| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50456$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$783.4635514$ |
1.036547827 |
\( 4389623576 a^{3} - 14764975849 a^{2} + 2575154231 a + 9657368279 \) |
\( \bigl[a^{2} - 2 a - 2\) , \( -a^{3} + 2 a^{2} + 2 a - 2\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 3 a^{2} + 2 a - 8\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-2\right){x}^{2}+\left(a^{3}-2a^{2}-2a+1\right){x}-a^{3}+3a^{2}+2a-8$ |
| 1.1-a2 |
1.1-a |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.50456$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$87.05150571$ |
1.036547827 |
\( -4799936 a^{3} + 16798101 a^{2} + 4501953 a - 37268866 \) |
\( \bigl[a^{2} - a - 1\) , \( a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - 1\) , \( 4 a^{2} - 6\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a^{3}-1\right){x}+4a^{2}-6$ |
| 1.1-b1 |
1.1-b |
$2$ |
$7$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$7.50456$ |
$\textsf{none}$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3, 7$ |
3Ns, 7B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1903.735524$ |
0.462619134 |
\( 7397 a^{3} - 6292 a^{2} - 36621 a - 19482 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{2} - a - 1\) , \( a^{2} - 2 a - 1\) , \( 3 a^{2} - 2 a - 3\) , \( a^{3} - a^{2} - a\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(3a^{2}-2a-3\right){x}+a^{3}-a^{2}-a$ |
| 1.1-b2 |
1.1-b |
$2$ |
$7$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$7.50456$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3, 7$ |
3Ns, 7B.1.3 |
$49$ |
\( 1 \) |
$1$ |
$0.792892763$ |
0.462619134 |
\( 100197108838743917 a^{3} + 51374873198321556 a^{2} - 121430706569246490 a - 74253359981203398 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( 325 a^{3} - 314 a^{2} - 1618 a - 850\) , \( 29017 a^{3} - 25311 a^{2} - 144721 a - 76835\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{3}-2a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-3\right){x}^{2}+\left(325a^{3}-314a^{2}-1618a-850\right){x}+29017a^{3}-25311a^{2}-144721a-76835$ |
| 7.1-a1 |
7.1-a |
$1$ |
$1$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$9.57112$ |
$(a^2-a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \) |
$1$ |
$53.09225165$ |
1.264370044 |
\( -\frac{747129832975565}{117649} a^{3} - \frac{96019398403357}{16807} a^{2} + \frac{1039577084374530}{117649} a + \frac{772992558015852}{117649} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( -a^{3} + a^{2} + 6 a\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( -6 a^{3} + 8 a^{2} + 16 a - 2\) , \( -2 a^{3} - 16 a^{2} + 21 a + 17\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a\right){x}^{2}+\left(-6a^{3}+8a^{2}+16a-2\right){x}-2a^{3}-16a^{2}+21a+17$ |
| 7.1-b1 |
7.1-b |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$9.57112$ |
$(a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.019710037$ |
$326.5989441$ |
1.839613224 |
\( \frac{475347547188}{117649} a^{3} - \frac{59120507539}{16807} a^{2} - \frac{2364148602912}{117649} a - \frac{1254392975256}{117649} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( a^{2} - a - 1\) , \( -3 a^{2} + a + 3\) , \( a^{3} - 2 a^{2} + 1\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-1\right){x}^{2}+\left(-3a^{2}+a+3\right){x}+a^{3}-2a^{2}+1$ |
| 7.1-b2 |
7.1-b |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$9.57112$ |
$(a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.059130111$ |
$326.5989441$ |
1.839613224 |
\( -\frac{381684}{49} a^{3} + \frac{147601}{7} a^{2} + \frac{821514}{49} a - \frac{1702929}{49} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 4 a^{2} - a - 8\) , \( -7 a^{3} + 9 a^{2} + 37 a + 15\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a^{2}-a-8\right){x}-7a^{3}+9a^{2}+37a+15$ |
| 7.1-c1 |
7.1-c |
$2$ |
$2$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{6} \) |
$9.57112$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$164.0560200$ |
0.976731589 |
\( \frac{10015913719882025}{117649} a^{3} - \frac{3819534044657287}{16807} a^{2} - \frac{22165384223792070}{117649} a + \frac{44885823198338802}{117649} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{3} - 3 a^{2} + 3\) , \( 1\) , \( -10 a^{3} + 29 a^{2} + 21 a - 44\) , \( -37 a^{3} + 103 a^{2} + 79 a - 178\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+{y}={x}^{3}+\left(a^{3}-3a^{2}+3\right){x}^{2}+\left(-10a^{3}+29a^{2}+21a-44\right){x}-37a^{3}+103a^{2}+79a-178$ |
| 7.1-c2 |
7.1-c |
$2$ |
$2$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{3} \) |
$9.57112$ |
$(a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$328.1120400$ |
0.976731589 |
\( -\frac{48199351}{343} a^{3} + \frac{18150081}{49} a^{2} + \frac{109133355}{343} a - \frac{209595681}{343} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{3} - 3 a^{2} + 3\) , \( 1\) , \( 4 a^{2} - 4 a - 4\) , \( a^{3} - a - 4\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+{y}={x}^{3}+\left(a^{3}-3a^{2}+3\right){x}^{2}+\left(4a^{2}-4a-4\right){x}+a^{3}-a-4$ |
| 9.1-a1 |
9.1-a |
$2$ |
$7$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$9.87656$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 7$ |
3Ns, 7B.6.3 |
$1$ |
\( 1 \) |
$1.732613581$ |
$23.56462697$ |
1.944622618 |
\( 100197108838743917 a^{3} + 51374873198321556 a^{2} - 121430706569246490 a - 74253359981203398 \) |
\( \bigl[a\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( a + 1\) , \( -62 a^{3} + 246 a^{2} - 53 a - 690\) , \( -1283 a^{3} - 942 a^{2} + 9967 a + 12088\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-3\right){x}^{2}+\left(-62a^{3}+246a^{2}-53a-690\right){x}-1283a^{3}-942a^{2}+9967a+12088$ |
| 9.1-a2 |
9.1-a |
$2$ |
$7$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$9.87656$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3, 7$ |
3Ns, 7B.6.1 |
$1$ |
\( 1 \) |
$0.247516225$ |
$164.9523887$ |
1.944622618 |
\( 7397 a^{3} - 6292 a^{2} - 36621 a - 19482 \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - a^{2} - 6 a\) , \( a^{2} - 2 a - 2\) , \( 2 a^{3} - 7 a^{2} - 3 a + 18\) , \( 4 a^{3} - 9 a^{2} - 11 a + 10\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a\right){x}^{2}+\left(2a^{3}-7a^{2}-3a+18\right){x}+4a^{3}-9a^{2}-11a+10$ |
| 9.1-b1 |
9.1-b |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$9.87656$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.028460386$ |
$663.6272249$ |
1.799152757 |
\( 4389623576 a^{3} - 14764975849 a^{2} + 2575154231 a + 9657368279 \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a\) , \( -a^{3} - a^{2} + 7 a + 6\) , \( a^{3} - 4 a^{2} - a + 10\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(-a^{3}-a^{2}+7a+6\right){x}+a^{3}-4a^{2}-a+10$ |
| 9.1-b2 |
9.1-b |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$9.87656$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.009486795$ |
$1990.881674$ |
1.799152757 |
\( -4799936 a^{3} + 16798101 a^{2} + 4501953 a - 37268866 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} + a^{2} - 2 a - 9\) , \( -4 a^{3} + 9 a^{2} + 14 a + 1\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(a^{3}+a^{2}-2a-9\right){x}-4a^{3}+9a^{2}+14a+1$ |
| 9.2-a1 |
9.2-a |
$2$ |
$5$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{20} \) |
$9.87656$ |
$(-a^3+3a^2+2a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$2.157688456$ |
1.284611485 |
\( \frac{2224058621675000}{59049} a^{3} - \frac{1828455598396549}{59049} a^{2} - \frac{402950453601565}{2187} a - \frac{1932181793729915}{19683} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( -96 a^{3} + 308 a^{2} - 16 a - 204\) , \( 21400 a^{3} - 72000 a^{2} + 12606 a + 47085\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-96a^{3}+308a^{2}-16a-204\right){x}+21400a^{3}-72000a^{2}+12606a+47085$ |
| 9.2-a2 |
9.2-a |
$2$ |
$5$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$9.87656$ |
$(-a^3+3a^2+2a-4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1348.555285$ |
1.284611485 |
\( \frac{16630}{9} a^{3} - \frac{49373}{9} a^{2} + 735 a + \frac{10574}{3} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{2} - a - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{2} - 2 a - 4\) , \( a^{3} - a^{2} - 6 a - 4\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(a^{2}-2a-4\right){x}+a^{3}-a^{2}-6a-4$ |
| 9.2-b1 |
9.2-b |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{12} \) |
$9.87656$ |
$(-a^3+3a^2+2a-4)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.075113322$ |
$663.1504323$ |
1.581651580 |
\( -\frac{377966281}{729} a^{3} + \frac{337060457}{243} a^{2} + \frac{277783957}{243} a - \frac{63047282}{27} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( -a^{3} + 3 a^{2} + 2 a - 5\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( 2 a^{3} - 5 a^{2} - 5 a + 5\) , \( 4 a^{3} - 16 a^{2} + 8 a + 8\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{3}-2a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-5\right){x}^{2}+\left(2a^{3}-5a^{2}-5a+5\right){x}+4a^{3}-16a^{2}+8a+8$ |
| 9.2-b2 |
9.2-b |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{4} \) |
$9.87656$ |
$(-a^3+3a^2+2a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.225339967$ |
$73.68338137$ |
1.581651580 |
\( \frac{381169922}{9} a^{3} - \frac{584888374}{9} a^{2} - 11097564 a + \frac{103197841}{3} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{3} - a^{2} - 5 a\) , \( -21 a^{3} + 16 a^{2} + 109 a + 62\) , \( -22 a^{3} + 19 a^{2} + 110 a + 56\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(-21a^{3}+16a^{2}+109a+62\right){x}-22a^{3}+19a^{2}+110a+56$ |
| 13.2-a1 |
13.2-a |
$3$ |
$9$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
13.2 |
\( 13 \) |
\( - 13^{2} \) |
$10.34114$ |
$(a^3-a^2-2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.056900768$ |
$2755.962752$ |
1.659785677 |
\( \frac{857378401}{169} a^{3} - \frac{931181514}{169} a^{2} - \frac{403026028}{169} a + \frac{404529673}{169} \) |
\( \bigl[a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( -3 a^{3} + 21 a + 12\) , \( -6 a^{3} + 9 a^{2} + 19 a + 10\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){x}{y}+\left(a^{3}-2a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+1\right){x}^{2}+\left(-3a^{3}+21a+12\right){x}-6a^{3}+9a^{2}+19a+10$ |
| 13.2-a2 |
13.2-a |
$3$ |
$9$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
13.2 |
\( 13 \) |
\( - 13^{6} \) |
$10.34114$ |
$(a^3-a^2-2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.170702306$ |
$306.2180835$ |
1.659785677 |
\( \frac{724704642}{4826809} a^{3} - \frac{1453839794}{4826809} a^{2} - \frac{339132684}{4826809} a + \frac{4076993239}{4826809} \) |
\( \bigl[a^{2} - a - 1\) , \( -a + 1\) , \( 1\) , \( 1\) , \( -13 a^{3} + 44 a^{2} - 8 a - 29\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+{x}-13a^{3}+44a^{2}-8a-29$ |
| 13.2-a3 |
13.2-a |
$3$ |
$9$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
13.2 |
\( 13 \) |
\( - 13^{2} \) |
$10.34114$ |
$(a^3-a^2-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.512106918$ |
$34.02423150$ |
1.659785677 |
\( \frac{2097641781}{169} a^{3} + \frac{1901019332}{169} a^{2} - \frac{2929606023}{169} a - \frac{2211006077}{169} \) |
\( \bigl[a\) , \( a^{3} - 3 a^{2} - a + 5\) , \( a\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( -a^{3} - a^{2} + 12 a - 11\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{3}-3a^{2}-a+5\right){x}^{2}+\left(-a^{3}+2a^{2}+2a-3\right){x}-a^{3}-a^{2}+12a-11$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$10.61306$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.032638277$ |
$803.2388811$ |
2.497324618 |
\( \frac{15367845}{4} a^{3} - \frac{51609969}{4} a^{2} + 2213200 a + \frac{16801973}{2} \) |
\( \bigl[a\) , \( -a^{3} + 3 a^{2} + 2 a - 5\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} - 4 a^{2} + 6\) , \( a^{3} - 2 a^{2} - 5 a + 2\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-5\right){x}^{2}+\left(a^{3}-4a^{2}+6\right){x}+a^{3}-2a^{2}-5a+2$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$10.61306$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.039599098$ |
$198.3262739$ |
1.496230801 |
\( \frac{12547}{16} a^{3} - \frac{7935}{16} a^{2} - \frac{33517}{8} a - 2800 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -a^{3} + 3 a^{2} + 2 a - 3\) , \( a\) , \( a^{3} - 4 a - 1\) , \( a^{2} + a\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-3\right){x}^{2}+\left(a^{3}-4a-1\right){x}+a^{2}+a$ |
| 16.1-c1 |
16.1-c |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$10.61306$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$51.77945781$ |
1.233106401 |
\( \frac{100747072997}{16} a^{3} - \frac{21826586469}{4} a^{2} - \frac{501942165261}{16} a - \frac{133332626205}{8} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( a - 1\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( -2 a^{3} - 11 a^{2} + 17\) , \( -28 a^{3} - 7 a^{2} + 43 a + 1\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{3}-2a^{2}-2a+3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a^{3}-11a^{2}+17\right){x}-28a^{3}-7a^{2}+43a+1$ |
| 16.1-c2 |
16.1-c |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{48} \) |
$10.61306$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$51.77945781$ |
1.233106401 |
\( \frac{15537947}{4096} a^{3} + \frac{17761019}{4096} a^{2} - \frac{25216389}{4096} a - \frac{29120181}{4096} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{2} - 2 a - 1\) , \( a^{2} - 2 a - 1\) , \( 7 a^{3} - 22 a^{2} + 12\) , \( 61 a^{3} - 204 a^{2} + 33 a + 132\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(7a^{3}-22a^{2}+12\right){x}+61a^{3}-204a^{2}+33a+132$ |
| 19.1-a1 |
19.1-a |
$1$ |
$1$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{2} \) |
$10.84351$ |
$(a^3-2a^2-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.160130428$ |
$167.2763911$ |
2.551593939 |
\( \frac{93185661}{361} a^{3} + \frac{85621256}{361} a^{2} - \frac{129283686}{361} a - \frac{99343718}{361} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( a^{3} - a^{2} - 6 a\) , \( a^{2} - 2 a - 1\) , \( -a^{3} + 2 a^{2} + a + 3\) , \( 2 a^{2} - 5 a - 3\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a\right){x}^{2}+\left(-a^{3}+2a^{2}+a+3\right){x}+2a^{2}-5a-3$ |
| 19.1-b1 |
19.1-b |
$1$ |
$1$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{4} \) |
$10.84351$ |
$(a^3-2a^2-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.011268578$ |
$795.2768543$ |
1.707341993 |
\( -\frac{257421120941}{130321} a^{3} + \frac{687138289753}{130321} a^{2} + \frac{569719177254}{130321} a - \frac{1153510765000}{130321} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( a^{2} - 2 a - 1\) , \( -6 a^{3} + 6 a^{2} + 31 a + 16\) , \( -9 a^{3} + 8 a^{2} + 50 a + 27\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a+1\right){x}^{2}+\left(-6a^{3}+6a^{2}+31a+16\right){x}-9a^{3}+8a^{2}+50a+27$ |
| 21.1-a1 |
21.1-a |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{24} \cdot 7^{2} \) |
$10.98001$ |
$(-a), (a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.358426641$ |
$31.43876854$ |
2.146835904 |
\( -\frac{31446036035}{26040609} a^{3} + \frac{8521849619}{3720087} a^{2} + \frac{17636745986}{8680203} a - \frac{106455205621}{26040609} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( a^{2} - 2 a - 2\) , \( a^{2} - a - 2\) , \( -15 a^{3} + 42 a^{2} + 24 a - 60\) , \( 40 a^{3} - 107 a^{2} - 89 a + 179\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-15a^{3}+42a^{2}+24a-60\right){x}+40a^{3}-107a^{2}-89a+179$ |
| 21.1-a2 |
21.1-a |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7^{6} \) |
$10.98001$ |
$(-a), (a^2-a-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.119475547$ |
$282.9489169$ |
2.146835904 |
\( -\frac{230530703460876016}{9529569} a^{3} + \frac{1085334503511228}{16807} a^{2} + \frac{510168299909965628}{9529569} a - \frac{1033112053364066113}{9529569} \) |
\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a^{3} + 3 a^{2} + 2 a - 4\) , \( a^{2} - a - 2\) , \( -20 a^{3} + 18 a^{2} + 106 a + 60\) , \( -207 a^{3} + 184 a^{2} + 1040 a + 551\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-4\right){x}^{2}+\left(-20a^{3}+18a^{2}+106a+60\right){x}-207a^{3}+184a^{2}+1040a+551$ |
| 21.1-b1 |
21.1-b |
$1$ |
$1$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7^{2} \) |
$10.98001$ |
$(-a), (a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \) |
$0.009818676$ |
$362.8808751$ |
2.715251435 |
\( \frac{3452000359}{3969} a^{3} - \frac{1658000038}{567} a^{2} + \frac{671091599}{1323} a + \frac{7585795517}{3969} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 7 a^{2} + 7 a + 21\) , \( 7 a^{3} - 22 a^{2} - 2 a + 53\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(a^{3}-7a^{2}+7a+21\right){x}+7a^{3}-22a^{2}-2a+53$ |
| 21.1-c1 |
21.1-c |
$2$ |
$2$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3 \cdot 7^{2} \) |
$10.98001$ |
$(-a), (a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.091102584$ |
$880.3940946$ |
1.910076982 |
\( \frac{8645431674270313}{147} a^{3} + \frac{1111091531023099}{21} a^{2} - \frac{12029490687232420}{147} a - \frac{2981569591995795}{49} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( -222 a^{3} + 591 a^{2} + 497 a - 1001\) , \( -2470 a^{3} + 6598 a^{2} + 5448 a - 11055\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+1\right){x}^{2}+\left(-222a^{3}+591a^{2}+497a-1001\right){x}-2470a^{3}+6598a^{2}+5448a-11055$ |
| 21.1-c2 |
21.1-c |
$2$ |
$2$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7 \) |
$10.98001$ |
$(-a), (a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.045551292$ |
$1760.788189$ |
1.910076982 |
\( -\frac{31115143}{21} a^{3} - \frac{3987215}{3} a^{2} + \frac{14494659}{7} a + \frac{32292226}{21} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 28 a^{3} - 74 a^{2} - 63 a + 124\) , \( -176 a^{3} + 470 a^{2} + 389 a - 789\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+1\right){x}^{2}+\left(28a^{3}-74a^{2}-63a+124\right){x}-176a^{3}+470a^{2}+389a-789$ |
| 27.1-a1 |
27.1-a |
$1$ |
$1$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{5} \) |
$11.33042$ |
$(-a), (-a^3+3a^2+2a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$100.1545493$ |
1.192569612 |
\( \frac{366674}{9} a^{3} - \frac{325081}{9} a^{2} - \frac{1813796}{9} a - \frac{315425}{3} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( -a^{3} + 3 a^{2} + a - 4\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - a^{2} - 3 a + 3\) , \( -3 a^{3} + 7 a^{2} + 6 a - 12\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{3}-2a^{2}-3a+3\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+a-4\right){x}^{2}+\left(a^{3}-a^{2}-3a+3\right){x}-3a^{3}+7a^{2}+6a-12$ |
| 27.1-b1 |
27.1-b |
$1$ |
$1$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{11} \) |
$11.33042$ |
$(-a), (-a^3+3a^2+2a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$60.90325651$ |
0.725192949 |
\( -\frac{22789909}{243} a^{3} + \frac{60283448}{243} a^{2} + \frac{50655823}{243} a - \frac{34011007}{81} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( -a^{3} + 3 a^{2} + a - 5\) , \( a^{2} - 2 a - 1\) , \( 2 a^{3} - 6 a^{2} - 2 a + 5\) , \( -1\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+a-5\right){x}^{2}+\left(2a^{3}-6a^{2}-2a+5\right){x}-1$ |
| 27.2-a1 |
27.2-a |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{9} \) |
$11.33042$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$124.3484113$ |
1.480653028 |
\( 194159 a^{3} - 518903 a^{2} - 427758 a + 870135 \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 6 a - 1\) , \( a + 1\) , \( -2 a^{3} + 2 a^{2} + 10 a + 7\) , \( 2 a^{3} - 3 a^{2} - 11 a - 5\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a-1\right){x}^{2}+\left(-2a^{3}+2a^{2}+10a+7\right){x}+2a^{3}-3a^{2}-11a-5$ |
| 27.2-a2 |
27.2-a |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{11} \) |
$11.33042$ |
$(-a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1119.135701$ |
1.480653028 |
\( 1716 a^{3} - 3694 a^{2} - 5626 a + 4971 \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 3\) , \( 0\) , \( a^{2} - 2 a - 2\) , \( a^{3} - 3 a^{2} - 3 a + 3\) , \( a^{3} - a^{2} - 2 a\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+3\right){x}{y}+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+3\right){x}+a^{3}-a^{2}-2a$ |
| 27.2-b1 |
27.2-b |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{3} \) |
$11.33042$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.071947108$ |
$704.5323087$ |
2.414278173 |
\( 194159 a^{3} - 518903 a^{2} - 427758 a + 870135 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{2} - 2 a - 1\) , \( a^{2} - a - 1\) , \( -2 a^{3} + 4 a^{2} + 5 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(-2a^{3}+4a^{2}+5a+1\right){x}$ |
| 27.2-b2 |
27.2-b |
$2$ |
$3$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{5} \) |
$11.33042$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.215841325$ |
$234.8441029$ |
2.414278173 |
\( 1716 a^{3} - 3694 a^{2} - 5626 a + 4971 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( -19 a^{3} + 53 a^{2} + 43 a - 87\) , \( -58 a^{3} + 158 a^{2} + 128 a - 266\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{3}-2a^{2}-3a+2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-19a^{3}+53a^{2}+43a-87\right){x}-58a^{3}+158a^{2}+128a-266$ |
| 29.1-a1 |
29.1-a |
$1$ |
$1$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$11.43208$ |
$(a^2-3a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$256.4926656$ |
3.054133447 |
\( \frac{3644243}{29} a^{3} - \frac{12276295}{29} a^{2} + \frac{2186163}{29} a + \frac{7996350}{29} \) |
\( \bigl[a^{3} - 2 a^{2} - 3 a + 2\) , \( -a^{2} + a + 2\) , \( 0\) , \( -a^{3} + 3 a + 2\) , \( -a^{3} - a^{2} + 2 a + 2\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-3a+2\right){x}{y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-a^{3}+3a+2\right){x}-a^{3}-a^{2}+2a+2$ |
| 31.1-a1 |
31.1-a |
$8$ |
$12$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$11.52778$ |
$(a^3-2a^2-4a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$719.8965190$ |
0.535751195 |
\( \frac{132064}{31} a^{3} - \frac{152664}{31} a^{2} - \frac{591312}{31} a - \frac{219321}{31} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 3 a^{2} - a + 3\) , \( 0\) , \( -a^{3} + 6 a + 7\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}={x}^{3}+\left(a^{3}-3a^{2}-a+3\right){x}^{2}+\left(-a^{3}+6a+7\right){x}$ |
| 31.1-a2 |
31.1-a |
$8$ |
$12$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31 \) |
$11.52778$ |
$(a^3-2a^2-4a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$179.9741297$ |
0.535751195 |
\( -\frac{11683372712386}{31} a^{3} + \frac{53093598463426}{31} a^{2} - \frac{62487708909366}{31} a + \frac{19630166901621}{31} \) |
\( \bigl[1\) , \( -a^{3} + 3 a^{2} + 2 a - 4\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( 161 a^{3} - 160 a^{2} - 844 a - 446\) , \( 2515 a^{3} - 2058 a^{2} - 12287 a - 6551\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-4\right){x}^{2}+\left(161a^{3}-160a^{2}-844a-446\right){x}+2515a^{3}-2058a^{2}-12287a-6551$ |
| 31.1-a3 |
31.1-a |
$8$ |
$12$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{4} \) |
$11.52778$ |
$(a^3-2a^2-4a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$22.49676621$ |
0.535751195 |
\( -\frac{88624798831927880659202}{923521} a^{3} + \frac{76801333346495104759042}{923521} a^{2} + \frac{441546621483730679753994}{923521} a + \frac{234579114573372121448805}{923521} \) |
\( \bigl[1\) , \( a^{3} - 3 a^{2} - a + 5\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 10 a^{3} - 52 a^{2} + 76 a - 31\) , \( -364 a^{3} + 1067 a^{2} + 421 a - 1323\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-a+5\right){x}^{2}+\left(10a^{3}-52a^{2}+76a-31\right){x}-364a^{3}+1067a^{2}+421a-1323$ |
| 31.1-a4 |
31.1-a |
$8$ |
$12$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{2} \) |
$11.52778$ |
$(a^3-2a^2-4a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1$ |
$359.9482595$ |
0.535751195 |
\( -\frac{105568534528}{961} a^{3} + \frac{91719725308}{961} a^{2} + \frac{524987400192}{961} a + \frac{280295003589}{961} \) |
\( \bigl[a + 1\) , \( a^{2} - 3 a - 1\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( -11 a^{3} - 6 a^{2} + 15 a + 8\) , \( 47 a^{3} + 46 a^{2} - 65 a - 54\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a^{2}-2a+3\right){y}={x}^{3}+\left(a^{2}-3a-1\right){x}^{2}+\left(-11a^{3}-6a^{2}+15a+8\right){x}+47a^{3}+46a^{2}-65a-54$ |
| 31.1-a5 |
31.1-a |
$8$ |
$12$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{3} \) |
$11.52778$ |
$(a^3-2a^2-4a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$719.8965190$ |
0.535751195 |
\( \frac{97579855891}{29791} a^{3} - \frac{266748888134}{29791} a^{2} - \frac{217378557279}{29791} a + \frac{447019479969}{29791} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{2} - a - 2\) , \( -5 a^{3} + 11 a^{2} + 10 a - 18\) , \( 4 a^{3} - 10 a^{2} - 9 a + 16\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(-5a^{3}+11a^{2}+10a-18\right){x}+4a^{3}-10a^{2}-9a+16$ |
| 31.1-a6 |
31.1-a |
$8$ |
$12$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{6} \) |
$11.52778$ |
$(a^3-2a^2-4a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$1$ |
$359.9482595$ |
0.535751195 |
\( \frac{82707461324628693161}{887503681} a^{3} + \frac{74405643238092359599}{887503681} a^{2} - \frac{115081430094022369359}{887503681} a - \frac{85570523773379934078}{887503681} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{2} - a - 2\) , \( -15 a^{3} + a^{2} + 25 a - 8\) , \( 58 a^{3} + 44 a^{2} - 82 a - 49\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(-15a^{3}+a^{2}+25a-8\right){x}+58a^{3}+44a^{2}-82a-49$ |
| 31.1-a7 |
31.1-a |
$8$ |
$12$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{3} \) |
$11.52778$ |
$(a^3-2a^2-4a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$179.9741297$ |
0.535751195 |
\( \frac{6952951385562597153458837393}{29791} a^{3} + \frac{6255044210971168389026378887}{29791} a^{2} - \frac{9674527181594265551021456352}{29791} a - \frac{7193640211384060671716771463}{29791} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{2} - a - 2\) , \( -200 a^{3} - 89 a^{2} + 305 a + 57\) , \( 4166 a^{3} + 4347 a^{2} - 5668 a - 5223\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(-200a^{3}-89a^{2}+305a+57\right){x}+4166a^{3}+4347a^{2}-5668a-5223$ |
| 31.1-a8 |
31.1-a |
$8$ |
$12$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{12} \) |
$11.52778$ |
$(a^3-2a^2-4a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$22.49676621$ |
0.535751195 |
\( -\frac{971068527462837450406799}{787662783788549761} a^{3} + \frac{3237972148068356964306087}{787662783788549761} a^{2} - \frac{157208778348322141269984}{787662783788549761} a - \frac{1847162839175011070746839}{787662783788549761} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{2} - a - 2\) , \( 10 a^{3} - 69 a^{2} - 15 a + 87\) , \( 146 a^{3} - 203 a^{2} - 228 a + 305\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(10a^{3}-69a^{2}-15a+87\right){x}+146a^{3}-203a^{2}-228a+305$ |
| 39.1-a1 |
39.1-a |
$4$ |
$6$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{3} \cdot 13^{3} \) |
$11.86338$ |
$(-a), (a^3-3a^2-a+5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.262666303$ |
$2356.805065$ |
2.457083004 |
\( -\frac{2664174017}{19773} a^{3} + \frac{7095870787}{19773} a^{2} + \frac{5837712122}{19773} a - \frac{3692621425}{6591} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{2} - 2 a - 2\) , \( 2 a^{3} - 4 a^{2} - 5 a + 2\) , \( -a^{3} + 7 a + 5\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(2a^{3}-4a^{2}-5a+2\right){x}-a^{3}+7a+5$ |
| 39.1-a2 |
39.1-a |
$4$ |
$6$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{6} \cdot 13^{6} \) |
$11.86338$ |
$(-a), (a^3-3a^2-a+5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.525332606$ |
$294.6006331$ |
2.457083004 |
\( \frac{3021665795040719227}{43441281} a^{3} - \frac{24198340044240145240}{130323843} a^{2} - \frac{20060990685675723184}{130323843} a + \frac{40624341730636509967}{130323843} \) |
\( \bigl[a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( a^{3} - a^{2} - 5 a\) , \( a^{3} - 6 a^{2} + 6 a + 18\) , \( -261 a^{3} + 235 a^{2} + 1335 a + 720\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a+1\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+4\right){x}^{2}+\left(a^{3}-6a^{2}+6a+18\right){x}-261a^{3}+235a^{2}+1335a+720$ |
| 39.1-a3 |
39.1-a |
$4$ |
$6$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{18} \cdot 13^{2} \) |
$11.86338$ |
$(-a), (a^3-3a^2-a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1.575997819$ |
$32.73340368$ |
2.457083004 |
\( -\frac{1770055917625936}{3326427} a^{3} + \frac{5953779271554862}{3326427} a^{2} - \frac{115379065320514}{369603} a - \frac{3894189375132473}{3326427} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( -a^{2} + 3 a + 2\) , \( a^{2} - a - 2\) , \( -3 a^{3} + 43 a - 39\) , \( 66 a^{3} - 197 a^{2} - 55 a + 221\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+3a+2\right){x}^{2}+\left(-3a^{3}+43a-39\right){x}+66a^{3}-197a^{2}-55a+221$ |
| 39.1-a4 |
39.1-a |
$4$ |
$6$ |
4.4.7053.1 |
$4$ |
$[4, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{9} \cdot 13 \) |
$11.86338$ |
$(-a), (a^3-3a^2-a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$0.787998909$ |
$261.8672294$ |
2.457083004 |
\( -\frac{44105264}{3159} a^{3} + \frac{128114824}{3159} a^{2} + \frac{114906344}{3159} a + \frac{787907}{351} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( -a^{2} + 3 a + 2\) , \( a^{2} - a - 2\) , \( 2 a^{3} - 5 a^{2} - 2 a + 11\) , \( 5 a^{3} - 12 a^{2} - 10 a + 21\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+3a+2\right){x}^{2}+\left(2a^{3}-5a^{2}-2a+11\right){x}+5a^{3}-12a^{2}-10a+21$ |
*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.
