| 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 |
| 3.1-a1 |
3.1-a |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$5.268762449$ |
$1.586572668$ |
2.140103632 |
\( -\frac{17992211390738276384364348856}{3} a^{3} + \frac{40295560191118068974791663867}{9} a^{2} + \frac{603956405252064822024479075264}{9} a + \frac{638870246718937884048814634923}{9} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 1\) , \( 2 a^{3} - 5 a^{2} - 14 a\) , \( a^{3} - 3 a^{2} - 5 a + 3\) , \( 221 a^{3} - 75 a^{2} - 2703 a - 3197\) , \( 7620 a^{3} - 8684 a^{2} - 77530 a - 70905\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-1\right){x}{y}+\left(a^{3}-3a^{2}-5a+3\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-14a\right){x}^{2}+\left(221a^{3}-75a^{2}-2703a-3197\right){x}+7620a^{3}-8684a^{2}-77530a-70905$ |
| 3.1-a2 |
3.1-a |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$2.634381224$ |
$6.346290673$ |
2.140103632 |
\( \frac{176849408215499}{3} a^{3} + \frac{319817823991919}{3} a^{2} - \frac{445538336461037}{3} a - \frac{801374762828726}{3} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 1\) , \( 2 a^{3} - 5 a^{2} - 14 a\) , \( a^{3} - 3 a^{2} - 5 a + 3\) , \( 81 a^{3} - 195 a^{2} - 558 a - 87\) , \( 372 a^{3} - 870 a^{2} - 2640 a - 597\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-1\right){x}{y}+\left(a^{3}-3a^{2}-5a+3\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-14a\right){x}^{2}+\left(81a^{3}-195a^{2}-558a-87\right){x}+372a^{3}-870a^{2}-2640a-597$ |
| 3.1-a3 |
3.1-a |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.756254149$ |
$128.5123861$ |
2.140103632 |
\( \frac{899953417066}{729} a^{3} - \frac{899953417066}{243} a^{2} - \frac{1799906834132}{243} a + \frac{4772251031671}{729} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 1\) , \( 2 a^{3} - 5 a^{2} - 14 a\) , \( a^{3} - 3 a^{2} - 5 a + 3\) , \( 6 a^{3} - 10 a^{2} - 48 a - 32\) , \( -48 a^{3} + 152 a^{2} + 242 a - 171\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-1\right){x}{y}+\left(a^{3}-3a^{2}-5a+3\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-14a\right){x}^{2}+\left(6a^{3}-10a^{2}-48a-32\right){x}-48a^{3}+152a^{2}+242a-171$ |
| 3.1-a4 |
3.1-a |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.878127074$ |
$514.0495445$ |
2.140103632 |
\( -\frac{1790960}{27} a^{3} + \frac{1790960}{9} a^{2} + \frac{3581920}{9} a - \frac{4820993}{27} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 1\) , \( 2 a^{3} - 5 a^{2} - 14 a\) , \( a^{3} - 3 a^{2} - 5 a + 3\) , \( 11 a^{3} - 30 a^{2} - 63 a + 18\) , \( -34 a^{3} + 98 a^{2} + 198 a - 57\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-1\right){x}{y}+\left(a^{3}-3a^{2}-5a+3\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-14a\right){x}^{2}+\left(11a^{3}-30a^{2}-63a+18\right){x}-34a^{3}+98a^{2}+198a-57$ |
| 3.1-a5 |
3.1-a |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$5.268762449$ |
$128.5123861$ |
2.140103632 |
\( \frac{274098477236641416163423536761}{9} a^{3} - \frac{700661089384397830005783134446}{9} a^{2} - \frac{1924687463638624344086462016422}{9} a + \frac{528386500015768853637977102377}{9} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 1\) , \( 2 a^{3} - 5 a^{2} - 14 a\) , \( a^{3} - 3 a^{2} - 5 a + 3\) , \( 676 a^{3} - 1960 a^{2} - 3708 a + 1003\) , \( -17436 a^{3} + 49882 a^{2} + 99122 a - 28101\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-1\right){x}{y}+\left(a^{3}-3a^{2}-5a+3\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-14a\right){x}^{2}+\left(676a^{3}-1960a^{2}-3708a+1003\right){x}-17436a^{3}+49882a^{2}+99122a-28101$ |
| 3.1-a6 |
3.1-a |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$2.634381224$ |
$514.0495445$ |
2.140103632 |
\( -1563512982602846 a^{3} + \frac{13221250794787198}{3} a^{2} + \frac{27527675574019271}{3} a - \frac{7750245393155093}{3} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 1\) , \( 2 a^{3} - 5 a^{2} - 14 a\) , \( a^{3} - 3 a^{2} - 5 a + 3\) , \( 841 a^{3} - 2390 a^{2} - 4848 a + 1383\) , \( -18862 a^{3} + 53522 a^{2} + 109146 a - 30813\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-1\right){x}{y}+\left(a^{3}-3a^{2}-5a+3\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-14a\right){x}^{2}+\left(841a^{3}-2390a^{2}-4848a+1383\right){x}-18862a^{3}+53522a^{2}+109146a-30813$ |
| 3.1-b1 |
3.1-b |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2 \) |
$1$ |
$14.27915401$ |
1.827842200 |
\( -\frac{17992211390738276384364348856}{3} a^{3} + \frac{40295560191118068974791663867}{9} a^{2} + \frac{603956405252064822024479075264}{9} a + \frac{638870246718937884048814634923}{9} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 2\) , \( 1\) , \( a + 1\) , \( -103 a^{3} + 252 a^{2} + 552 a - 162\) , \( -4415 a^{3} + 12896 a^{2} + 26023 a - 7369\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-103a^{3}+252a^{2}+552a-162\right){x}-4415a^{3}+12896a^{2}+26023a-7369$ |
| 3.1-b2 |
3.1-b |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \) |
$1$ |
$128.5123861$ |
1.827842200 |
\( \frac{899953417066}{729} a^{3} - \frac{899953417066}{243} a^{2} - \frac{1799906834132}{243} a + \frac{4772251031671}{729} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 2\) , \( 1\) , \( a + 1\) , \( 2 a^{3} - 8 a^{2} - 3 a + 3\) , \( 184 a^{3} - 519 a^{2} - 1073 a + 302\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2a^{3}-8a^{2}-3a+3\right){x}+184a^{3}-519a^{2}-1073a+302$ |
| 3.1-b3 |
3.1-b |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2 \) |
$1$ |
$14.27915401$ |
1.827842200 |
\( \frac{274098477236641416163423536761}{9} a^{3} - \frac{700661089384397830005783134446}{9} a^{2} - \frac{1924687463638624344086462016422}{9} a + \frac{528386500015768853637977102377}{9} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 2\) , \( 1\) , \( a + 1\) , \( 1207 a^{3} - 3598 a^{2} - 6213 a + 1788\) , \( 68564 a^{3} - 191838 a^{2} - 408815 a + 114827\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1207a^{3}-3598a^{2}-6213a+1788\right){x}+68564a^{3}-191838a^{2}-408815a+114827$ |
| 3.1-b4 |
3.1-b |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$57.11661605$ |
1.827842200 |
\( -1563512982602846 a^{3} + \frac{13221250794787198}{3} a^{2} + \frac{27527675574019271}{3} a - \frac{7750245393155093}{3} \) |
\( \bigl[a^{3} - 3 a^{2} - 5 a + 3\) , \( -2 a^{3} + 5 a^{2} + 14 a - 1\) , \( 1\) , \( -4636 a^{3} + 11847 a^{2} + 32568 a - 8934\) , \( 212397 a^{3} - 542959 a^{2} - 1491333 a + 409424\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-5a+3\right){x}{y}+{y}={x}^{3}+\left(-2a^{3}+5a^{2}+14a-1\right){x}^{2}+\left(-4636a^{3}+11847a^{2}+32568a-8934\right){x}+212397a^{3}-542959a^{2}-1491333a+409424$ |
| 3.1-b5 |
3.1-b |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \) |
$1$ |
$514.0495445$ |
1.827842200 |
\( -\frac{1790960}{27} a^{3} + \frac{1790960}{9} a^{2} + \frac{3581920}{9} a - \frac{4820993}{27} \) |
\( \bigl[a^{3} - 3 a^{2} - 5 a + 3\) , \( -2 a^{3} + 5 a^{2} + 14 a - 1\) , \( 1\) , \( -61 a^{3} + 157 a^{2} + 423 a - 114\) , \( 343 a^{3} - 876 a^{2} - 2412 a + 662\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-5a+3\right){x}{y}+{y}={x}^{3}+\left(-2a^{3}+5a^{2}+14a-1\right){x}^{2}+\left(-61a^{3}+157a^{2}+423a-114\right){x}+343a^{3}-876a^{2}-2412a+662$ |
| 3.1-b6 |
3.1-b |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$57.11661605$ |
1.827842200 |
\( \frac{176849408215499}{3} a^{3} + \frac{319817823991919}{3} a^{2} - \frac{445538336461037}{3} a - \frac{801374762828726}{3} \) |
\( \bigl[a^{3} - 3 a^{2} - 5 a + 3\) , \( -2 a^{3} + 5 a^{2} + 14 a - 1\) , \( 1\) , \( 214 a^{3} - 538 a^{2} - 1527 a + 351\) , \( 1214 a^{3} - 3065 a^{2} - 8613 a + 2054\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-5a+3\right){x}{y}+{y}={x}^{3}+\left(-2a^{3}+5a^{2}+14a-1\right){x}^{2}+\left(214a^{3}-538a^{2}-1527a+351\right){x}+1214a^{3}-3065a^{2}-8613a+2054$ |
| 3.1-c1 |
3.1-c |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$5.268762449$ |
$1.586572668$ |
2.140103632 |
\( \frac{274098477236641416163423536761}{9} a^{3} - \frac{700661089384397830005783134446}{9} a^{2} - \frac{1924687463638624344086462016422}{9} a + \frac{528386500015768853637977102377}{9} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 2\) , \( -a^{2} + 2 a + 6\) , \( a^{3} - 3 a^{2} - 6 a + 3\) , \( -1338 a^{3} + 3422 a^{2} + 9421 a - 2556\) , \( -32455 a^{3} + 82760 a^{2} + 227595 a - 62457\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-2\right){x}{y}+\left(a^{3}-3a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-1338a^{3}+3422a^{2}+9421a-2556\right){x}-32455a^{3}+82760a^{2}+227595a-62457$ |
| 3.1-c2 |
3.1-c |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$5.268762449$ |
$128.5123861$ |
2.140103632 |
\( -\frac{17992211390738276384364348856}{3} a^{3} + \frac{40295560191118068974791663867}{9} a^{2} + \frac{603956405252064822024479075264}{9} a + \frac{638870246718937884048814634923}{9} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 2\) , \( -a^{2} + 2 a + 6\) , \( a^{3} - 3 a^{2} - 6 a + 3\) , \( -8 a^{3} - 48 a^{2} - 284 a - 411\) , \( 208 a^{3} + 1603 a^{2} + 3291 a + 1926\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-2\right){x}{y}+\left(a^{3}-3a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-8a^{3}-48a^{2}-284a-411\right){x}+208a^{3}+1603a^{2}+3291a+1926$ |
| 3.1-c3 |
3.1-c |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$2.634381224$ |
$6.346290673$ |
2.140103632 |
\( -1563512982602846 a^{3} + \frac{13221250794787198}{3} a^{2} + \frac{27527675574019271}{3} a - \frac{7750245393155093}{3} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 2\) , \( -a^{2} + 2 a + 6\) , \( a^{3} - 3 a^{2} - 6 a + 3\) , \( -83 a^{3} + 197 a^{2} + 586 a - 121\) , \( -525 a^{3} + 1265 a^{2} + 3598 a - 940\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-2\right){x}{y}+\left(a^{3}-3a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-83a^{3}+197a^{2}+586a-121\right){x}-525a^{3}+1265a^{2}+3598a-940$ |
| 3.1-c4 |
3.1-c |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.756254149$ |
$128.5123861$ |
2.140103632 |
\( \frac{899953417066}{729} a^{3} - \frac{899953417066}{243} a^{2} - \frac{1799906834132}{243} a + \frac{4772251031671}{729} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 2\) , \( -a^{2} + 2 a + 6\) , \( a^{3} - 3 a^{2} - 6 a + 3\) , \( -18 a^{3} + 42 a^{2} + 136 a - 6\) , \( -47 a^{3} + 124 a^{2} + 348 a - 72\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-2\right){x}{y}+\left(a^{3}-3a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-18a^{3}+42a^{2}+136a-6\right){x}-47a^{3}+124a^{2}+348a-72$ |
| 3.1-c5 |
3.1-c |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$2.634381224$ |
$514.0495445$ |
2.140103632 |
\( \frac{176849408215499}{3} a^{3} + \frac{319817823991919}{3} a^{2} - \frac{445538336461037}{3} a - \frac{801374762828726}{3} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 2\) , \( -a^{2} + 2 a + 6\) , \( a^{3} - 3 a^{2} - 6 a + 3\) , \( -18 a^{3} - 83 a^{2} - 74 a + 29\) , \( 434 a^{3} + 1378 a^{2} + 892 a - 322\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-2\right){x}{y}+\left(a^{3}-3a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-18a^{3}-83a^{2}-74a+29\right){x}+434a^{3}+1378a^{2}+892a-322$ |
| 3.1-c6 |
3.1-c |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.878127074$ |
$514.0495445$ |
2.140103632 |
\( -\frac{1790960}{27} a^{3} + \frac{1790960}{9} a^{2} + \frac{3581920}{9} a - \frac{4820993}{27} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 2\) , \( -a^{2} + 2 a + 6\) , \( a^{3} - 3 a^{2} - 6 a + 3\) , \( -3 a^{3} + 2 a^{2} + 31 a + 29\) , \( -3 a^{3} + 4 a^{2} + 34 a + 29\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-2\right){x}{y}+\left(a^{3}-3a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-3a^{3}+2a^{2}+31a+29\right){x}-3a^{3}+4a^{2}+34a+29$ |
| 3.1-d1 |
3.1-d |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$57.11661605$ |
1.827842200 |
\( \frac{176849408215499}{3} a^{3} + \frac{319817823991919}{3} a^{2} - \frac{445538336461037}{3} a - \frac{801374762828726}{3} \) |
\( \bigl[a\) , \( a^{3} - 2 a^{2} - 8 a - 1\) , \( 1\) , \( 917 a^{3} - 690 a^{2} - 10255 a - 10824\) , \( -41812 a^{3} + 31204 a^{2} + 467823 a + 494885\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{3}-2a^{2}-8a-1\right){x}^{2}+\left(917a^{3}-690a^{2}-10255a-10824\right){x}-41812a^{3}+31204a^{2}+467823a+494885$ |
| 3.1-d2 |
3.1-d |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \) |
$1$ |
$514.0495445$ |
1.827842200 |
\( -\frac{1790960}{27} a^{3} + \frac{1790960}{9} a^{2} + \frac{3581920}{9} a - \frac{4820993}{27} \) |
\( \bigl[a\) , \( a^{3} - 2 a^{2} - 8 a - 1\) , \( 1\) , \( 12 a^{3} - 10 a^{2} - 130 a - 129\) , \( -68 a^{3} + 51 a^{2} + 762 a + 806\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{3}-2a^{2}-8a-1\right){x}^{2}+\left(12a^{3}-10a^{2}-130a-129\right){x}-68a^{3}+51a^{2}+762a+806$ |
| 3.1-d3 |
3.1-d |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$57.11661605$ |
1.827842200 |
\( -1563512982602846 a^{3} + \frac{13221250794787198}{3} a^{2} + \frac{27527675574019271}{3} a - \frac{7750245393155093}{3} \) |
\( \bigl[a\) , \( a^{3} - 2 a^{2} - 8 a - 1\) , \( 1\) , \( -63 a^{3} + 85 a^{2} + 620 a + 456\) , \( -342 a^{3} + 449 a^{2} + 3381 a + 2579\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{3}-2a^{2}-8a-1\right){x}^{2}+\left(-63a^{3}+85a^{2}+620a+456\right){x}-342a^{3}+449a^{2}+3381a+2579$ |
| 3.1-d4 |
3.1-d |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2 \) |
$1$ |
$14.27915401$ |
1.827842200 |
\( -\frac{17992211390738276384364348856}{3} a^{3} + \frac{40295560191118068974791663867}{9} a^{2} + \frac{603956405252064822024479075264}{9} a + \frac{638870246718937884048814634923}{9} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 1\) , \( 1\) , \( a^{3} - 3 a^{2} - 5 a + 4\) , \( 61 a^{3} - 207 a^{2} - 1394 a - 1438\) , \( -3276 a^{3} - 4026 a^{2} + 17086 a + 23993\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+1\right){x}{y}+\left(a^{3}-3a^{2}-5a+4\right){y}={x}^{3}+{x}^{2}+\left(61a^{3}-207a^{2}-1394a-1438\right){x}-3276a^{3}-4026a^{2}+17086a+23993$ |
| 3.1-d5 |
3.1-d |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \) |
$1$ |
$128.5123861$ |
1.827842200 |
\( \frac{899953417066}{729} a^{3} - \frac{899953417066}{243} a^{2} - \frac{1799906834132}{243} a + \frac{4772251031671}{729} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 1\) , \( 1\) , \( a^{3} - 3 a^{2} - 5 a + 4\) , \( a^{3} - 2 a^{2} - 14 a - 13\) , \( -13 a^{3} + 6 a^{2} + 46 a + 8\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+1\right){x}{y}+\left(a^{3}-3a^{2}-5a+4\right){y}={x}^{3}+{x}^{2}+\left(a^{3}-2a^{2}-14a-13\right){x}-13a^{3}+6a^{2}+46a+8$ |
| 3.1-d6 |
3.1-d |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(2a^3-5a^2-14a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2 \) |
$1$ |
$14.27915401$ |
1.827842200 |
\( \frac{274098477236641416163423536761}{9} a^{3} - \frac{700661089384397830005783134446}{9} a^{2} - \frac{1924687463638624344086462016422}{9} a + \frac{528386500015768853637977102377}{9} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 1\) , \( 1\) , \( a^{3} - 3 a^{2} - 5 a + 4\) , \( 246 a^{3} - 682 a^{2} - 1409 a + 377\) , \( -2204 a^{3} + 6961 a^{2} + 13690 a - 3877\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+1\right){x}{y}+\left(a^{3}-3a^{2}-5a+4\right){y}={x}^{3}+{x}^{2}+\left(246a^{3}-682a^{2}-1409a+377\right){x}-2204a^{3}+6961a^{2}+13690a-3877$ |
| 3.2-a1 |
3.2-a |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$2.634381224$ |
$514.0495445$ |
2.140103632 |
\( \frac{5306097060640495}{3} a^{3} - \frac{13602000971812696}{3} a^{2} - 12439842944232988 a + 3415518079208701 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 2\) , \( 2 a^{3} - 5 a^{2} - 13 a\) , \( a^{3} - 2 a^{2} - 7 a - 2\) , \( -1036 a^{3} + 2648 a^{2} + 7269 a - 1997\) , \( 20994 a^{3} - 53667 a^{2} - 147411 a + 40466\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+2\right){x}{y}+\left(a^{3}-2a^{2}-7a-2\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-13a\right){x}^{2}+\left(-1036a^{3}+2648a^{2}+7269a-1997\right){x}+20994a^{3}-53667a^{2}-147411a+40466$ |
| 3.2-a2 |
3.2-a |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$5.268762449$ |
$128.5123861$ |
2.140103632 |
\( 666458109126047882499695455 a^{3} + \frac{18833546621319717309454066897}{9} a^{2} + \frac{3996591099091270851870744301}{3} a - \frac{1448854623283352655343211090}{3} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 2\) , \( 2 a^{3} - 5 a^{2} - 13 a\) , \( a^{3} - 2 a^{2} - 7 a - 2\) , \( -1021 a^{3} + 2583 a^{2} + 7154 a - 1962\) , \( 21026 a^{3} - 53606 a^{2} - 147399 a + 40458\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+2\right){x}{y}+\left(a^{3}-2a^{2}-7a-2\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-13a\right){x}^{2}+\left(-1021a^{3}+2583a^{2}+7154a-1962\right){x}+21026a^{3}-53606a^{2}-147399a+40458$ |
| 3.2-a3 |
3.2-a |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$2.634381224$ |
$6.346290673$ |
2.140103632 |
\( -264135840349152 a^{3} + \frac{60932353033579}{3} a^{2} + 3412463865046910 a + 4265884127847117 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 2\) , \( 2 a^{3} - 5 a^{2} - 13 a\) , \( a^{3} - 2 a^{2} - 7 a - 2\) , \( -6 a^{3} - 2 a^{2} + 124 a - 47\) , \( -123 a^{3} + 216 a^{2} + 1302 a - 355\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+2\right){x}{y}+\left(a^{3}-2a^{2}-7a-2\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-13a\right){x}^{2}+\left(-6a^{3}-2a^{2}+124a-47\right){x}-123a^{3}+216a^{2}+1302a-355$ |
| 3.2-a4 |
3.2-a |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{6} \) |
$14.41501$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.878127074$ |
$514.0495445$ |
2.140103632 |
\( \frac{1790960}{27} a^{3} - \frac{1790960}{9} a^{2} - \frac{3581920}{9} a + \frac{857303}{3} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 2\) , \( 2 a^{3} - 5 a^{2} - 13 a\) , \( a^{3} - 2 a^{2} - 7 a - 2\) , \( -11 a^{3} + 28 a^{2} + 79 a - 22\) , \( 21 a^{3} - 53 a^{2} - 148 a + 36\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+2\right){x}{y}+\left(a^{3}-2a^{2}-7a-2\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-13a\right){x}^{2}+\left(-11a^{3}+28a^{2}+79a-22\right){x}+21a^{3}-53a^{2}-148a+36$ |
| 3.2-a5 |
3.2-a |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{12} \) |
$14.41501$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.756254149$ |
$128.5123861$ |
2.140103632 |
\( -\frac{899953417066}{729} a^{3} + \frac{899953417066}{243} a^{2} + \frac{1799906834132}{243} a - \frac{169713654199}{81} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 2\) , \( 2 a^{3} - 5 a^{2} - 13 a\) , \( a^{3} - 2 a^{2} - 7 a - 2\) , \( 9 a^{3} - 27 a^{2} - 46 a + 13\) , \( 85 a^{3} - 224 a^{2} - 567 a + 152\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+2\right){x}{y}+\left(a^{3}-2a^{2}-7a-2\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-13a\right){x}^{2}+\left(9a^{3}-27a^{2}-46a+13\right){x}+85a^{3}-224a^{2}-567a+152$ |
| 3.2-a6 |
3.2-a |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$5.268762449$ |
$1.586572668$ |
2.140103632 |
\( -\frac{226119966046561017952827749288}{9} a^{3} + \frac{641531982571960043721537403682}{9} a^{2} + 145415698343253967722930078695 a - \frac{123083196948809771139830686927}{3} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 2\) , \( 2 a^{3} - 5 a^{2} - 13 a\) , \( a^{3} - 2 a^{2} - 7 a - 2\) , \( 1159 a^{3} - 3272 a^{2} - 6776 a + 1893\) , \( 24001 a^{3} - 68554 a^{2} - 136891 a + 38697\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+2\right){x}{y}+\left(a^{3}-2a^{2}-7a-2\right){y}={x}^{3}+\left(2a^{3}-5a^{2}-13a\right){x}^{2}+\left(1159a^{3}-3272a^{2}-6776a+1893\right){x}+24001a^{3}-68554a^{2}-136891a+38697$ |
| 3.2-b1 |
3.2-b |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2 \) |
$1$ |
$14.27915401$ |
1.827842200 |
\( 666458109126047882499695455 a^{3} + \frac{18833546621319717309454066897}{9} a^{2} + \frac{3996591099091270851870744301}{3} a - \frac{1448854623283352655343211090}{3} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 2\) , \( a^{3} - 3 a^{2} - 7 a + 4\) , \( a^{3} - 2 a^{2} - 8 a - 1\) , \( -2236 a^{3} + 5632 a^{2} + 15590 a - 4230\) , \( -71134 a^{3} + 183124 a^{2} + 501214 a - 138317\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-2\right){x}{y}+\left(a^{3}-2a^{2}-8a-1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-7a+4\right){x}^{2}+\left(-2236a^{3}+5632a^{2}+15590a-4230\right){x}-71134a^{3}+183124a^{2}+501214a-138317$ |
| 3.2-b2 |
3.2-b |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2 \) |
$1$ |
$14.27915401$ |
1.827842200 |
\( -\frac{226119966046561017952827749288}{9} a^{3} + \frac{641531982571960043721537403682}{9} a^{2} + 145415698343253967722930078695 a - \frac{123083196948809771139830686927}{3} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 2\) , \( a^{3} - 3 a^{2} - 7 a + 4\) , \( a^{3} - 2 a^{2} - 8 a - 1\) , \( 169 a^{3} - 328 a^{2} - 1430 a - 480\) , \( 4881 a^{3} - 13479 a^{2} - 31963 a + 17020\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-2\right){x}{y}+\left(a^{3}-2a^{2}-8a-1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-7a+4\right){x}^{2}+\left(169a^{3}-328a^{2}-1430a-480\right){x}+4881a^{3}-13479a^{2}-31963a+17020$ |
| 3.2-b3 |
3.2-b |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{12} \) |
$14.41501$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \) |
$1$ |
$128.5123861$ |
1.827842200 |
\( -\frac{899953417066}{729} a^{3} + \frac{899953417066}{243} a^{2} + \frac{1799906834132}{243} a - \frac{169713654199}{81} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 2\) , \( a^{3} - 3 a^{2} - 7 a + 4\) , \( a^{3} - 2 a^{2} - 8 a - 1\) , \( -11 a^{3} + 27 a^{2} + 75 a - 20\) , \( -216 a^{3} + 550 a^{2} + 1525 a - 394\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-2\right){x}{y}+\left(a^{3}-2a^{2}-8a-1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-7a+4\right){x}^{2}+\left(-11a^{3}+27a^{2}+75a-20\right){x}-216a^{3}+550a^{2}+1525a-394$ |
| 3.2-b4 |
3.2-b |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{6} \) |
$14.41501$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \) |
$1$ |
$514.0495445$ |
1.827842200 |
\( \frac{1790960}{27} a^{3} - \frac{1790960}{9} a^{2} - \frac{3581920}{9} a + \frac{857303}{3} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 14 a + 2\) , \( -a + 1\) , \( 1\) , \( 2 a^{3} - 12 a^{2} - 26 a + 9\) , \( 11 a^{3} + 15 a^{2} - 9 a + 1\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-14a+2\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a^{3}-12a^{2}-26a+9\right){x}+11a^{3}+15a^{2}-9a+1$ |
| 3.2-b5 |
3.2-b |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$57.11661605$ |
1.827842200 |
\( -264135840349152 a^{3} + \frac{60932353033579}{3} a^{2} + 3412463865046910 a + 4265884127847117 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 14 a + 2\) , \( -a + 1\) , \( 1\) , \( 27 a^{3} - 47 a^{2} - 126 a + 29\) , \( 115 a^{3} - 170 a^{2} - 463 a + 130\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-14a+2\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(27a^{3}-47a^{2}-126a+29\right){x}+115a^{3}-170a^{2}-463a+130$ |
| 3.2-b6 |
3.2-b |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$57.11661605$ |
1.827842200 |
\( \frac{5306097060640495}{3} a^{3} - \frac{13602000971812696}{3} a^{2} - 12439842944232988 a + 3415518079208701 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 14 a + 2\) , \( -a + 1\) , \( 1\) , \( -118 a^{3} - 277 a^{2} - 91 a + 44\) , \( 4554 a^{3} + 14825 a^{2} + 9934 a - 3545\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-14a+2\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-118a^{3}-277a^{2}-91a+44\right){x}+4554a^{3}+14825a^{2}+9934a-3545$ |
| 3.2-c1 |
3.2-c |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$2.634381224$ |
$514.0495445$ |
2.140103632 |
\( -264135840349152 a^{3} + \frac{60932353033579}{3} a^{2} + 3412463865046910 a + 4265884127847117 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 1\) , \( -2 a^{3} + 5 a^{2} + 13 a\) , \( a^{3} - 3 a^{2} - 6 a + 4\) , \( 202 a^{3} - 149 a^{2} - 2262 a - 2401\) , \( -3930 a^{3} + 2934 a^{2} + 43972 a + 46512\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+1\right){x}{y}+\left(a^{3}-3a^{2}-6a+4\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+13a\right){x}^{2}+\left(202a^{3}-149a^{2}-2262a-2401\right){x}-3930a^{3}+2934a^{2}+43972a+46512$ |
| 3.2-c2 |
3.2-c |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$5.268762449$ |
$128.5123861$ |
2.140103632 |
\( -\frac{226119966046561017952827749288}{9} a^{3} + \frac{641531982571960043721537403682}{9} a^{2} + 145415698343253967722930078695 a - \frac{123083196948809771139830686927}{3} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 1\) , \( -2 a^{3} + 5 a^{2} + 13 a\) , \( a^{3} - 3 a^{2} - 6 a + 4\) , \( 342 a^{3} - 549 a^{2} - 3077 a - 2171\) , \( -4747 a^{3} + 5248 a^{2} + 48695 a + 45180\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+1\right){x}{y}+\left(a^{3}-3a^{2}-6a+4\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+13a\right){x}^{2}+\left(342a^{3}-549a^{2}-3077a-2171\right){x}-4747a^{3}+5248a^{2}+48695a+45180$ |
| 3.2-c3 |
3.2-c |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$2.634381224$ |
$6.346290673$ |
2.140103632 |
\( \frac{5306097060640495}{3} a^{3} - \frac{13602000971812696}{3} a^{2} - 12439842944232988 a + 3415518079208701 \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 1\) , \( -2 a^{3} + 5 a^{2} + 13 a\) , \( a^{3} - 3 a^{2} - 6 a + 4\) , \( -3 a^{3} + 26 a^{2} - 67 a - 196\) , \( 77 a^{3} - 59 a^{2} - 1116 a - 1329\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+1\right){x}{y}+\left(a^{3}-3a^{2}-6a+4\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+13a\right){x}^{2}+\left(-3a^{3}+26a^{2}-67a-196\right){x}+77a^{3}-59a^{2}-1116a-1329$ |
| 3.2-c4 |
3.2-c |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{6} \) |
$14.41501$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.878127074$ |
$514.0495445$ |
2.140103632 |
\( \frac{1790960}{27} a^{3} - \frac{1790960}{9} a^{2} - \frac{3581920}{9} a + \frac{857303}{3} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 1\) , \( -2 a^{3} + 5 a^{2} + 13 a\) , \( a^{3} - 3 a^{2} - 6 a + 4\) , \( -8 a^{3} + 26 a^{2} + 38 a - 36\) , \( -13 a^{3} + 33 a^{2} + 85 a + 2\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+1\right){x}{y}+\left(a^{3}-3a^{2}-6a+4\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+13a\right){x}^{2}+\left(-8a^{3}+26a^{2}+38a-36\right){x}-13a^{3}+33a^{2}+85a+2$ |
| 3.2-c5 |
3.2-c |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{12} \) |
$14.41501$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.756254149$ |
$128.5123861$ |
2.140103632 |
\( -\frac{899953417066}{729} a^{3} + \frac{899953417066}{243} a^{2} + \frac{1799906834132}{243} a - \frac{169713654199}{81} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 1\) , \( -2 a^{3} + 5 a^{2} + 13 a\) , \( a^{3} - 3 a^{2} - 6 a + 4\) , \( -8 a^{3} + 21 a^{2} + 43 a - 16\) , \( -19 a^{3} + 25 a^{2} + 161 a + 117\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+1\right){x}{y}+\left(a^{3}-3a^{2}-6a+4\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+13a\right){x}^{2}+\left(-8a^{3}+21a^{2}+43a-16\right){x}-19a^{3}+25a^{2}+161a+117$ |
| 3.2-c6 |
3.2-c |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$5.268762449$ |
$1.586572668$ |
2.140103632 |
\( 666458109126047882499695455 a^{3} + \frac{18833546621319717309454066897}{9} a^{2} + \frac{3996591099091270851870744301}{3} a - \frac{1448854623283352655343211090}{3} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 13 a + 1\) , \( -2 a^{3} + 5 a^{2} + 13 a\) , \( a^{3} - 3 a^{2} - 6 a + 4\) , \( -53 a^{3} - 49 a^{2} + 143 a + 124\) , \( -410 a^{3} - 2425 a^{2} - 4835 a - 3222\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-13a+1\right){x}{y}+\left(a^{3}-3a^{2}-6a+4\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+13a\right){x}^{2}+\left(-53a^{3}-49a^{2}+143a+124\right){x}-410a^{3}-2425a^{2}-4835a-3222$ |
| 3.2-d1 |
3.2-d |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$57.11661605$ |
1.827842200 |
\( \frac{5306097060640495}{3} a^{3} - \frac{13602000971812696}{3} a^{2} - 12439842944232988 a + 3415518079208701 \) |
\( \bigl[a^{3} - 2 a^{2} - 8 a - 2\) , \( a^{3} - 3 a^{2} - 5 a + 4\) , \( 1\) , \( -180 a^{3} + 505 a^{2} + 1046 a - 281\) , \( -987 a^{3} + 2786 a^{2} + 5695 a - 1601\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-8a-2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-3a^{2}-5a+4\right){x}^{2}+\left(-180a^{3}+505a^{2}+1046a-281\right){x}-987a^{3}+2786a^{2}+5695a-1601$ |
| 3.2-d2 |
3.2-d |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{6} \) |
$14.41501$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \) |
$1$ |
$514.0495445$ |
1.827842200 |
\( \frac{1790960}{27} a^{3} - \frac{1790960}{9} a^{2} - \frac{3581920}{9} a + \frac{857303}{3} \) |
\( \bigl[a^{3} - 2 a^{2} - 8 a - 2\) , \( a^{3} - 3 a^{2} - 5 a + 4\) , \( 1\) , \( 45 a^{3} - 130 a^{2} - 254 a + 89\) , \( -286 a^{3} + 810 a^{2} + 1659 a - 458\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-8a-2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-3a^{2}-5a+4\right){x}^{2}+\left(45a^{3}-130a^{2}-254a+89\right){x}-286a^{3}+810a^{2}+1659a-458$ |
| 3.2-d3 |
3.2-d |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{2} \) |
$14.41501$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$57.11661605$ |
1.827842200 |
\( -264135840349152 a^{3} + \frac{60932353033579}{3} a^{2} + 3412463865046910 a + 4265884127847117 \) |
\( \bigl[a^{3} - 2 a^{2} - 8 a - 2\) , \( a^{3} - 3 a^{2} - 5 a + 4\) , \( 1\) , \( 3835 a^{3} - 10875 a^{2} - 22209 a + 6229\) , \( -175139 a^{3} + 496930 a^{2} + 1013576 a - 286241\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-8a-2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-3a^{2}-5a+4\right){x}^{2}+\left(3835a^{3}-10875a^{2}-22209a+6229\right){x}-175139a^{3}+496930a^{2}+1013576a-286241$ |
| 3.2-d4 |
3.2-d |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2 \) |
$1$ |
$14.27915401$ |
1.827842200 |
\( -\frac{226119966046561017952827749288}{9} a^{3} + \frac{641531982571960043721537403682}{9} a^{2} + 145415698343253967722930078695 a - \frac{123083196948809771139830686927}{3} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 1\) , \( a^{3} - 3 a^{2} - 5 a + 4\) , \( a^{3} - 3 a^{2} - 6 a + 4\) , \( 966 a^{3} - 1821 a^{2} - 7962 a - 4299\) , \( 4986 a^{3} + 15409 a^{2} - 105070 a - 182783\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-1\right){x}{y}+\left(a^{3}-3a^{2}-6a+4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-5a+4\right){x}^{2}+\left(966a^{3}-1821a^{2}-7962a-4299\right){x}+4986a^{3}+15409a^{2}-105070a-182783$ |
| 3.2-d5 |
3.2-d |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{4} \) |
$14.41501$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$36$ |
\( 2 \) |
$1$ |
$14.27915401$ |
1.827842200 |
\( 666458109126047882499695455 a^{3} + \frac{18833546621319717309454066897}{9} a^{2} + \frac{3996591099091270851870744301}{3} a - \frac{1448854623283352655343211090}{3} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 1\) , \( a^{3} - 3 a^{2} - 5 a + 4\) , \( a^{3} - 3 a^{2} - 6 a + 4\) , \( -314 a^{3} + 764 a^{2} + 2308 a - 309\) , \( 2183 a^{3} - 7519 a^{2} - 10865 a + 19003\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-1\right){x}{y}+\left(a^{3}-3a^{2}-6a+4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-5a+4\right){x}^{2}+\left(-314a^{3}+764a^{2}+2308a-309\right){x}+2183a^{3}-7519a^{2}-10865a+19003$ |
| 3.2-d6 |
3.2-d |
$6$ |
$18$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{12} \) |
$14.41501$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2 \) |
$1$ |
$128.5123861$ |
1.827842200 |
\( -\frac{899953417066}{729} a^{3} + \frac{899953417066}{243} a^{2} + \frac{1799906834132}{243} a - \frac{169713654199}{81} \) |
\( \bigl[a^{3} - 2 a^{2} - 7 a - 1\) , \( a^{3} - 3 a^{2} - 5 a + 4\) , \( a^{3} - 3 a^{2} - 6 a + 4\) , \( 6 a^{3} - 11 a^{2} - 37 a - 14\) , \( 35 a^{3} - 3 a^{2} - 438 a - 517\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-7a-1\right){x}{y}+\left(a^{3}-3a^{2}-6a+4\right){y}={x}^{3}+\left(a^{3}-3a^{2}-5a+4\right){x}^{2}+\left(6a^{3}-11a^{2}-37a-14\right){x}+35a^{3}-3a^{2}-438a-517$ |
| 9.2-a1 |
9.2-a |
$12$ |
$24$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{28} \) |
$16.53694$ |
$(2a^3-5a^2-14a+3), (a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$10.13673188$ |
$2.932550357$ |
3.382416917 |
\( \frac{16961124145384625}{6561} a^{3} - \frac{16961124145384625}{2187} a^{2} - \frac{33922248290769250}{2187} a + \frac{9993448434629125}{729} \) |
\( \bigl[a^{3} - 3 a^{2} - 6 a + 3\) , \( a^{3} - 3 a^{2} - 6 a + 2\) , \( 0\) , \( -265 a^{3} + 795 a^{2} + 1590 a - 1389\) , \( -3141 a^{3} + 9423 a^{2} + 18846 a - 16641\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-6a+3\right){x}{y}={x}^{3}+\left(a^{3}-3a^{2}-6a+2\right){x}^{2}+\left(-265a^{3}+795a^{2}+1590a-1389\right){x}-3141a^{3}+9423a^{2}+18846a-16641$ |
| 9.2-a2 |
9.2-a |
$12$ |
$24$ |
4.4.19773.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{32} \) |
$16.53694$ |
$(2a^3-5a^2-14a+3), (a+1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$2.534182972$ |
$46.92080572$ |
3.382416917 |
\( \frac{449577713875}{531441} a^{3} - \frac{449577713875}{177147} a^{2} - \frac{899155427750}{177147} a + \frac{2385924022000}{531441} \) |
\( \bigl[a^{3} - 3 a^{2} - 6 a + 3\) , \( a^{3} - 3 a^{2} - 6 a + 2\) , \( 0\) , \( -15 a^{3} + 45 a^{2} + 90 a - 84\) , \( -54 a^{3} + 162 a^{2} + 324 a - 279\bigr] \) |
${y}^2+\left(a^{3}-3a^{2}-6a+3\right){x}{y}={x}^{3}+\left(a^{3}-3a^{2}-6a+2\right){x}^{2}+\left(-15a^{3}+45a^{2}+90a-84\right){x}-54a^{3}+162a^{2}+324a-279$ |
*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.
