| 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 |
| 9.1-a1 |
9.1-a |
$4$ |
$10$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{40} \) |
$11.63736$ |
$(a^3-3a^2-2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$100$ |
\( 2 \) |
$1$ |
$1.605094755$ |
0.811026374 |
\( -\frac{873722816}{59049} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( a^{3} - 3 a^{2} - 3 a + 3\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( 39 a^{3} - 117 a^{2} - 117 a + 96\) , \( 152 a^{3} - 456 a^{2} - 456 a + 388\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a^{3}-3a^{2}-3a+5\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+3\right){x}^{2}+\left(39a^{3}-117a^{2}-117a+96\right){x}+152a^{3}-456a^{2}-456a+388$ |
| 9.1-a2 |
9.1-a |
$4$ |
$10$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$11.63736$ |
$(a^3-3a^2-2a+5)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$1003.184222$ |
0.811026374 |
\( \frac{64}{9} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( -a^{3} + 3 a^{2} + 3 a - 5\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a^{3}-3a^{2}-3a+5\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-5\right){x}^{2}$ |
| 9.1-a3 |
9.1-a |
$4$ |
$10$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$11.63736$ |
$(a^3-3a^2-2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$6.420379023$ |
0.811026374 |
\( \frac{58591911104}{243} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( -a^{3} + 3 a^{2} + 3 a - 4\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( 161 a^{3} - 483 a^{2} - 483 a + 401\) , \( 1494 a^{3} - 4482 a^{2} - 4482 a + 3846\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a^{3}-3a^{2}-3a+5\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-4\right){x}^{2}+\left(161a^{3}-483a^{2}-483a+401\right){x}+1494a^{3}-4482a^{2}-4482a+3846$ |
| 9.1-a4 |
9.1-a |
$4$ |
$10$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$11.63736$ |
$(a^3-3a^2-2a+5)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$4012.736889$ |
0.811026374 |
\( \frac{85184}{3} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( a^{3} - 3 a^{2} - 3 a + 4\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( -2 a^{3} + 6 a^{2} + 6 a - 11\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a^{3}-3a^{2}-3a+5\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+4\right){x}^{2}+\left(-2a^{3}+6a^{2}+6a-11\right){x}$ |
| 9.1-b1 |
9.1-b |
$4$ |
$10$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$11.63736$ |
$(a^3-3a^2-2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \cdot 5 \) |
$0.038073707$ |
$571.6658535$ |
2.199539245 |
\( \frac{58591911104}{243} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 3 a^{2} - 3 a + 3\) , \( -a^{3} + 4 a^{2} + 2 a - 8\) , \( 162 a^{3} - 726 a^{2} - 325 a + 966\) , \( -1656 a^{3} + 8052 a^{2} + 3376 a - 10778\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(-a^{3}+4a^{2}+2a-8\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+3\right){x}^{2}+\left(162a^{3}-726a^{2}-325a+966\right){x}-1656a^{3}+8052a^{2}+3376a-10778$ |
| 9.1-b2 |
9.1-b |
$4$ |
$10$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$11.63736$ |
$(a^3-3a^2-2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$0.190368536$ |
$571.6658535$ |
2.199539245 |
\( \frac{85184}{3} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 3 a^{2} - 3 a + 3\) , \( -a^{3} + 4 a^{2} + 2 a - 8\) , \( 2 a^{3} - 6 a^{2} - 5 a + 6\) , \( -a^{3} - 3 a^{2} + a + 2\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(-a^{3}+4a^{2}+2a-8\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+3\right){x}^{2}+\left(2a^{3}-6a^{2}-5a+6\right){x}-a^{3}-3a^{2}+a+2$ |
| 9.1-b3 |
9.1-b |
$4$ |
$10$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$11.63736$ |
$(a^3-3a^2-2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.380737072$ |
$142.9164633$ |
2.199539245 |
\( \frac{64}{9} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( -a^{3} + 4 a^{2} - 9\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( -3 a^{3} + 7 a^{2} + 15 a + 1\) , \( 19 a^{3} - 16 a^{2} - 159 a - 137\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a^{3}-3a^{2}-3a+5\right){y}={x}^{3}+\left(-a^{3}+4a^{2}-9\right){x}^{2}+\left(-3a^{3}+7a^{2}+15a+1\right){x}+19a^{3}-16a^{2}-159a-137$ |
| 9.1-b4 |
9.1-b |
$4$ |
$10$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{40} \) |
$11.63736$ |
$(a^3-3a^2-2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.076147414$ |
$142.9164633$ |
2.199539245 |
\( -\frac{873722816}{59049} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( -a^{2} + 3 a + 4\) , \( 1\) , \( 755 a^{3} - 2665 a^{2} - 1225 a + 3448\) , \( -19446 a^{3} + 67992 a^{2} + 34443 a - 90763\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+3a+4\right){x}^{2}+\left(755a^{3}-2665a^{2}-1225a+3448\right){x}-19446a^{3}+67992a^{2}+34443a-90763$ |
| 17.1-a1 |
17.1-a |
$4$ |
$6$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{12} \) |
$12.60029$ |
$(a^3-3a^2-2a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.923526946$ |
$180.7559717$ |
2.249289004 |
\( -\frac{1522678220544}{24137569} a^{3} + \frac{4568034661632}{24137569} a^{2} + \frac{4568034661632}{24137569} a - \frac{8238458077888}{24137569} \) |
\( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( a^{3} - 3 a^{2} - 3 a + 3\) , \( 1\) , \( -62 a^{3} + 192 a^{2} + 210 a - 313\) , \( 255 a^{3} - 872 a^{2} - 674 a + 1751\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+2a-7\right){x}{y}+{y}={x}^{3}+\left(a^{3}-3a^{2}-3a+3\right){x}^{2}+\left(-62a^{3}+192a^{2}+210a-313\right){x}+255a^{3}-872a^{2}-674a+1751$ |
| 17.1-a2 |
17.1-a |
$4$ |
$6$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$12.60029$ |
$(a^3-3a^2-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.307842315$ |
$180.7559717$ |
2.249289004 |
\( \frac{94464}{289} a^{3} - \frac{283392}{289} a^{2} - \frac{283392}{289} a + \frac{436544}{289} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 2 a + 3\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a^{3} - 4 a^{2} + 3 a + 12\) , \( 3 a^{3} - 9 a^{2} - a + 16\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-3a^{2}-3a+5\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(a^{3}-4a^{2}+3a+12\right){x}+3a^{3}-9a^{2}-a+16$ |
| 17.1-a3 |
17.1-a |
$4$ |
$6$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$12.60029$ |
$(a^3-3a^2-2a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.461763473$ |
$723.0238868$ |
2.249289004 |
\( \frac{55615383938816}{4913} a^{3} - \frac{166846151816448}{4913} a^{2} - \frac{166846151816448}{4913} a + \frac{301113605197120}{4913} \) |
\( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( 2 a^{3} - 7 a^{2} - 3 a + 12\) , \( 1\) , \( -226 a^{3} + 751 a^{2} + 653 a - 1418\) , \( 2180 a^{3} - 7069 a^{2} - 6601 a + 12877\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+2a-7\right){x}{y}+{y}={x}^{3}+\left(2a^{3}-7a^{2}-3a+12\right){x}^{2}+\left(-226a^{3}+751a^{2}+653a-1418\right){x}+2180a^{3}-7069a^{2}-6601a+12877$ |
| 17.1-a4 |
17.1-a |
$4$ |
$6$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$12.60029$ |
$(a^3-3a^2-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.153921157$ |
$723.0238868$ |
2.249289004 |
\( -\frac{3690752}{17} a^{3} + \frac{11072256}{17} a^{2} + \frac{11072256}{17} a - \frac{9475776}{17} \) |
\( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( 2 a^{3} - 7 a^{2} - 3 a + 12\) , \( 1\) , \( -a^{3} + 11 a^{2} - 7 a - 33\) , \( 10 a^{3} - 10 a^{2} - 68 a - 49\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+2a-7\right){x}{y}+{y}={x}^{3}+\left(2a^{3}-7a^{2}-3a+12\right){x}^{2}+\left(-a^{3}+11a^{2}-7a-33\right){x}+10a^{3}-10a^{2}-68a-49$ |
| 17.1-b1 |
17.1-b |
$4$ |
$6$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$12.60029$ |
$(a^3-3a^2-2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1976.978914$ |
1.109925501 |
\( -\frac{3690752}{17} a^{3} + \frac{11072256}{17} a^{2} + \frac{11072256}{17} a - \frac{9475776}{17} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( -a^{3} + 3 a^{2} + 3 a - 3\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( -2 a^{3} + 6 a^{2} + 6 a - 9\) , \( -a^{3} + 3 a^{2} + 3 a - 5\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a^{3}-3a^{2}-3a+5\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-3\right){x}^{2}+\left(-2a^{3}+6a^{2}+6a-9\right){x}-a^{3}+3a^{2}+3a-5$ |
| 17.1-b2 |
17.1-b |
$4$ |
$6$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$12.60029$ |
$(a^3-3a^2-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$24.40714709$ |
1.109925501 |
\( \frac{55615383938816}{4913} a^{3} - \frac{166846151816448}{4913} a^{2} - \frac{166846151816448}{4913} a + \frac{301113605197120}{4913} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( -1\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( 33 a^{3} - 99 a^{2} - 99 a + 79\) , \( 112 a^{3} - 336 a^{2} - 336 a + 285\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a^{3}-3a^{2}-3a+5\right){y}={x}^{3}-{x}^{2}+\left(33a^{3}-99a^{2}-99a+79\right){x}+112a^{3}-336a^{2}-336a+285$ |
| 17.1-b3 |
17.1-b |
$4$ |
$6$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{12} \) |
$12.60029$ |
$(a^3-3a^2-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 2 \) |
$1$ |
$6.101786773$ |
1.109925501 |
\( -\frac{1522678220544}{24137569} a^{3} + \frac{4568034661632}{24137569} a^{2} + \frac{4568034661632}{24137569} a - \frac{8238458077888}{24137569} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( -14 a^{3} + 42 a^{2} + 42 a - 75\) , \( -48 a^{3} + 144 a^{2} + 144 a - 261\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a^{3}-3a^{2}-3a+5\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+5\right){x}^{2}+\left(-14a^{3}+42a^{2}+42a-75\right){x}-48a^{3}+144a^{2}+144a-261$ |
| 17.1-b4 |
17.1-b |
$4$ |
$6$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$12.60029$ |
$(a^3-3a^2-2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$494.2447286$ |
1.109925501 |
\( \frac{94464}{289} a^{3} - \frac{283392}{289} a^{2} - \frac{283392}{289} a + \frac{436544}{289} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a^{3}-3a^{2}-3a+5\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+5\right){x}^{2}+\left(a^{3}-3a^{2}-3a+5\right){x}$ |
| 23.1-a1 |
23.1-a |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$13.08550$ |
$(-2a^3+7a^2+4a-12)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.054175544$ |
$858.4398146$ |
1.879911589 |
\( -\frac{329984}{23} a^{3} + \frac{1154880}{23} a^{2} + \frac{471424}{23} a - \frac{1114560}{23} \) |
\( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( -a^{3} + 4 a^{2} + a - 9\) , \( a^{2} - 2 a - 4\) , \( -3 a^{3} + 10 a^{2} + 10 a - 17\) , \( -a^{3} + 5 a^{2} + a - 14\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+2a-7\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a^{3}+4a^{2}+a-9\right){x}^{2}+\left(-3a^{3}+10a^{2}+10a-17\right){x}-a^{3}+5a^{2}+a-14$ |
| 23.1-a2 |
23.1-a |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$13.08550$ |
$(-2a^3+7a^2+4a-12)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.108351088$ |
$858.4398146$ |
1.879911589 |
\( -\frac{292992}{529} a^{3} + \frac{1110464}{529} a^{2} + \frac{567552}{529} a - \frac{1473536}{529} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( a^{3} - 3 a^{2} - 4 a + 4\) , \( a\) , \( 2 a^{3} - 7 a^{2} - 5 a + 13\) , \( -a^{3} + 3 a^{2} + 3 a - 6\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-3a^{2}-4a+4\right){x}^{2}+\left(2a^{3}-7a^{2}-5a+13\right){x}-a^{3}+3a^{2}+3a-6$ |
| 23.1-b1 |
23.1-b |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$13.08550$ |
$(-2a^3+7a^2+4a-12)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.040324429$ |
$1905.707856$ |
3.106338982 |
\( -\frac{329984}{23} a^{3} + \frac{1154880}{23} a^{2} + \frac{471424}{23} a - \frac{1114560}{23} \) |
\( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( a^{3} - 3 a^{2} - 2 a + 3\) , \( a^{2} - 2 a - 4\) , \( 8 a^{3} - 5 a^{2} - 63 a - 55\) , \( 29 a^{3} - 26 a^{2} - 225 a - 183\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+2a-7\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+3\right){x}^{2}+\left(8a^{3}-5a^{2}-63a-55\right){x}+29a^{3}-26a^{2}-225a-183$ |
| 23.1-b2 |
23.1-b |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$13.08550$ |
$(-2a^3+7a^2+4a-12)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.040324429$ |
$952.8539281$ |
3.106338982 |
\( -\frac{292992}{529} a^{3} + \frac{1110464}{529} a^{2} + \frac{567552}{529} a - \frac{1473536}{529} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( -a^{3} + 4 a^{2} + 2 a - 8\) , \( a^{2} - 2 a - 3\) , \( -2 a^{3} + 3 a^{2} + 14 a + 10\) , \( 18 a^{3} - 17 a^{2} - 143 a - 117\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{3}+4a^{2}+2a-8\right){x}^{2}+\left(-2a^{3}+3a^{2}+14a+10\right){x}+18a^{3}-17a^{2}-143a-117$ |
| 23.1-c1 |
23.1-c |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$13.08550$ |
$(-2a^3+7a^2+4a-12)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$101.8377941$ |
1.029137210 |
\( \frac{8304579072}{23} a^{3} - \frac{26887423424}{23} a^{2} - \frac{25270107520}{23} a + \frac{48777311808}{23} \) |
\( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( -a^{3} + 3 a^{2} + 2 a - 4\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( -3 a^{3} + 9 a^{2} + 5 a - 15\) , \( -3 a^{3} + 2 a^{2} + 4 a - 7\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+2a-7\right){x}{y}+\left(a^{3}-3a^{2}-2a+5\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-4\right){x}^{2}+\left(-3a^{3}+9a^{2}+5a-15\right){x}-3a^{3}+2a^{2}+4a-7$ |
| 23.1-c2 |
23.1-c |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$13.08550$ |
$(-2a^3+7a^2+4a-12)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$50.91889708$ |
1.029137210 |
\( -\frac{120560501120}{529} a^{3} + \frac{419952880064}{529} a^{2} + \frac{221018115840}{529} a - \frac{568963346176}{529} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( -2 a^{3} + 7 a^{2} + 4 a - 13\) , \( a\) , \( -a^{3} - 4 a^{2} + 8\) , \( -5 a^{3} - 6 a^{2} + 6 a + 6\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+a{y}={x}^{3}+\left(-2a^{3}+7a^{2}+4a-13\right){x}^{2}+\left(-a^{3}-4a^{2}+8\right){x}-5a^{3}-6a^{2}+6a+6$ |
| 23.1-d1 |
23.1-d |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$13.08550$ |
$(-2a^3+7a^2+4a-12)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.017426561$ |
$2881.079239$ |
2.029509997 |
\( \frac{8304579072}{23} a^{3} - \frac{26887423424}{23} a^{2} - \frac{25270107520}{23} a + \frac{48777311808}{23} \) |
\( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( -2 a^{3} + 7 a^{2} + 4 a - 11\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( 29 a^{3} - 102 a^{2} - 49 a + 134\) , \( -75 a^{3} + 263 a^{2} + 130 a - 348\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+2a-7\right){x}{y}+\left(a^{3}-3a^{2}-2a+5\right){y}={x}^{3}+\left(-2a^{3}+7a^{2}+4a-11\right){x}^{2}+\left(29a^{3}-102a^{2}-49a+134\right){x}-75a^{3}+263a^{2}+130a-348$ |
| 23.1-d2 |
23.1-d |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$13.08550$ |
$(-2a^3+7a^2+4a-12)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.034853122$ |
$2881.079239$ |
2.029509997 |
\( -\frac{120560501120}{529} a^{3} + \frac{419952880064}{529} a^{2} + \frac{221018115840}{529} a - \frac{568963346176}{529} \) |
\( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( 2 a^{3} - 7 a^{2} - 5 a + 11\) , \( -a^{3} + 4 a^{2} + a - 7\) , \( 4 a^{3} - 6 a^{2} - 27 a - 16\) , \( -7 a^{3} + 4 a^{2} + 62 a + 57\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+2a-7\right){x}{y}+\left(-a^{3}+4a^{2}+a-7\right){y}={x}^{3}+\left(2a^{3}-7a^{2}-5a+11\right){x}^{2}+\left(4a^{3}-6a^{2}-27a-16\right){x}-7a^{3}+4a^{2}+62a+57$ |
| 23.2-a1 |
23.2-a |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$13.08550$ |
$(a^3-3a^2-2a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.054175544$ |
$858.4398146$ |
1.879911589 |
\( -\frac{188800}{23} a^{3} + \frac{401472}{23} a^{2} + \frac{1084928}{23} a + \frac{416000}{23} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 2 a - 3\) , \( a^{3} + a^{2} - 4 a - 4\) , \( a^{3} - 3 a - 2\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(a^{3}+a^{2}-4a-4\right){x}+a^{3}-3a-2$ |
| 23.2-a2 |
23.2-a |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( 23^{2} \) |
$13.08550$ |
$(a^3-3a^2-2a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.108351088$ |
$858.4398146$ |
1.879911589 |
\( \frac{321536}{529} a^{3} - \frac{1196096}{529} a^{2} - \frac{653184}{529} a + \frac{2756544}{529} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( a - 1\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( 0\) , \( -a^{2} + 1\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a^{3}-3a^{2}-2a+5\right){y}={x}^{3}+\left(a-1\right){x}^{2}-a^{2}+1$ |
| 23.2-b1 |
23.2-b |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$13.08550$ |
$(a^3-3a^2-2a+6)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.040324429$ |
$1905.707856$ |
3.106338982 |
\( -\frac{188800}{23} a^{3} + \frac{401472}{23} a^{2} + \frac{1084928}{23} a + \frac{416000}{23} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 4 a^{2} - 2 a + 8\) , \( -a^{3} + 4 a^{2} + a - 7\) , \( 34 a^{3} - 118 a^{2} - 62 a + 163\) , \( 117 a^{3} - 407 a^{2} - 214 a + 553\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(-a^{3}+4a^{2}+a-7\right){y}={x}^{3}+\left(a^{3}-4a^{2}-2a+8\right){x}^{2}+\left(34a^{3}-118a^{2}-62a+163\right){x}+117a^{3}-407a^{2}-214a+553$ |
| 23.2-b2 |
23.2-b |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( 23^{2} \) |
$13.08550$ |
$(a^3-3a^2-2a+6)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.040324429$ |
$952.8539281$ |
3.106338982 |
\( \frac{321536}{529} a^{3} - \frac{1196096}{529} a^{2} - \frac{653184}{529} a + \frac{2756544}{529} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( 2 a^{3} - 7 a^{2} - 5 a + 12\) , \( a^{2} - 2 a - 4\) , \( -6 a^{3} + 22 a^{2} + 7 a - 28\) , \( 77 a^{3} - 267 a^{2} - 145 a + 360\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(2a^{3}-7a^{2}-5a+12\right){x}^{2}+\left(-6a^{3}+22a^{2}+7a-28\right){x}+77a^{3}-267a^{2}-145a+360$ |
| 23.2-c1 |
23.2-c |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$13.08550$ |
$(a^3-3a^2-2a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$101.8377941$ |
1.029137210 |
\( \frac{53463936}{23} a^{3} + \frac{1813294400}{23} a^{2} + \frac{195978496}{23} a - \frac{2346694912}{23} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 3 a + 3\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( -3 a^{3} + 9 a^{2} + 15 a - 6\) , \( -31 a^{3} + 100 a^{2} + 102 a - 172\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-3a^{2}-2a+4\right){y}={x}^{3}+\left(-a^{2}+3a+3\right){x}^{2}+\left(-3a^{3}+9a^{2}+15a-6\right){x}-31a^{3}+100a^{2}+102a-172$ |
| 23.2-c2 |
23.2-c |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( 23^{2} \) |
$13.08550$ |
$(a^3-3a^2-2a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$50.91889708$ |
1.029137210 |
\( -\frac{28138381824}{529} a^{3} + \frac{26143768768}{529} a^{2} + \frac{225078532992}{529} a + \frac{184504133824}{529} \) |
\( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( -a^{2} + 2 a + 5\) , \( a + 1\) , \( -31 a^{3} + 97 a^{2} + 101 a - 166\) , \( -128 a^{3} + 410 a^{2} + 398 a - 730\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-3a+4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-31a^{3}+97a^{2}+101a-166\right){x}-128a^{3}+410a^{2}+398a-730$ |
| 23.2-d1 |
23.2-d |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$13.08550$ |
$(a^3-3a^2-2a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$0.017426561$ |
$2881.079239$ |
2.029509997 |
\( \frac{53463936}{23} a^{3} + \frac{1813294400}{23} a^{2} + \frac{195978496}{23} a - \frac{2346694912}{23} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + 4 a^{2} + a - 8\) , \( a^{2} - 2 a - 3\) , \( 9 a^{3} - 7 a^{2} - 71 a - 59\) , \( -39 a^{3} + 37 a^{2} + 315 a + 258\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{3}+4a^{2}+a-8\right){x}^{2}+\left(9a^{3}-7a^{2}-71a-59\right){x}-39a^{3}+37a^{2}+315a+258$ |
| 23.2-d2 |
23.2-d |
$2$ |
$2$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( 23^{2} \) |
$13.08550$ |
$(a^3-3a^2-2a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.034853122$ |
$2881.079239$ |
2.029509997 |
\( -\frac{28138381824}{529} a^{3} + \frac{26143768768}{529} a^{2} + \frac{225078532992}{529} a + \frac{184504133824}{529} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{3} - 3 a^{2} - 2 a + 3\) , \( a^{2} - 2 a - 4\) , \( 13 a^{3} - 39 a^{2} - 26 a + 49\) , \( -51 a^{3} + 187 a^{2} + 92 a - 256\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+3\right){x}^{2}+\left(13a^{3}-39a^{2}-26a+49\right){x}-51a^{3}+187a^{2}+92a-256$ |
| 36.1-a1 |
36.1-a |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{2} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$128.7182515$ |
1.300781732 |
\( -\frac{2240392722766771819}{8} a^{3} - \frac{5522297380891621979}{12} a^{2} + \frac{3630089700724133759}{12} a + \frac{13074436924466614051}{24} \) |
\( \bigl[-a^{3} + 4 a^{2} + 2 a - 8\) , \( a^{3} - 4 a^{2} + 7\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( -545 a^{3} + 1664 a^{2} + 2046 a - 3391\) , \( 11445 a^{3} - 35734 a^{2} - 40291 a + 69868\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+2a-8\right){x}{y}+\left(a^{3}-3a^{2}-2a+4\right){y}={x}^{3}+\left(a^{3}-4a^{2}+7\right){x}^{2}+\left(-545a^{3}+1664a^{2}+2046a-3391\right){x}+11445a^{3}-35734a^{2}-40291a+69868$ |
| 36.1-a2 |
36.1-a |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{10} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$128.7182515$ |
1.300781732 |
\( \frac{7769042107}{27} a^{3} - \frac{4821837803}{18} a^{2} - \frac{124228493479}{54} a - \frac{101732420597}{54} \) |
\( \bigl[-a^{3} + 4 a^{2} + 2 a - 8\) , \( a^{3} - 4 a^{2} + 7\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( -10 a^{3} + 34 a^{2} + 26 a - 61\) , \( -15 a^{3} + 55 a^{2} + 33 a - 124\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+2a-8\right){x}{y}+\left(a^{3}-3a^{2}-2a+4\right){y}={x}^{3}+\left(a^{3}-4a^{2}+7\right){x}^{2}+\left(-10a^{3}+34a^{2}+26a-61\right){x}-15a^{3}+55a^{2}+33a-124$ |
| 36.1-b1 |
36.1-b |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{10} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$3.407084799$ |
1.721540502 |
\( \frac{76847592208429853}{864} a^{3} + \frac{125275986986772941}{864} a^{2} - \frac{577484854103149}{6} a - \frac{148183293619169353}{864} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a^{3} + 3 a^{2} + 2 a - 4\) , \( a + 1\) , \( -108 a^{3} + 370 a^{2} + 226 a - 529\) , \( 1447 a^{3} - 5049 a^{2} - 2590 a + 6708\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-4\right){x}^{2}+\left(-108a^{3}+370a^{2}+226a-529\right){x}+1447a^{3}-5049a^{2}-2590a+6708$ |
| 36.1-b2 |
36.1-b |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{4} \cdot 3^{2} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$2129.427999$ |
1.721540502 |
\( \frac{98225}{6} a^{3} - \frac{170425}{3} a^{2} - \frac{180341}{6} a + \frac{153763}{2} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( -2 a^{3} + 7 a^{2} + 3 a - 13\) , \( a\) , \( -3 a^{3} + 9 a^{2} + 5 a - 10\) , \( -2 a^{3} + 7 a^{2} + 4 a - 10\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+a{y}={x}^{3}+\left(-2a^{3}+7a^{2}+3a-13\right){x}^{2}+\left(-3a^{3}+9a^{2}+5a-10\right){x}-2a^{3}+7a^{2}+4a-10$ |
| 36.1-c1 |
36.1-c |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{10} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \cdot 5 \) |
$0.040106866$ |
$192.6722033$ |
3.123648015 |
\( \frac{76847592208429853}{864} a^{3} + \frac{125275986986772941}{864} a^{2} - \frac{577484854103149}{6} a - \frac{148183293619169353}{864} \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 5\) , \( a^{2} - a - 3\) , \( a\) , \( 22 a^{3} - 5 a^{2} - 206 a - 223\) , \( -357 a^{3} + 303 a^{2} + 2919 a + 2498\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(22a^{3}-5a^{2}-206a-223\right){x}-357a^{3}+303a^{2}+2919a+2498$ |
| 36.1-c2 |
36.1-c |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{4} \cdot 3^{2} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.200534334$ |
$192.6722033$ |
3.123648015 |
\( \frac{98225}{6} a^{3} - \frac{170425}{3} a^{2} - \frac{180341}{6} a + \frac{153763}{2} \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 5\) , \( a^{2} - a - 3\) , \( a\) , \( 2 a^{3} - 6 a - 3\) , \( 4 a^{3} + 2 a^{2} - 17 a - 17\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(2a^{3}-6a-3\right){x}+4a^{3}+2a^{2}-17a-17$ |
| 36.1-d1 |
36.1-d |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{2} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$8.717478747$ |
$0.362426267$ |
3.192823130 |
\( -\frac{2240392722766771819}{8} a^{3} - \frac{5522297380891621979}{12} a^{2} + \frac{3630089700724133759}{12} a + \frac{13074436924466614051}{24} \) |
\( \bigl[1\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( 0\) , \( -1420 a^{3} + 1299 a^{2} + 11345 a + 9299\) , \( -199304 a^{3} + 185398 a^{2} + 1593168 a + 1304734\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{3}-3a^{2}-2a+5\right){x}^{2}+\left(-1420a^{3}+1299a^{2}+11345a+9299\right){x}-199304a^{3}+185398a^{2}+1593168a+1304734$ |
| 36.1-d2 |
36.1-d |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{10} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1.743495749$ |
$226.5164170$ |
3.192823130 |
\( \frac{7769042107}{27} a^{3} - \frac{4821837803}{18} a^{2} - \frac{124228493479}{54} a - \frac{101732420597}{54} \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 4\) , \( 0\) , \( -2 a^{3} + 5 a^{2} + 8 a - 7\) , \( a^{3} - 11 a^{2} - 6 a + 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-2a^{3}+5a^{2}+8a-7\right){x}+a^{3}-11a^{2}-6a+16$ |
| 36.1-e1 |
36.1-e |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{2} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$128.7182515$ |
1.300781732 |
\( -\frac{24076175056414959271}{4} a^{3} + \frac{464579280282153457207}{24} a^{2} + \frac{446274506118921945731}{24} a - \frac{831645570259901538439}{24} \) |
\( \bigl[a^{2} - a - 4\) , \( -2 a^{3} + 7 a^{2} + 4 a - 11\) , \( 1\) , \( -18 a^{3} + 27 a^{2} - 358 a - 617\) , \( 71 a^{3} + 1113 a^{2} + 4748 a + 4759\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+{y}={x}^{3}+\left(-2a^{3}+7a^{2}+4a-11\right){x}^{2}+\left(-18a^{3}+27a^{2}-358a-617\right){x}+71a^{3}+1113a^{2}+4748a+4759$ |
| 36.1-e2 |
36.1-e |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{10} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$128.7182515$ |
1.300781732 |
\( \frac{66518800309}{54} a^{3} - \frac{38617523360}{9} a^{2} - \frac{60971080045}{27} a + \frac{313914856043}{54} \) |
\( \bigl[a^{2} - a - 4\) , \( -2 a^{3} + 7 a^{2} + 4 a - 11\) , \( 1\) , \( 2 a^{3} - 8 a^{2} - 3 a + 13\) , \( 11 a^{3} - 46 a^{2} - 21 a + 62\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+{y}={x}^{3}+\left(-2a^{3}+7a^{2}+4a-11\right){x}^{2}+\left(2a^{3}-8a^{2}-3a+13\right){x}+11a^{3}-46a^{2}-21a+62$ |
| 36.1-f1 |
36.1-f |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{4} \cdot 3^{2} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$2129.427999$ |
1.721540502 |
\( \frac{27859}{6} a^{3} - \frac{18701}{3} a^{2} - \frac{197911}{6} a - 20236 \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a^{3} + 3 a^{2} + 3 a - 3\) , \( -a^{3} + 4 a^{2} + 2 a - 7\) , \( -7 a^{3} + 19 a^{2} + 28 a - 22\) , \( -5 a^{3} + 12 a^{2} + 23 a - 9\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(-a^{3}+4a^{2}+2a-7\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-3\right){x}^{2}+\left(-7a^{3}+19a^{2}+28a-22\right){x}-5a^{3}+12a^{2}+23a-9$ |
| 36.1-f2 |
36.1-f |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{10} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$3.407084799$ |
1.721540502 |
\( \frac{411876901072778989}{216} a^{3} - \frac{165573174265169074}{27} a^{2} - \frac{565545307834198219}{96} a + \frac{4742105292427286831}{432} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 2 a - 3\) , \( -16 a^{3} + a^{2} + 149 a + 150\) , \( 392 a^{3} - 414 a^{2} - 3077 a - 2425\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-16a^{3}+a^{2}+149a+150\right){x}+392a^{3}-414a^{2}-3077a-2425$ |
| 36.1-g1 |
36.1-g |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{4} \cdot 3^{2} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.200534334$ |
$192.6722033$ |
3.123648015 |
\( \frac{27859}{6} a^{3} - \frac{18701}{3} a^{2} - \frac{197911}{6} a - 20236 \) |
\( \bigl[a\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( 2 a^{3} - 8 a^{2} - a + 14\) , \( 12 a^{3} - 41 a^{2} - 24 a + 53\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(2a^{3}-8a^{2}-a+14\right){x}+12a^{3}-41a^{2}-24a+53$ |
| 36.1-g2 |
36.1-g |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{10} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \cdot 5 \) |
$0.040106866$ |
$192.6722033$ |
3.123648015 |
\( \frac{411876901072778989}{216} a^{3} - \frac{165573174265169074}{27} a^{2} - \frac{565545307834198219}{96} a + \frac{4742105292427286831}{432} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( 102 a^{3} - 363 a^{2} - 161 a + 469\) , \( -1349 a^{3} + 4714 a^{2} + 2406 a - 6317\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(102a^{3}-363a^{2}-161a+469\right){x}-1349a^{3}+4714a^{2}+2406a-6317$ |
| 36.1-h1 |
36.1-h |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{2} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$8.717478747$ |
$0.362426267$ |
3.192823130 |
\( -\frac{24076175056414959271}{4} a^{3} + \frac{464579280282153457207}{24} a^{2} + \frac{446274506118921945731}{24} a - \frac{831645570259901538439}{24} \) |
\( \bigl[1\) , \( -a^{3} + 3 a^{2} + 2 a - 5\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( -6184 a^{3} + 21515 a^{2} + 11467 a - 29331\) , \( -856340 a^{3} + 2982695 a^{2} + 1570802 a - 4042118\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-3a^{2}-3a+5\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-5\right){x}^{2}+\left(-6184a^{3}+21515a^{2}+11467a-29331\right){x}-856340a^{3}+2982695a^{2}+1570802a-4042118$ |
| 36.1-h2 |
36.1-h |
$2$ |
$5$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{10} \) |
$13.83923$ |
$(a^3-3a^2-3a+4), (a^3-3a^2-2a+5)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1.743495749$ |
$226.5164170$ |
3.192823130 |
\( \frac{66518800309}{54} a^{3} - \frac{38617523360}{9} a^{2} - \frac{60971080045}{27} a + \frac{313914856043}{54} \) |
\( \bigl[a^{3} - 3 a^{2} - 2 a + 4\) , \( -2 a^{3} + 7 a^{2} + 5 a - 13\) , \( a\) , \( -6 a^{3} + 20 a^{2} + 18 a - 35\) , \( -6 a^{3} + 20 a^{2} + 18 a - 36\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-2a+4\right){x}{y}+a{y}={x}^{3}+\left(-2a^{3}+7a^{2}+5a-13\right){x}^{2}+\left(-6a^{3}+20a^{2}+18a-35\right){x}-6a^{3}+20a^{2}+18a-36$ |
| 49.1-a1 |
49.1-a |
$4$ |
$6$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{18} \) |
$14.38298$ |
$(a), (-a^3+3a^2+4a-5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$156.3038415$ |
3.159104158 |
\( -\frac{2045231824844308992}{13841287201} a^{3} + \frac{7124220547143074752}{13841287201} a^{2} + \frac{76514026177954688}{282475249} a - \frac{9652071911852920640}{13841287201} \) |
\( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( -2 a^{3} + 7 a^{2} + 5 a - 11\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( 88 a^{3} - 83 a^{2} - 699 a - 562\) , \( -1237 a^{3} + 1154 a^{2} + 9889 a + 8092\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+2a-7\right){x}{y}+\left(a^{3}-3a^{2}-2a+5\right){y}={x}^{3}+\left(-2a^{3}+7a^{2}+5a-11\right){x}^{2}+\left(88a^{3}-83a^{2}-699a-562\right){x}-1237a^{3}+1154a^{2}+9889a+8092$ |
| 49.1-a2 |
49.1-a |
$4$ |
$6$ |
4.4.9792.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$14.38298$ |
$(a), (-a^3+3a^2+4a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$156.3038415$ |
3.159104158 |
\( \frac{569331456}{2401} a^{3} + \frac{947788224}{2401} a^{2} - \frac{1772928}{7} a - \frac{1124905024}{2401} \) |
\( \bigl[-a^{3} + 4 a^{2} + 2 a - 7\) , \( -2 a^{3} + 7 a^{2} + 5 a - 11\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( -7 a^{3} + 12 a^{2} + 46 a + 28\) , \( -6 a^{3} + 9 a^{2} + 45 a + 30\bigr] \) |
${y}^2+\left(-a^{3}+4a^{2}+2a-7\right){x}{y}+\left(a^{3}-3a^{2}-2a+5\right){y}={x}^{3}+\left(-2a^{3}+7a^{2}+5a-11\right){x}^{2}+\left(-7a^{3}+12a^{2}+46a+28\right){x}-6a^{3}+9a^{2}+45a+30$ |
*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.
