.1-b |
$4$ |
$4$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{8} \) |
$13.57920$ |
$(-a^3+6a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$23.65718443$ |
1.588381248 |
\( -\frac{177029572592635145413}{5764801} a^{3} + \frac{368229654852243015235}{5764801} a^{2} + \frac{296242310134216787736}{5764801} a - \frac{85107980008329276696}{5764801} \) |
\( \bigl[-a^{3} + a^{2} + 6 a - 1\) , \( a^{3} - 6 a - 1\) , \( a\) , \( 24 a^{3} - 101 a^{2} - 96 a + 23\) , \( 367 a^{3} - 334 a^{2} - 398 a + 103\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+6a-1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-6a-1\right){x}^{2}+\left(24a^{3}-101a^{2}-96a+23\right){x}+367a^{3}-334a^{2}-398a+103$ |
| 7.1-c1 |
7.1-c |
$4$ |
$4$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{8} \) |
$13.57920$ |
$(-a^3+6a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.228061470$ |
$33.85418230$ |
2.791413215 |
\( -\frac{177029572592635145413}{5764801} a^{3} + \frac{368229654852243015235}{5764801} a^{2} + \frac{296242310134216787736}{5764801} a - \frac{85107980008329276696}{5764801} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 7 a - 2\) , \( -a^{3} + a^{2} + 6 a\) , \( 23 a^{3} - 13 a^{2} - 126 a - 77\) , \( -53 a^{3} - 131 a^{2} + 472 a + 429\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(-a^{3}+a^{2}+6a\right){y}={x}^{3}+\left(a^{3}-7a-2\right){x}^{2}+\left(23a^{3}-13a^{2}-126a-77\right){x}-53a^{3}-131a^{2}+472a+429$ |
| 7.1-c2 |
7.1-c |
$4$ |
$4$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$13.57920$ |
$(-a^3+6a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.456122941$ |
$135.4167292$ |
2.791413215 |
\( \frac{8467122384327}{2401} a^{3} + \frac{22405155329415}{2401} a^{2} + \frac{8405048898123}{2401} a - \frac{3205235424655}{2401} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 7 a - 2\) , \( -a^{3} + a^{2} + 6 a\) , \( -2 a^{3} - 3 a^{2} - 6 a - 2\) , \( -8 a^{3} - 15 a^{2} + 9 a + 10\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(-a^{3}+a^{2}+6a\right){y}={x}^{3}+\left(a^{3}-7a-2\right){x}^{2}+\left(-2a^{3}-3a^{2}-6a-2\right){x}-8a^{3}-15a^{2}+9a+10$ |
| 7.1-c3 |
7.1-c |
$4$ |
$4$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$13.57920$ |
$(-a^3+6a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.228061470$ |
$541.6669168$ |
2.791413215 |
\( -\frac{150393}{49} a^{3} - \frac{1452302}{49} a^{2} - \frac{2211513}{49} a + \frac{591904}{49} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 7 a - 2\) , \( -a^{3} + a^{2} + 6 a\) , \( -2 a^{3} + 2 a^{2} + 4 a + 3\) , \( -2 a^{3} + 3 a^{2} + 4 a - 2\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(-a^{3}+a^{2}+6a\right){y}={x}^{3}+\left(a^{3}-7a-2\right){x}^{2}+\left(-2a^{3}+2a^{2}+4a+3\right){x}-2a^{3}+3a^{2}+4a-2$ |
| 7.1-c4 |
7.1-c |
$4$ |
$4$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$13.57920$ |
$(-a^3+6a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$4.912245882$ |
$8.463545575$ |
2.791413215 |
\( \frac{23917904519087604710389}{49} a^{3} + \frac{63242615342045880483181}{49} a^{2} + \frac{23715767212974947739240}{49} a - \frac{9045580317799654704024}{49} \) |
\( \bigl[a\) , \( a^{3} - 7 a - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( -629 a^{3} + 500 a^{2} + 3375 a - 799\) , \( -13618 a^{3} + 10802 a^{2} + 73139 a - 17167\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{3}+a^{2}+5a-1\right){y}={x}^{3}+\left(a^{3}-7a-2\right){x}^{2}+\left(-629a^{3}+500a^{2}+3375a-799\right){x}-13618a^{3}+10802a^{2}+73139a-17167$ |
| 7.1-d1 |
7.1-d |
$1$ |
$1$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$13.57920$ |
$(-a^3+6a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.021873934$ |
$1826.258856$ |
2.682136906 |
\( \frac{12424402469369}{49} a^{3} + \frac{2847594258273}{49} a^{2} - \frac{73893764301934}{49} a - \frac{54209189647314}{49} \) |
\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 3\) , \( -a^{3} + 6 a + 2\) , \( a^{3} - 7 a\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a-1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-a^{3}+6a+2\right){x}+a^{3}-7a$ |
| 9.2-a1 |
9.2-a |
$2$ |
$3$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{6} \) |
$14.01255$ |
$(-a^2+a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$231.3874507$ |
1.941965499 |
\( -\frac{99751858}{27} a^{3} + \frac{26237141}{9} a^{2} + \frac{536966018}{27} a - \frac{126003172}{27} \) |
\( \bigl[a + 1\) , \( a\) , \( a^{2} - 2\) , \( a^{3} - a^{2} - 3 a - 1\) , \( 4 a^{3} + 4 a^{2} - 29 a - 24\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+a{x}^{2}+\left(a^{3}-a^{2}-3a-1\right){x}+4a^{3}+4a^{2}-29a-24$ |
| 9.2-a2 |
9.2-a |
$2$ |
$3$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{2} \) |
$14.01255$ |
$(-a^2+a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$25.70971674$ |
1.941965499 |
\( -\frac{3125819837349295086832}{3} a^{3} + 826571068922800008657 a^{2} + \frac{16787762275536798680114}{3} a - \frac{3940274072379513958723}{3} \) |
\( \bigl[a + 1\) , \( a\) , \( a^{2} - 2\) , \( -9 a^{3} + 4 a^{2} + 42 a + 19\) , \( -142 a^{3} - 23 a^{2} + 827 a + 593\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+a{x}^{2}+\left(-9a^{3}+4a^{2}+42a+19\right){x}-142a^{3}-23a^{2}+827a+593$ |
| 9.2-b1 |
9.2-b |
$2$ |
$3$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{2} \) |
$14.01255$ |
$(-a^2+a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1.682767830$ |
$5.279138547$ |
2.684055367 |
\( -\frac{3125819837349295086832}{3} a^{3} + 826571068922800008657 a^{2} + \frac{16787762275536798680114}{3} a - \frac{3940274072379513958723}{3} \) |
\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( 2 a^{3} - a^{2} - 11 a - 1\) , \( a\) , \( -6 a^{3} + 8 a^{2} - 12 a + 8\) , \( -47 a^{3} + 75 a^{2} + 39 a - 25\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a-1\right){x}{y}+a{y}={x}^{3}+\left(2a^{3}-a^{2}-11a-1\right){x}^{2}+\left(-6a^{3}+8a^{2}-12a+8\right){x}-47a^{3}+75a^{2}+39a-25$ |
| 9.2-b2 |
9.2-b |
$2$ |
$3$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{6} \) |
$14.01255$ |
$(-a^2+a+4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.560922610$ |
$427.6102223$ |
2.684055367 |
\( -\frac{99751858}{27} a^{3} + \frac{26237141}{9} a^{2} + \frac{536966018}{27} a - \frac{126003172}{27} \) |
\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( 2 a^{3} - a^{2} - 11 a - 1\) , \( a\) , \( 9 a^{3} - 12 a^{2} - 37 a + 13\) , \( 10 a^{2} - 29 a + 5\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a-1\right){x}{y}+a{y}={x}^{3}+\left(2a^{3}-a^{2}-11a-1\right){x}^{2}+\left(9a^{3}-12a^{2}-37a+13\right){x}+10a^{2}-29a+5$ |
| 31.1-a1 |
31.1-a |
$1$ |
$1$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$16.35525$ |
$(a^3-6a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.403634516$ |
$237.4356003$ |
3.217331673 |
\( -\frac{17712960}{31} a^{3} - \frac{2367560}{31} a^{2} + \frac{104377942}{31} a + \frac{67983825}{31} \) |
\( \bigl[a^{2} - 2\) , \( -2 a^{3} + a^{2} + 12 a + 2\) , \( a^{3} - 5 a - 2\) , \( a^{3} - a^{2} - 3 a + 8\) , \( -a^{3} + 2 a^{2} + 9 a + 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(-2a^{3}+a^{2}+12a+2\right){x}^{2}+\left(a^{3}-a^{2}-3a+8\right){x}-a^{3}+2a^{2}+9a+1$ |
| 31.1-b1 |
31.1-b |
$2$ |
$2$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{4} \) |
$16.35525$ |
$(a^3-6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$149.6646941$ |
2.512181812 |
\( -\frac{2985938384414926}{923521} a^{3} - \frac{684541052030056}{923521} a^{2} + \frac{17758909370461096}{923521} a + \frac{13029075667504793}{923521} \) |
\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( -a^{3} + 6 a + 3\) , \( a\) , \( -6 a^{3} - 11 a^{2} + 6 a + 5\) , \( 18 a^{3} + 55 a^{2} + 30 a - 8\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+6a+3\right){x}^{2}+\left(-6a^{3}-11a^{2}+6a+5\right){x}+18a^{3}+55a^{2}+30a-8$ |
| 31.1-b2 |
31.1-b |
$2$ |
$2$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$16.35525$ |
$(a^3-6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$598.6587766$ |
2.512181812 |
\( -\frac{7382992}{961} a^{3} + \frac{68438684}{961} a^{2} - \frac{86435752}{961} a - \frac{113471127}{961} \) |
\( \bigl[-a^{3} + a^{2} + 5 a\) , \( a^{3} - a^{2} - 6 a + 1\) , \( a^{2} - a - 3\) , \( 5 a^{3} - 2 a^{2} - 27 a - 6\) , \( 6 a^{3} - a^{2} - 34 a - 15\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a+1\right){x}^{2}+\left(5a^{3}-2a^{2}-27a-6\right){x}+6a^{3}-a^{2}-34a-15$ |
| 31.1-c1 |
31.1-c |
$2$ |
$2$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{4} \) |
$16.35525$ |
$(a^3-6a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.275640559$ |
$299.6122540$ |
2.772454287 |
\( -\frac{2985938384414926}{923521} a^{3} - \frac{684541052030056}{923521} a^{2} + \frac{17758909370461096}{923521} a + \frac{13029075667504793}{923521} \) |
\( \bigl[a + 1\) , \( a^{3} - 6 a - 2\) , \( 0\) , \( -4 a - 8\) , \( -9 a^{3} - 4 a^{2} + 39 a + 18\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{3}-6a-2\right){x}^{2}+\left(-4a-8\right){x}-9a^{3}-4a^{2}+39a+18$ |
| 31.1-c2 |
31.1-c |
$2$ |
$2$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$16.35525$ |
$(a^3-6a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.137820279$ |
$1198.449016$ |
2.772454287 |
\( -\frac{7382992}{961} a^{3} + \frac{68438684}{961} a^{2} - \frac{86435752}{961} a - \frac{113471127}{961} \) |
\( \bigl[a + 1\) , \( a^{3} - 6 a - 2\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{3}-6a-2\right){x}^{2}+\left(a+2\right){x}$ |
| 31.1-d1 |
31.1-d |
$1$ |
$1$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$16.35525$ |
$(a^3-6a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$238.1306052$ |
1.998558774 |
\( -\frac{17712960}{31} a^{3} - \frac{2367560}{31} a^{2} + \frac{104377942}{31} a + \frac{67983825}{31} \) |
\( \bigl[a^{2} - a - 3\) , \( 2 a^{3} - a^{2} - 11 a - 1\) , \( a\) , \( -8 a^{2} - 17 a + 5\) , \( -13 a^{3} - 41 a^{2} - 25 a + 8\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+a{y}={x}^{3}+\left(2a^{3}-a^{2}-11a-1\right){x}^{2}+\left(-8a^{2}-17a+5\right){x}-13a^{3}-41a^{2}-25a+8$ |
| 31.2-a1 |
31.2-a |
$2$ |
$2$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$16.35525$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$733.1446324$ |
3.076531545 |
\( -\frac{4748453282421413}{961} a^{3} + \frac{9877007140380215}{961} a^{2} + \frac{7946078315008171}{961} a - \frac{2282858387875356}{961} \) |
\( \bigl[a^{3} - 6 a - 2\) , \( a + 1\) , \( a^{3} - 6 a - 2\) , \( 8 a^{3} - 42 a - 33\) , \( 13 a^{3} + 8 a^{2} - 86 a - 68\bigr] \) |
${y}^2+\left(a^{3}-6a-2\right){x}{y}+\left(a^{3}-6a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a^{3}-42a-33\right){x}+13a^{3}+8a^{2}-86a-68$ |
| 31.2-a2 |
31.2-a |
$2$ |
$2$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$16.35525$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1466.289264$ |
3.076531545 |
\( -\frac{18337193}{31} a^{3} + \frac{38211380}{31} a^{2} + \frac{30491303}{31} a - \frac{8725495}{31} \) |
\( \bigl[a^{3} - 6 a - 2\) , \( a + 1\) , \( a^{3} - 6 a - 2\) , \( -2 a^{3} + 13 a + 7\) , \( -2 a^{3} + 12 a + 7\bigr] \) |
${y}^2+\left(a^{3}-6a-2\right){x}{y}+\left(a^{3}-6a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a^{3}+13a+7\right){x}-2a^{3}+12a+7$ |
| 31.2-b1 |
31.2-b |
$2$ |
$2$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$16.35525$ |
$(a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.123194124$ |
$1443.732183$ |
2.985439933 |
\( -\frac{4748453282421413}{961} a^{3} + \frac{9877007140380215}{961} a^{2} + \frac{7946078315008171}{961} a - \frac{2282858387875356}{961} \) |
\( \bigl[-a^{3} + a^{2} + 5 a\) , \( -a^{2} + 2 a + 2\) , \( -a^{3} + a^{2} + 5 a\) , \( 4 a^{3} - 10 a^{2} - 4 a + 1\) , \( -24 a^{3} + 50 a^{2} + 41 a - 13\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a\right){x}{y}+\left(-a^{3}+a^{2}+5a\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(4a^{3}-10a^{2}-4a+1\right){x}-24a^{3}+50a^{2}+41a-13$ |
| 31.2-b2 |
31.2-b |
$2$ |
$2$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$16.35525$ |
$(a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.246388248$ |
$1443.732183$ |
2.985439933 |
\( -\frac{18337193}{31} a^{3} + \frac{38211380}{31} a^{2} + \frac{30491303}{31} a - \frac{8725495}{31} \) |
\( \bigl[-a^{3} + a^{2} + 5 a\) , \( -a^{2} + 2 a + 2\) , \( -a^{3} + a^{2} + 5 a\) , \( -a^{3} + 6 a + 1\) , \( -a^{3} + a^{2} + 4 a\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a\right){x}{y}+\left(-a^{3}+a^{2}+5a\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-a^{3}+6a+1\right){x}-a^{3}+a^{2}+4a$ |
| 37.3-a1 |
37.3-a |
$3$ |
$9$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.3 |
\( 37 \) |
\( 37^{3} \) |
$16.72099$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$9$ |
\( 3 \) |
$1.443531857$ |
$3.095824734$ |
4.050682493 |
\( \frac{21101454496171620813530006703}{50653} a^{3} + \frac{4836319554071606684975733401}{50653} a^{2} - \frac{125500273208123868117808748550}{50653} a - \frac{92068230236758336815296011677}{50653} \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( -a^{3} + a^{2} + 6 a\) , \( -92 a^{3} - 49 a^{2} + 527 a - 177\) , \( -290 a^{3} + 1584 a^{2} + 6745 a - 1499\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{3}+a^{2}+6a\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-92a^{3}-49a^{2}+527a-177\right){x}-290a^{3}+1584a^{2}+6745a-1499$ |
| 37.3-a2 |
37.3-a |
$3$ |
$9$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.3 |
\( 37 \) |
\( 37^{9} \) |
$16.72099$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs |
$1$ |
\( 3^{2} \) |
$0.481177285$ |
$27.86242260$ |
4.050682493 |
\( \frac{3039228675242758906116}{129961739795077} a^{3} + \frac{698439153329207128522}{129961739795077} a^{2} - \frac{18076791977476164565272}{129961739795077} a - \frac{13270713587185149261741}{129961739795077} \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( -a^{3} + a^{2} + 6 a\) , \( -2 a^{3} + 11 a^{2} + 17 a - 2\) , \( -16 a^{3} - 54 a^{2} - 8 a + 5\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{3}+a^{2}+6a\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-2a^{3}+11a^{2}+17a-2\right){x}-16a^{3}-54a^{2}-8a+5$ |
| 37.3-a3 |
37.3-a |
$3$ |
$9$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.3 |
\( 37 \) |
\( 37^{3} \) |
$16.72099$ |
$(-a^3+a^2+4a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.160392428$ |
$250.7618034$ |
4.050682493 |
\( -\frac{590182593}{50653} a^{3} - \frac{1632589228}{50653} a^{2} - \frac{688347540}{50653} a + \frac{246771867}{50653} \) |
\( \bigl[1\) , \( -a^{3} + 6 a + 2\) , \( a^{2} - 3\) , \( -a^{2} + 4\) , \( -a^{3} + 5 a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+6a+2\right){x}^{2}+\left(-a^{2}+4\right){x}-a^{3}+5a+1$ |
| 37.3-b1 |
37.3-b |
$3$ |
$9$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.3 |
\( 37 \) |
\( 37^{3} \) |
$16.72099$ |
$(-a^3+a^2+4a-2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
|
\( 3 \) |
$1$ |
$0.080075420$ |
3.572240559 |
\( \frac{21101454496171620813530006703}{50653} a^{3} + \frac{4836319554071606684975733401}{50653} a^{2} - \frac{125500273208123868117808748550}{50653} a - \frac{92068230236758336815296011677}{50653} \) |
\( \bigl[a^{2} - 3\) , \( 0\) , \( 1\) , \( 15 a^{3} + 179 a^{2} - 180 a - 1167\) , \( 510 a^{3} + 2439 a^{2} - 4470 a - 16014\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(15a^{3}+179a^{2}-180a-1167\right){x}+510a^{3}+2439a^{2}-4470a-16014$ |
| 37.3-b2 |
37.3-b |
$3$ |
$9$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.3 |
\( 37 \) |
\( 37^{9} \) |
$16.72099$ |
$(-a^3+a^2+4a-2)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
|
\( 3^{2} \) |
$1$ |
$6.486109072$ |
3.572240559 |
\( \frac{3039228675242758906116}{129961739795077} a^{3} + \frac{698439153329207128522}{129961739795077} a^{2} - \frac{18076791977476164565272}{129961739795077} a - \frac{13270713587185149261741}{129961739795077} \) |
\( \bigl[a^{2} - 3\) , \( 0\) , \( 1\) , \( 4 a^{2} - 12\) , \( 3 a^{3} + 8 a^{2} - 9 a - 31\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(4a^{2}-12\right){x}+3a^{3}+8a^{2}-9a-31$ |
| 37.3-b3 |
37.3-b |
$3$ |
$9$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.3 |
\( 37 \) |
\( 37^{3} \) |
$16.72099$ |
$(-a^3+a^2+4a-2)$ |
$0 \le r \le 1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 3 \) |
$1$ |
$525.3748348$ |
3.572240559 |
\( -\frac{590182593}{50653} a^{3} - \frac{1632589228}{50653} a^{2} - \frac{688347540}{50653} a + \frac{246771867}{50653} \) |
\( \bigl[a^{2} - 3\) , \( 0\) , \( 1\) , \( -a^{2} + 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}$ |
| 37.4-a1 |
37.4-a |
$2$ |
$3$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.4 |
\( 37 \) |
\( 37^{3} \) |
$16.72099$ |
$(a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$298.8531484$ |
2.508184873 |
\( \frac{543605082}{50653} a^{3} + \frac{1439901892}{50653} a^{2} + \frac{515637153}{50653} a - \frac{168514383}{50653} \) |
\( \bigl[a^{3} - 6 a - 1\) , \( a - 1\) , \( a^{2} - a - 3\) , \( 2 a^{3} - 2 a^{2} - 11 a - 1\) , \( -a^{2} - 2 a - 2\bigr] \) |
${y}^2+\left(a^{3}-6a-1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a^{3}-2a^{2}-11a-1\right){x}-a^{2}-2a-2$ |
| 37.4-a2 |
37.4-a |
$2$ |
$3$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.4 |
\( 37 \) |
\( 37^{9} \) |
$16.72099$ |
$(a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$33.20590538$ |
2.508184873 |
\( -\frac{317120920004812447698}{129961739795077} a^{3} + \frac{657239722057512058868}{129961739795077} a^{2} + \frac{538121474323635876993}{129961739795077} a - \frac{154151513877144293916}{129961739795077} \) |
\( \bigl[-a^{3} + a^{2} + 6 a - 1\) , \( -a - 1\) , \( a^{2} - 2\) , \( -19 a^{3} + 27 a^{2} + 94 a - 95\) , \( -290 a^{3} + 149 a^{2} + 1603 a + 75\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+6a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-19a^{3}+27a^{2}+94a-95\right){x}-290a^{3}+149a^{2}+1603a+75$ |
| 37.4-b1 |
37.4-b |
$2$ |
$3$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.4 |
\( 37 \) |
\( 37^{6} \) |
$16.72099$ |
$(a^2-3)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 2 \cdot 3 \) |
$1$ |
$18.84013585$ |
3.735078874 |
\( -\frac{57993709488556}{2565726409} a^{3} + \frac{17024840689515}{2565726409} a^{2} + \frac{255953608109786}{2565726409} a - \frac{60148006870869}{2565726409} \) |
\( \bigl[a^{2} - 2\) , \( a - 1\) , \( a^{3} - 6 a - 1\) , \( 2 a^{3} + 3 a^{2} - 15 a - 10\) , \( 4 a^{3} + 2 a^{2} - 29 a - 25\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-6a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a^{3}+3a^{2}-15a-10\right){x}+4a^{3}+2a^{2}-29a-25$ |
| 37.4-b2 |
37.4-b |
$2$ |
$3$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.4 |
\( 37 \) |
\( 37^{2} \) |
$16.72099$ |
$(a^2-3)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
|
\( 2 \) |
$1$ |
$0.232594269$ |
3.735078874 |
\( -\frac{285379335696651160}{1369} a^{3} - \frac{48813868023853209}{1369} a^{2} + \frac{1023314135352504824}{1369} a - \frac{228538846262599104}{1369} \) |
\( \bigl[-a^{3} + a^{2} + 6 a - 1\) , \( a^{3} - 5 a - 1\) , \( a^{3} - 5 a - 1\) , \( -188 a^{3} + 226 a^{2} + 997 a - 735\) , \( -4067 a^{3} + 3855 a^{2} + 21667 a - 9061\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+6a-1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(-188a^{3}+226a^{2}+997a-735\right){x}-4067a^{3}+3855a^{2}+21667a-9061$ |
| 37.4-c1 |
37.4-c |
$2$ |
$3$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.4 |
\( 37 \) |
\( 37^{6} \) |
$16.72099$ |
$(a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$157.2370166$ |
2.639286276 |
\( -\frac{57993709488556}{2565726409} a^{3} + \frac{17024840689515}{2565726409} a^{2} + \frac{255953608109786}{2565726409} a - \frac{60148006870869}{2565726409} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 5 a - 2\) , \( -8 a^{3} + 12 a^{2} + 4 a - 7\) , \( -28 a^{3} + 79 a^{2} + 57 a - 19\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-8a^{3}+12a^{2}+4a-7\right){x}-28a^{3}+79a^{2}+57a-19$ |
| 37.4-c2 |
37.4-c |
$2$ |
$3$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.4 |
\( 37 \) |
\( 37^{2} \) |
$16.72099$ |
$(a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$9$ |
\( 2 \) |
$1$ |
$17.47077962$ |
2.639286276 |
\( -\frac{285379335696651160}{1369} a^{3} - \frac{48813868023853209}{1369} a^{2} + \frac{1023314135352504824}{1369} a - \frac{228538846262599104}{1369} \) |
\( \bigl[-a^{3} + a^{2} + 6 a\) , \( a^{2} - a - 2\) , \( 0\) , \( -136 a^{3} + 57 a^{2} + 883 a - 229\) , \( -1608 a^{3} + 495 a^{2} + 10853 a - 2428\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+6a\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-136a^{3}+57a^{2}+883a-229\right){x}-1608a^{3}+495a^{2}+10853a-2428$ |
| 37.4-d1 |
37.4-d |
$2$ |
$3$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.4 |
\( 37 \) |
\( 37^{9} \) |
$16.72099$ |
$(a^2-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1.273728172$ |
$9.823093946$ |
3.780326074 |
\( -\frac{317120920004812447698}{129961739795077} a^{3} + \frac{657239722057512058868}{129961739795077} a^{2} + \frac{538121474323635876993}{129961739795077} a - \frac{154151513877144293916}{129961739795077} \) |
\( \bigl[-a^{3} + a^{2} + 6 a\) , \( -a\) , \( -a^{3} + a^{2} + 5 a\) , \( -19 a^{3} + 14 a^{2} + 104 a - 29\) , \( -103 a^{3} + 79 a^{2} + 560 a - 137\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+6a\right){x}{y}+\left(-a^{3}+a^{2}+5a\right){y}={x}^{3}-a{x}^{2}+\left(-19a^{3}+14a^{2}+104a-29\right){x}-103a^{3}+79a^{2}+560a-137$ |
| 37.4-d2 |
37.4-d |
$2$ |
$3$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
37.4 |
\( 37 \) |
\( 37^{3} \) |
$16.72099$ |
$(a^2-3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.424576057$ |
$795.6706096$ |
3.780326074 |
\( \frac{543605082}{50653} a^{3} + \frac{1439901892}{50653} a^{2} + \frac{515637153}{50653} a - \frac{168514383}{50653} \) |
\( \bigl[-a^{3} + a^{2} + 6 a\) , \( -a\) , \( -a^{3} + a^{2} + 5 a\) , \( a^{3} - a^{2} - 6 a + 1\) , \( a^{3} - a^{2} - 5 a + 1\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+6a\right){x}{y}+\left(-a^{3}+a^{2}+5a\right){y}={x}^{3}-a{x}^{2}+\left(a^{3}-a^{2}-6a+1\right){x}+a^{3}-a^{2}-5a+1$ |
| 47.1-a1 |
47.1-a |
$2$ |
$2$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{4} \) |
$17.22856$ |
$(-2a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.297398547$ |
$503.6798146$ |
5.028692620 |
\( -\frac{17924817515415700}{4879681} a^{3} - \frac{4106197327280224}{4879681} a^{2} + \frac{106613235842785561}{4879681} a + \frac{78211581543599618}{4879681} \) |
\( \bigl[a\) , \( -2 a^{3} + a^{2} + 11 a + 1\) , \( a^{3} - 5 a - 1\) , \( -5 a^{3} - 12 a^{2} - 2 a + 5\) , \( 22 a^{3} + 49 a^{2} + 5 a - 4\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(-2a^{3}+a^{2}+11a+1\right){x}^{2}+\left(-5a^{3}-12a^{2}-2a+5\right){x}+22a^{3}+49a^{2}+5a-4$ |
| 47.1-a2 |
47.1-a |
$2$ |
$2$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{2} \) |
$17.22856$ |
$(-2a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.148699273$ |
$2014.719258$ |
5.028692620 |
\( \frac{165576160}{2209} a^{3} - \frac{73121967}{2209} a^{2} - \frac{926640900}{2209} a - \frac{103842708}{2209} \) |
\( \bigl[a\) , \( -2 a^{3} + a^{2} + 11 a + 1\) , \( a^{3} - 5 a - 1\) , \( -2 a^{2} - 2 a + 5\) , \( 3 a^{3} - 2 a^{2} - 15 a + 4\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(-2a^{3}+a^{2}+11a+1\right){x}^{2}+\left(-2a^{2}-2a+5\right){x}+3a^{3}-2a^{2}-15a+4$ |
| 47.1-b1 |
47.1-b |
$6$ |
$8$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{16} \) |
$17.22856$ |
$(-2a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$1.793995870$ |
1.927228092 |
\( -\frac{1511881059587547003474507073105920}{566977372488557307219621121} a^{3} + \frac{1199300441127848743579990637265391}{566977372488557307219621121} a^{2} + \frac{8119792398475463876686673755911123}{566977372488557307219621121} a - \frac{1905211014230435059397420147741753}{566977372488557307219621121} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( a^{2} - a - 2\) , \( -185 a^{3} + 355 a^{2} + 389 a - 88\) , \( 3992 a^{3} - 8374 a^{2} - 6490 a + 1921\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-1\right){x}^{2}+\left(-185a^{3}+355a^{2}+389a-88\right){x}+3992a^{3}-8374a^{2}-6490a+1921$ |
| 47.1-b2 |
47.1-b |
$6$ |
$8$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{2} \) |
$17.22856$ |
$(-2a-3)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$114.8157357$ |
1.927228092 |
\( \frac{1627479772261443194310}{2209} a^{3} + \frac{4303319192935747742287}{2209} a^{2} + \frac{1613761541023944563427}{2209} a - \frac{615480480870855330320}{2209} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( a^{2} - a - 2\) , \( -5 a^{3} + 35 a^{2} - 61 a - 73\) , \( -706 a^{3} + 1404 a^{2} + 1358 a - 160\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-1\right){x}^{2}+\left(-5a^{3}+35a^{2}-61a-73\right){x}-706a^{3}+1404a^{2}+1358a-160$ |
| 47.1-b3 |
47.1-b |
$6$ |
$8$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{4} \) |
$17.22856$ |
$(-2a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$459.2629428$ |
1.927228092 |
\( \frac{678698962393374}{4879681} a^{3} + \frac{1757454822964191}{4879681} a^{2} + \frac{611950251199251}{4879681} a - \frac{222863408629597}{4879681} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( a^{2} - a - 2\) , \( 25 a^{3} - 50 a^{2} - 46 a + 7\) , \( -136 a^{3} + 283 a^{2} + 227 a - 66\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-1\right){x}^{2}+\left(25a^{3}-50a^{2}-46a+7\right){x}-136a^{3}+283a^{2}+227a-66$ |
| 47.1-b4 |
47.1-b |
$6$ |
$8$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{8} \) |
$17.22856$ |
$(-2a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$64$ |
\( 2 \) |
$1$ |
$28.70393392$ |
1.927228092 |
\( \frac{765698248629270498938595066}{23811286661761} a^{3} - \frac{607428501272722693777476207}{23811286661761} a^{2} - \frac{4112316397241004483722272899}{23811286661761} a + \frac{965206286133698843561735648}{23811286661761} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( a^{2} - a - 2\) , \( 55 a^{3} - 135 a^{2} - 31 a + 7\) , \( 698 a^{3} - 1506 a^{2} - 1012 a + 300\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-1\right){x}^{2}+\left(55a^{3}-135a^{2}-31a+7\right){x}+698a^{3}-1506a^{2}-1012a+300$ |
| 47.1-b5 |
47.1-b |
$6$ |
$8$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{2} \) |
$17.22856$ |
$(-2a-3)$ |
$0 \le r \le 2$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1837.051771$ |
1.927228092 |
\( -\frac{39201262254}{2209} a^{3} + \frac{81524985449}{2209} a^{2} + \frac{65578816389}{2209} a - \frac{18843570932}{2209} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( a^{3} - a^{2} - 5 a\) , \( a^{3} - 6 a - 1\) , \( 20 a^{3} + 2 a^{2} - 115 a - 82\) , \( -107 a^{3} - 17 a^{2} + 623 a + 449\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{3}-6a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a\right){x}^{2}+\left(20a^{3}+2a^{2}-115a-82\right){x}-107a^{3}-17a^{2}+623a+449$ |
| 47.1-b6 |
47.1-b |
$6$ |
$8$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{4} \) |
$17.22856$ |
$(-2a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$1.793995870$ |
1.927228092 |
\( \frac{22820846893156659267847371978461184}{4879681} a^{3} - \frac{18103780248124282649102062969122223}{4879681} a^{2} - \frac{122563350578008371062026140580583571}{4879681} a + \frac{28766978265484451406011251584629833}{4879681} \) |
\( \bigl[a^{3} - 6 a - 1\) , \( a^{2} - a - 2\) , \( -a^{3} + a^{2} + 5 a\) , \( 1426 a^{3} - 3145 a^{2} - 2580 a + 648\) , \( 82669 a^{3} - 173511 a^{2} - 139517 a + 39783\bigr] \) |
${y}^2+\left(a^{3}-6a-1\right){x}{y}+\left(-a^{3}+a^{2}+5a\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(1426a^{3}-3145a^{2}-2580a+648\right){x}+82669a^{3}-173511a^{2}-139517a+39783$ |
| 47.1-c1 |
47.1-c |
$6$ |
$8$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{2} \) |
$17.22856$ |
$(-2a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$3.346382356$ |
0.898725881 |
\( \frac{1627479772261443194310}{2209} a^{3} + \frac{4303319192935747742287}{2209} a^{2} + \frac{1613761541023944563427}{2209} a - \frac{615480480870855330320}{2209} \) |
\( \bigl[a^{2} - 2\) , \( -2 a^{3} + a^{2} + 10 a\) , \( a^{3} - 6 a - 2\) , \( 279 a^{3} + 72 a^{2} - 1679 a - 1233\) , \( 4594 a^{3} + 1230 a^{2} - 27657 a - 20425\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-6a-2\right){y}={x}^{3}+\left(-2a^{3}+a^{2}+10a\right){x}^{2}+\left(279a^{3}+72a^{2}-1679a-1233\right){x}+4594a^{3}+1230a^{2}-27657a-20425$ |
| 47.1-c2 |
47.1-c |
$6$ |
$8$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{8} \) |
$17.22856$ |
$(-2a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$64$ |
\( 2 \) |
$1$ |
$13.38552942$ |
0.898725881 |
\( \frac{765698248629270498938595066}{23811286661761} a^{3} - \frac{607428501272722693777476207}{23811286661761} a^{2} - \frac{4112316397241004483722272899}{23811286661761} a + \frac{965206286133698843561735648}{23811286661761} \) |
\( \bigl[a^{2} - 2\) , \( -2 a^{3} + a^{2} + 10 a\) , \( a^{3} - 6 a - 2\) , \( 9 a^{3} - 8 a^{2} + a - 113\) , \( 84 a^{3} - 110 a^{2} - 157 a - 369\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-6a-2\right){y}={x}^{3}+\left(-2a^{3}+a^{2}+10a\right){x}^{2}+\left(9a^{3}-8a^{2}+a-113\right){x}+84a^{3}-110a^{2}-157a-369$ |
| 47.1-c3 |
47.1-c |
$6$ |
$8$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{4} \) |
$17.22856$ |
$(-2a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$53.54211770$ |
0.898725881 |
\( \frac{678698962393374}{4879681} a^{3} + \frac{1757454822964191}{4879681} a^{2} + \frac{611950251199251}{4879681} a - \frac{222863408629597}{4879681} \) |
\( \bigl[a^{2} - 2\) , \( -2 a^{3} + a^{2} + 10 a\) , \( a^{3} - 6 a - 2\) , \( 24 a^{3} - 8 a^{2} - 119 a - 73\) , \( 75 a^{3} + 46 a^{2} - 499 a - 389\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-6a-2\right){y}={x}^{3}+\left(-2a^{3}+a^{2}+10a\right){x}^{2}+\left(24a^{3}-8a^{2}-119a-73\right){x}+75a^{3}+46a^{2}-499a-389$ |
| 47.1-c4 |
47.1-c |
$6$ |
$8$ |
4.4.14197.1 |
$4$ |
$[4, 0]$ |
47.1 |
\( 47 \) |
\( 47^{2} \) |
$17.22856$ |
$(-2a-3)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$214.1684708$ |
0.898725881 |
\( -\frac{39201262254}{2209} a^{3} + \frac{81524985449}{2209} a^{2} + \frac{65578816389}{2209} a - \frac{18843570932}{2209} \) |
\( \bigl[a^{2} - 2\) , \( -2 a^{3} + a^{2} + 10 a\) , \( a^{3} - 6 a - 2\) , \( 9 a^{3} - 13 a^{2} - 29 a + 2\) , \( -12 a^{3} + 29 a^{2} + 15 a - 20\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-6a-2\right){y}={x}^{3}+\left(-2a^{3}+a^{2}+10a\right){x}^{2}+\left(9a^{3}-13a^{2}-29a+2\right){x}-12a^{3}+29a^{2}+15a-20$ |
*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.
