| 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 |
$8$ |
$28$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.67736$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$17910.40485$ |
1.07932 |
\( -3375 \) |
\( \bigl[a^{4} - 4 a^{2} + a + 2\) , \( a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 2 a\) , \( 1\) , \( 9 a^{5} - 15 a^{4} - 29 a^{3} + 51 a^{2} + 17 a - 29\) , \( 44 a^{5} - 80 a^{4} - 141 a^{3} + 255 a^{2} + 81 a - 147\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+2\right){x}{y}+{y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+2a\right){x}^{2}+\left(9a^{5}-15a^{4}-29a^{3}+51a^{2}+17a-29\right){x}+44a^{5}-80a^{4}-141a^{3}+255a^{2}+81a-147$ |
| 1.1-a2 |
1.1-a |
$8$ |
$28$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.67736$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$17910.40485$ |
1.07932 |
\( -3375 \) |
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + a\) , \( a^{5} - 5 a^{3} + 5 a\) , \( 9 a^{5} - 11 a^{4} - 28 a^{3} + 37 a^{2} + 17 a - 20\) , \( -26 a^{5} + 67 a^{4} + 82 a^{3} - 216 a^{2} - 47 a + 124\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-3a^{2}-3a+1\right){x}{y}+\left(a^{5}-5a^{3}+5a\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+a\right){x}^{2}+\left(9a^{5}-11a^{4}-28a^{3}+37a^{2}+17a-20\right){x}-26a^{5}+67a^{4}+82a^{3}-216a^{2}-47a+124$ |
| 1.1-a3 |
1.1-a |
$8$ |
$28$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.67736$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$17910.40485$ |
1.07932 |
\( 16581375 \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 5 a + 1\) , \( a^{3} - 2 a + 1\) , \( a^{5} - 5 a^{3} + a^{2} + 6 a - 1\) , \( 298 a^{5} + 459 a^{4} - 1360 a^{3} - 2083 a^{2} + 870 a + 1294\) , \( 5514 a^{5} + 8600 a^{4} - 25130 a^{3} - 39152 a^{2} + 15847 a + 24561\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-3a^{2}+5a+1\right){x}{y}+\left(a^{5}-5a^{3}+a^{2}+6a-1\right){y}={x}^{3}+\left(a^{3}-2a+1\right){x}^{2}+\left(298a^{5}+459a^{4}-1360a^{3}-2083a^{2}+870a+1294\right){x}+5514a^{5}+8600a^{4}-25130a^{3}-39152a^{2}+15847a+24561$ |
| 1.1-a4 |
1.1-a |
$8$ |
$28$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.67736$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$17910.40485$ |
1.07932 |
\( 16581375 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{5} + a^{4} - 4 a^{3} - 5 a^{2} + 3 a + 4\) , \( a^{5} - 5 a^{3} + 5 a\) , \( -21 a^{5} + 9 a^{4} + 106 a^{3} - 34 a^{2} - 105 a - 11\) , \( -71 a^{5} + 41 a^{4} + 375 a^{3} - 141 a^{2} - 397 a - 52\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{5}-5a^{3}+5a\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-5a^{2}+3a+4\right){x}^{2}+\left(-21a^{5}+9a^{4}+106a^{3}-34a^{2}-105a-11\right){x}-71a^{5}+41a^{4}+375a^{3}-141a^{2}-397a-52$ |
| 1.1-a5 |
1.1-a |
$8$ |
$28$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.67736$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$17910.40485$ |
1.07932 |
\( -51954490735875 a^{5} + 311726944415250 a^{3} - 363681435151125 a + 137458661985000 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{5} + a^{4} - 4 a^{3} - 5 a^{2} + 3 a + 4\) , \( a^{5} - 5 a^{3} + 5 a\) , \( -61 a^{5} - 71 a^{4} + 231 a^{3} + 226 a^{2} - 170 a - 171\) , \( 252 a^{5} + 657 a^{4} - 666 a^{3} - 2113 a^{2} + 206 a + 1105\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{5}-5a^{3}+5a\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-5a^{2}+3a+4\right){x}^{2}+\left(-61a^{5}-71a^{4}+231a^{3}+226a^{2}-170a-171\right){x}+252a^{5}+657a^{4}-666a^{3}-2113a^{2}+206a+1105$ |
| 1.1-a6 |
1.1-a |
$8$ |
$28$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.67736$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$16$ |
\( 1 \) |
$1$ |
$279.8500758$ |
1.07932 |
\( -51954490735875 a^{5} + 311726944415250 a^{3} - 363681435151125 a + 137458661985000 \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( -59 a^{5} - 72 a^{4} + 224 a^{3} + 232 a^{2} - 168 a - 178\) , \( -549 a^{5} - 1204 a^{4} + 1648 a^{3} + 3871 a^{2} - 819 a - 2157\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){x}{y}+\left(a^{5}-4a^{3}+a^{2}+2a-2\right){y}={x}^{3}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+3a+2\right){x}^{2}+\left(-59a^{5}-72a^{4}+224a^{3}+232a^{2}-168a-178\right){x}-549a^{5}-1204a^{4}+1648a^{3}+3871a^{2}-819a-2157$ |
| 1.1-a7 |
1.1-a |
$8$ |
$28$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.67736$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$16$ |
\( 1 \) |
$1$ |
$279.8500758$ |
1.07932 |
\( 51954490735875 a^{5} - 311726944415250 a^{3} + 363681435151125 a + 137458661985000 \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{4} + a^{3} + 3 a^{2} - 2 a - 1\) , \( a^{5} - 5 a^{3} + a^{2} + 5 a - 1\) , \( 316 a^{5} + 478 a^{4} - 1440 a^{3} - 2180 a^{2} + 918 a + 1353\) , \( -4343 a^{5} - 6794 a^{4} + 19792 a^{3} + 30934 a^{2} - 12457 a - 19434\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{5}-5a^{3}+a^{2}+5a-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-2a-1\right){x}^{2}+\left(316a^{5}+478a^{4}-1440a^{3}-2180a^{2}+918a+1353\right){x}-4343a^{5}-6794a^{4}+19792a^{3}+30934a^{2}-12457a-19434$ |
| 1.1-a8 |
1.1-a |
$8$ |
$28$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$92.67736$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$17910.40485$ |
1.07932 |
\( 51954490735875 a^{5} - 311726944415250 a^{3} + 363681435151125 a + 137458661985000 \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 5 a + 1\) , \( a^{3} - 2 a + 1\) , \( a^{5} - 5 a^{3} + a^{2} + 6 a - 1\) , \( 318 a^{5} + 479 a^{4} - 1445 a^{3} - 2183 a^{2} + 920 a + 1354\) , \( 4870 a^{5} + 7637 a^{4} - 22214 a^{3} - 34734 a^{2} + 14017 a + 21786\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-3a^{2}+5a+1\right){x}{y}+\left(a^{5}-5a^{3}+a^{2}+6a-1\right){y}={x}^{3}+\left(a^{3}-2a+1\right){x}^{2}+\left(318a^{5}+479a^{4}-1445a^{3}-2183a^{2}+920a+1354\right){x}+4870a^{5}+7637a^{4}-22214a^{3}-34734a^{2}+14017a+21786$ |
| 29.1-a1 |
29.1-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{5} \) |
$122.69875$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$2500$ |
\( 1 \) |
$1$ |
$3.174882953$ |
1.91325 |
\( -\frac{11638234485217781883211136}{20511149} a^{5} - \frac{18198212403326899210049344}{20511149} a^{4} + \frac{53011645292491172054518016}{20511149} a^{3} + \frac{82892143230766444798254144}{20511149} a^{2} - \frac{33319506678736418073967360}{20511149} a - \frac{52100363354606399695280960}{20511149} \) |
\( \bigl[a^{5} - 4 a^{3} + 3 a + 1\) , \( -a^{4} + 3 a^{2} - a + 1\) , \( a + 1\) , \( 650 a^{5} - 661 a^{4} - 2308 a^{3} + 1760 a^{2} + 1356 a - 997\) , \( 19074 a^{5} - 28520 a^{4} - 64332 a^{3} + 86026 a^{2} + 37584 a - 48789\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+3a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+3a^{2}-a+1\right){x}^{2}+\left(650a^{5}-661a^{4}-2308a^{3}+1760a^{2}+1356a-997\right){x}+19074a^{5}-28520a^{4}-64332a^{3}+86026a^{2}+37584a-48789$ |
| 29.1-a2 |
29.1-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^2+a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$49607.54615$ |
1.91325 |
\( \frac{4638720345728}{29} a^{5} - \frac{7253395255104}{29} a^{4} - \frac{21129176978176}{29} a^{3} + \frac{33038911702592}{29} a^{2} + \frac{13280362595072}{29} a - \frac{20766011147072}{29} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( -1\) , \( a^{3} - 3 a\) , \( 12 a^{5} - 24 a^{4} - 37 a^{3} + 75 a^{2} + 19 a - 41\) , \( -13 a^{5} + 25 a^{4} + 42 a^{3} - 80 a^{2} - 25 a + 46\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}-{x}^{2}+\left(12a^{5}-24a^{4}-37a^{3}+75a^{2}+19a-41\right){x}-13a^{5}+25a^{4}+42a^{3}-80a^{2}-25a+46$ |
| 29.1-a3 |
29.1-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^2+a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$99215.09230$ |
1.91325 |
\( \frac{221731072}{841} a^{5} + \frac{567808448}{841} a^{4} - \frac{1669715072}{841} a^{3} - \frac{3072857344}{841} a^{2} + \frac{3045057280}{841} a + \frac{3668603712}{841} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{4} + a^{3} + 3 a^{2} - 4 a - 1\) , \( a^{4} - 3 a^{2}\) , \( -a^{5} - 3 a^{4} + 5 a^{3} + 11 a^{2} - 5 a - 4\) , \( a^{5} + 2 a^{4} - 5 a^{3} - 10 a^{2} + 2 a + 7\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{4}-3a^{2}\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-4a-1\right){x}^{2}+\left(-a^{5}-3a^{4}+5a^{3}+11a^{2}-5a-4\right){x}+a^{5}+2a^{4}-5a^{3}-10a^{2}+2a+7$ |
| 29.1-a4 |
29.1-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{10} \) |
$122.69875$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$6.349765907$ |
1.91325 |
\( \frac{371616447238312134405571630848}{420707233300201} a^{5} + \frac{724598518850268810878778076608}{420707233300201} a^{4} - \frac{1188452621369136633895690492544}{420707233300201} a^{3} - \frac{2317311496622071051495542213888}{420707233300201} a^{2} + \frac{684207650538560590611209538304}{420707233300201} a + \frac{1334106793714863889269582323008}{420707233300201} \) |
\( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 2 a\) , \( a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 8 a + 2\) , \( a^{4} - 4 a^{2} + a + 2\) , \( -431 a^{5} - 1322 a^{4} + 1058 a^{3} + 4577 a^{2} - 205 a - 2996\) , \( -23213 a^{5} - 45459 a^{4} + 73063 a^{3} + 146021 a^{2} - 38977 a - 86683\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+2a\right){x}{y}+\left(a^{4}-4a^{2}+a+2\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+8a+2\right){x}^{2}+\left(-431a^{5}-1322a^{4}+1058a^{3}+4577a^{2}-205a-2996\right){x}-23213a^{5}-45459a^{4}+73063a^{3}+146021a^{2}-38977a-86683$ |
| 29.1-b1 |
29.1-b |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.013611174$ |
$75000.91466$ |
2.95290 |
\( \frac{1345536}{841} a^{5} + \frac{5028544}{841} a^{4} - \frac{2012288}{841} a^{3} - \frac{18927360}{841} a^{2} - \frac{3569408}{841} a + \frac{16913216}{841} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{5} + a^{4} + 5 a^{3} - 5 a^{2} - 6 a + 3\) , \( a^{5} - 4 a^{3} + 2 a\) , \( -a^{5} - 3 a^{4} + 3 a^{3} + 11 a^{2} - 2 a - 4\) , \( -a^{5} + 5 a^{3} - 4 a\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{5}-4a^{3}+2a\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-5a^{2}-6a+3\right){x}^{2}+\left(-a^{5}-3a^{4}+3a^{3}+11a^{2}-2a-4\right){x}-a^{5}+5a^{3}-4a$ |
| 29.1-b2 |
29.1-b |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.027222349$ |
$75000.91466$ |
2.95290 |
\( -\frac{1425536}{29} a^{5} + \frac{2761152}{29} a^{4} + \frac{4097280}{29} a^{3} - \frac{9025472}{29} a^{2} - \frac{1065984}{29} a + \frac{6285248}{29} \) |
\( \bigl[a^{5} - 4 a^{3} + 3 a + 1\) , \( a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 8 a + 2\) , \( a + 1\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 6 a^{2} - 10 a + 4\) , \( 5 a^{5} + 10 a^{4} - 17 a^{3} - 32 a^{2} + 11 a + 17\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+3a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+8a+2\right){x}^{2}+\left(-a^{5}+2a^{4}+7a^{3}-6a^{2}-10a+4\right){x}+5a^{5}+10a^{4}-17a^{3}-32a^{2}+11a+17$ |
| 29.1-c1 |
29.1-c |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{5} \) |
$122.69875$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$9244.014574$ |
2.22826 |
\( -\frac{11638234485217781883211136}{20511149} a^{5} - \frac{18198212403326899210049344}{20511149} a^{4} + \frac{53011645292491172054518016}{20511149} a^{3} + \frac{82892143230766444798254144}{20511149} a^{2} - \frac{33319506678736418073967360}{20511149} a - \frac{52100363354606399695280960}{20511149} \) |
\( \bigl[a^{5} - 4 a^{3} + 3 a + 1\) , \( -a^{5} - a^{4} + 4 a^{3} + 3 a^{2} - 2 a + 1\) , \( a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 3 a + 1\) , \( 647 a^{5} - 662 a^{4} - 2297 a^{3} + 1762 a^{2} + 1353 a - 997\) , \( -17776 a^{5} + 27199 a^{4} + 59723 a^{3} - 82511 a^{2} - 34872 a + 46795\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+3a+1\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+3a+1\right){y}={x}^{3}+\left(-a^{5}-a^{4}+4a^{3}+3a^{2}-2a+1\right){x}^{2}+\left(647a^{5}-662a^{4}-2297a^{3}+1762a^{2}+1353a-997\right){x}-17776a^{5}+27199a^{4}+59723a^{3}-82511a^{2}-34872a+46795$ |
| 29.1-c2 |
29.1-c |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$9244.014574$ |
2.22826 |
\( \frac{4638720345728}{29} a^{5} - \frac{7253395255104}{29} a^{4} - \frac{21129176978176}{29} a^{3} + \frac{33038911702592}{29} a^{2} + \frac{13280362595072}{29} a - \frac{20766011147072}{29} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( -a^{3} + 3 a - 1\) , \( a^{4} - 4 a^{2} + 2\) , \( 13 a^{5} - 25 a^{4} - 42 a^{3} + 80 a^{2} + 24 a - 46\) , \( 13 a^{5} - 25 a^{4} - 42 a^{3} + 80 a^{2} + 25 a - 47\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}+\left(13a^{5}-25a^{4}-42a^{3}+80a^{2}+24a-46\right){x}+13a^{5}-25a^{4}-42a^{3}+80a^{2}+25a-47$ |
| 29.1-c3 |
29.1-c |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$4622.007287$ |
2.22826 |
\( \frac{221731072}{841} a^{5} + \frac{567808448}{841} a^{4} - \frac{1669715072}{841} a^{3} - \frac{3072857344}{841} a^{2} + \frac{3045057280}{841} a + \frac{3668603712}{841} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{5} - a^{4} + 5 a^{3} + 3 a^{2} - 6 a\) , \( a + 1\) , \( -2 a^{5} - 2 a^{4} + 10 a^{3} + 6 a^{2} - 11 a\) , \( -2 a^{5} - 3 a^{4} + 10 a^{3} + 12 a^{2} - 9 a - 6\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{5}-a^{4}+5a^{3}+3a^{2}-6a\right){x}^{2}+\left(-2a^{5}-2a^{4}+10a^{3}+6a^{2}-11a\right){x}-2a^{5}-3a^{4}+10a^{3}+12a^{2}-9a-6$ |
| 29.1-c4 |
29.1-c |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{10} \) |
$122.69875$ |
$(a^2+a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$4622.007287$ |
2.22826 |
\( \frac{371616447238312134405571630848}{420707233300201} a^{5} + \frac{724598518850268810878778076608}{420707233300201} a^{4} - \frac{1188452621369136633895690492544}{420707233300201} a^{3} - \frac{2317311496622071051495542213888}{420707233300201} a^{2} + \frac{684207650538560590611209538304}{420707233300201} a + \frac{1334106793714863889269582323008}{420707233300201} \) |
\( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 2 a\) , \( -a^{5} - a^{4} + 5 a^{3} + 5 a^{2} - 5 a - 5\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 2 a + 3\) , \( -434 a^{5} - 1326 a^{4} + 1071 a^{3} + 4594 a^{2} - 214 a - 3010\) , \( 20358 a^{5} + 40138 a^{4} - 63695 a^{3} - 129232 a^{2} + 33155 a + 77393\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+2a\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(-a^{5}-a^{4}+5a^{3}+5a^{2}-5a-5\right){x}^{2}+\left(-434a^{5}-1326a^{4}+1071a^{3}+4594a^{2}-214a-3010\right){x}+20358a^{5}+40138a^{4}-63695a^{3}-129232a^{2}+33155a+77393$ |
| 29.1-d1 |
29.1-d |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.053838697$ |
$22728.25708$ |
3.53954 |
\( \frac{1345536}{841} a^{5} + \frac{5028544}{841} a^{4} - \frac{2012288}{841} a^{3} - \frac{18927360}{841} a^{2} - \frac{3569408}{841} a + \frac{16913216}{841} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a + 1\) , \( -a^{5} - a^{4} + 5 a^{3} + 2 a^{2} - 7 a + 3\) , \( -2 a^{5} - 4 a^{4} + 6 a^{3} + 10 a^{2} - 6 a - 4\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(-a^{5}-a^{4}+5a^{3}+2a^{2}-7a+3\right){x}-2a^{5}-4a^{4}+6a^{3}+10a^{2}-6a-4$ |
| 29.1-d2 |
29.1-d |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^2+a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.107677395$ |
$22728.25708$ |
3.53954 |
\( -\frac{1425536}{29} a^{5} + \frac{2761152}{29} a^{4} + \frac{4097280}{29} a^{3} - \frac{9025472}{29} a^{2} - \frac{1065984}{29} a + \frac{6285248}{29} \) |
\( \bigl[a^{5} - 4 a^{3} + 3 a + 1\) , \( a^{5} - 5 a^{3} + a^{2} + 4 a - 3\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -a^{5} + 6 a^{3} + 3 a^{2} - 8 a - 3\) , \( -3 a^{5} - 5 a^{4} + 11 a^{3} + 18 a^{2} - 10 a - 15\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+3a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{5}-5a^{3}+a^{2}+4a-3\right){x}^{2}+\left(-a^{5}+6a^{3}+3a^{2}-8a-3\right){x}-3a^{5}-5a^{4}+11a^{3}+18a^{2}-10a-15$ |
| 29.2-a1 |
29.2-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^5+a^4-4a^3-4a^2+3a+4)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$99215.09230$ |
1.91325 |
\( \frac{561059712}{841} a^{5} - \frac{801623552}{841} a^{4} - \frac{2552075776}{841} a^{3} + \frac{3440309312}{841} a^{2} + \frac{1823899136}{841} a - \frac{1942761152}{841} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( a^{5} - 5 a^{3} + 4 a\) , \( a^{5} - 5 a^{3} + 6 a\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 5 a - 4\) , \( -2 a^{4} - a^{3} + 8 a^{2} + 2 a - 7\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){x}{y}+\left(a^{5}-5a^{3}+6a\right){y}={x}^{3}+\left(a^{5}-5a^{3}+4a\right){x}^{2}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+5a-4\right){x}-2a^{4}-a^{3}+8a^{2}+2a-7$ |
| 29.2-a2 |
29.2-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^5+a^4-4a^3-4a^2+3a+4)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$49607.54615$ |
1.91325 |
\( -\frac{2064424750464}{29} a^{5} + \frac{4025330682176}{29} a^{4} + \frac{6602158870144}{29} a^{3} - \frac{12873258155776}{29} a^{2} - \frac{3800949451520}{29} a + \frac{7411303628160}{29} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{5} - a^{4} + 4 a^{3} + 3 a^{2} - 3 a + 1\) , \( a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 6 a + 1\) , \( -25 a^{5} - 23 a^{4} + 151 a^{3} + 135 a^{2} - 218 a - 189\) , \( -a^{5} - 2 a^{4} + 3 a^{3} + 7 a^{2} - 3\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-3a^{2}+6a+1\right){y}={x}^{3}+\left(-a^{5}-a^{4}+4a^{3}+3a^{2}-3a+1\right){x}^{2}+\left(-25a^{5}-23a^{4}+151a^{3}+135a^{2}-218a-189\right){x}-a^{5}-2a^{4}+3a^{3}+7a^{2}-3$ |
| 29.2-a3 |
29.2-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{10} \) |
$122.69875$ |
$(a^5+a^4-4a^3-4a^2+3a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$6.349765907$ |
1.91325 |
\( -\frac{669629614822424038132167661696}{420707233300201} a^{5} + \frac{581082578779004192019570092544}{420707233300201} a^{4} + \frac{4183162332926392223640692677632}{420707233300201} a^{3} - \frac{3630011412745289770976628539328}{420707233300201} a^{2} - \frac{6224807297793248424005973046784}{420707233300201} a + \frac{5401684845167893233406572970816}{420707233300201} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{5} + a^{4} + 5 a^{3} - 4 a^{2} - 5 a + 1\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( -229 a^{5} - 427 a^{4} + 686 a^{3} + 1298 a^{2} - 336 a - 781\) , \( -6692 a^{5} - 13042 a^{4} + 21145 a^{3} + 41388 a^{2} - 11926 a - 23947\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-4a^{2}-5a+1\right){x}^{2}+\left(-229a^{5}-427a^{4}+686a^{3}+1298a^{2}-336a-781\right){x}-6692a^{5}-13042a^{4}+21145a^{3}+41388a^{2}-11926a-23947$ |
| 29.2-a4 |
29.2-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{5} \) |
$122.69875$ |
$(a^5+a^4-4a^3-4a^2+3a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$2500$ |
\( 1 \) |
$1$ |
$3.174882953$ |
1.91325 |
\( \frac{5179527133597737361537664}{20511149} a^{5} + \frac{10099293617458847958056768}{20511149} a^{4} - \frac{16564551321429407550212992}{20511149} a^{3} - \frac{32298255683967340580234496}{20511149} a^{2} + \frac{9536617113528630918473472}{20511149} a + \frac{18594691967605536011116416}{20511149} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a\) , \( a + 1\) , \( 689 a^{5} - 764 a^{4} - 2409 a^{3} + 2098 a^{2} + 1385 a - 1185\) , \( 10562 a^{5} - 12257 a^{4} - 36958 a^{3} + 34173 a^{2} + 21743 a - 18876\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{4}+a^{3}-3a^{2}-2a\right){x}^{2}+\left(689a^{5}-764a^{4}-2409a^{3}+2098a^{2}+1385a-1185\right){x}+10562a^{5}-12257a^{4}-36958a^{3}+34173a^{2}+21743a-18876$ |
| 29.2-b1 |
29.2-b |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^5+a^4-4a^3-4a^2+3a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.013611174$ |
$75000.91466$ |
2.95290 |
\( -\frac{4715392}{841} a^{5} + \frac{1186816}{841} a^{4} + \frac{27426048}{841} a^{3} - \frac{10962624}{841} a^{2} - \frac{36469760}{841} a + \frac{25220928}{841} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( -a^{5} + 6 a^{3} - a^{2} - 8 a + 2\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -a^{5} + a^{4} + 5 a^{3} - 7 a^{2} - 7 a + 10\) , \( -a^{5} - a^{4} + 5 a^{3} + 3 a^{2} - 6 a - 1\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{5}+6a^{3}-a^{2}-8a+2\right){x}^{2}+\left(-a^{5}+a^{4}+5a^{3}-7a^{2}-7a+10\right){x}-a^{5}-a^{4}+5a^{3}+3a^{2}-6a-1$ |
| 29.2-b2 |
29.2-b |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^5+a^4-4a^3-4a^2+3a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.027222349$ |
$75000.91466$ |
2.95290 |
\( \frac{3030400}{29} a^{5} + \frac{2019136}{29} a^{4} - \frac{18181504}{29} a^{3} - \frac{12856832}{29} a^{2} + \frac{25666048}{29} a + \frac{20419200}{29} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 3 a - 1\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( -4 a^{5} + 2 a^{4} + 15 a^{3} - 8 a^{2} - 10 a + 4\) , \( a^{5} - 5 a^{4} - 3 a^{3} + 18 a^{2} - 12\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+3a-1\right){x}^{2}+\left(-4a^{5}+2a^{4}+15a^{3}-8a^{2}-10a+4\right){x}+a^{5}-5a^{4}-3a^{3}+18a^{2}-12$ |
| 29.2-c1 |
29.2-c |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^5+a^4-4a^3-4a^2+3a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$4622.007287$ |
2.22826 |
\( \frac{561059712}{841} a^{5} - \frac{801623552}{841} a^{4} - \frac{2552075776}{841} a^{3} + \frac{3440309312}{841} a^{2} + \frac{1823899136}{841} a - \frac{1942761152}{841} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -a^{5} + 5 a^{3} - 5 a + 1\) , \( a^{3} - 3 a + 1\) , \( -a^{5} - 2 a^{4} + 5 a^{3} + 11 a^{2} - 4 a - 11\) , \( a^{3} + 3 a^{2} - a - 6\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{5}+5a^{3}-5a+1\right){x}^{2}+\left(-a^{5}-2a^{4}+5a^{3}+11a^{2}-4a-11\right){x}+a^{3}+3a^{2}-a-6$ |
| 29.2-c2 |
29.2-c |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^5+a^4-4a^3-4a^2+3a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$9244.014574$ |
2.22826 |
\( -\frac{2064424750464}{29} a^{5} + \frac{4025330682176}{29} a^{4} + \frac{6602158870144}{29} a^{3} - \frac{12873258155776}{29} a^{2} - \frac{3800949451520}{29} a + \frac{7411303628160}{29} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( -a^{4} - a^{3} + 3 a^{2} + 2 a + 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -23 a^{5} - 21 a^{4} + 142 a^{3} + 127 a^{2} - 210 a - 183\) , \( -46 a^{5} - 40 a^{4} + 287 a^{3} + 249 a^{2} - 427 a - 370\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}-a^{3}+3a^{2}+2a+1\right){x}^{2}+\left(-23a^{5}-21a^{4}+142a^{3}+127a^{2}-210a-183\right){x}-46a^{5}-40a^{4}+287a^{3}+249a^{2}-427a-370$ |
| 29.2-c3 |
29.2-c |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{10} \) |
$122.69875$ |
$(a^5+a^4-4a^3-4a^2+3a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$4622.007287$ |
2.22826 |
\( -\frac{669629614822424038132167661696}{420707233300201} a^{5} + \frac{581082578779004192019570092544}{420707233300201} a^{4} + \frac{4183162332926392223640692677632}{420707233300201} a^{3} - \frac{3630011412745289770976628539328}{420707233300201} a^{2} - \frac{6224807297793248424005973046784}{420707233300201} a + \frac{5401684845167893233406572970816}{420707233300201} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 3 a + 3\) , \( -227 a^{5} - 421 a^{4} + 681 a^{3} + 1279 a^{2} - 334 a - 771\) , \( 4835 a^{5} + 9345 a^{4} - 15257 a^{3} - 29540 a^{2} + 8569 a + 17107\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+3a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-2a-2\right){x}^{2}+\left(-227a^{5}-421a^{4}+681a^{3}+1279a^{2}-334a-771\right){x}+4835a^{5}+9345a^{4}-15257a^{3}-29540a^{2}+8569a+17107$ |
| 29.2-c4 |
29.2-c |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{5} \) |
$122.69875$ |
$(a^5+a^4-4a^3-4a^2+3a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$9244.014574$ |
2.22826 |
\( \frac{5179527133597737361537664}{20511149} a^{5} + \frac{10099293617458847958056768}{20511149} a^{4} - \frac{16564551321429407550212992}{20511149} a^{3} - \frac{32298255683967340580234496}{20511149} a^{2} + \frac{9536617113528630918473472}{20511149} a + \frac{18594691967605536011116416}{20511149} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( -a^{4} + a^{3} + 3 a^{2} - 4 a + 1\) , \( a^{5} - 4 a^{3} + 2 a\) , \( 687 a^{5} - 766 a^{4} - 2398 a^{3} + 2101 a^{2} + 1366 a - 1178\) , \( -10833 a^{5} + 12885 a^{4} + 37775 a^{3} - 36259 a^{2} - 22164 a + 20124\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}{y}+\left(a^{5}-4a^{3}+2a\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-4a+1\right){x}^{2}+\left(687a^{5}-766a^{4}-2398a^{3}+2101a^{2}+1366a-1178\right){x}-10833a^{5}+12885a^{4}+37775a^{3}-36259a^{2}-22164a+20124$ |
| 29.2-d1 |
29.2-d |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^5+a^4-4a^3-4a^2+3a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.053838697$ |
$22728.25708$ |
3.53954 |
\( -\frac{4715392}{841} a^{5} + \frac{1186816}{841} a^{4} + \frac{27426048}{841} a^{3} - \frac{10962624}{841} a^{2} - \frac{36469760}{841} a + \frac{25220928}{841} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( a^{5} - 4 a^{3} + a^{2} + 2 a - 1\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 6 a + 2\) , \( 4 a^{5} - a^{4} - 19 a^{3} + 8 a^{2} + 17 a - 10\) , \( 3 a^{5} - a^{4} - 15 a^{3} + 8 a^{2} + 16 a - 12\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+6a+2\right){y}={x}^{3}+\left(a^{5}-4a^{3}+a^{2}+2a-1\right){x}^{2}+\left(4a^{5}-a^{4}-19a^{3}+8a^{2}+17a-10\right){x}+3a^{5}-a^{4}-15a^{3}+8a^{2}+16a-12$ |
| 29.2-d2 |
29.2-d |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^5+a^4-4a^3-4a^2+3a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.107677395$ |
$22728.25708$ |
3.53954 |
\( \frac{3030400}{29} a^{5} + \frac{2019136}{29} a^{4} - \frac{18181504}{29} a^{3} - \frac{12856832}{29} a^{2} + \frac{25666048}{29} a + \frac{20419200}{29} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -a^{5} + a^{4} + 4 a^{3} - 3 a^{2} - a - 1\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 3 a + 3\) , \( -a^{5} - 3 a^{4} + 4 a^{3} + 11 a^{2} - 5 a - 5\) , \( -2 a^{5} - 4 a^{4} + 6 a^{3} + 13 a^{2} - 2 a - 8\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+3a+3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-3a^{2}-a-1\right){x}^{2}+\left(-a^{5}-3a^{4}+4a^{3}+11a^{2}-5a-5\right){x}-2a^{5}-4a^{4}+6a^{3}+13a^{2}-2a-8$ |
| 29.3-a1 |
29.3-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{10} \) |
$122.69875$ |
$(a^5+a^4-5a^3-4a^2+5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$6.349765907$ |
1.91325 |
\( -\frac{835014258814272032979854369152}{420707233300201} a^{5} - \frac{1305681097629273002898348169152}{420707233300201} a^{4} + \frac{3803454846833048030493700214912}{420707233300201} a^{3} + \frac{5947322909367360822472170753216}{420707233300201} a^{2} - \frac{2390592337533999723550389291520}{420707233300201} a - \frac{3738082838237017786881864213248}{420707233300201} \) |
\( \bigl[a^{5} - 4 a^{3} + 3 a + 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + 3 a + 3\) , \( -127 a^{5} - 221 a^{4} + 255 a^{3} + 638 a^{2} + 230 a - 458\) , \( -3457 a^{5} - 6178 a^{4} + 10705 a^{3} + 19770 a^{2} - 4665 a - 13022\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+3a+1\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+3a+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(-127a^{5}-221a^{4}+255a^{3}+638a^{2}+230a-458\right){x}-3457a^{5}-6178a^{4}+10705a^{3}+19770a^{2}-4665a-13022$ |
| 29.3-a2 |
29.3-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^5+a^4-5a^3-4a^2+5a+3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$99215.09230$ |
1.91325 |
\( -\frac{253222784}{841} a^{5} + \frac{233815104}{841} a^{4} + \frac{1044382848}{841} a^{3} - \frac{367451968}{841} a^{2} - \frac{1161980416}{841} a - \frac{306055424}{841} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( -a^{3} + 2 a\) , \( a^{3} - 2 a\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 10 a^{2} - 7 a + 10\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 8 a - 7\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}+2a\right){x}^{2}+\left(-a^{5}+2a^{4}+5a^{3}-10a^{2}-7a+10\right){x}+a^{5}-a^{4}-6a^{3}+5a^{2}+8a-7$ |
| 29.3-a3 |
29.3-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^5+a^4-5a^3-4a^2+5a+3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$49607.54615$ |
1.91325 |
\( \frac{3719964882176}{29} a^{5} + \frac{3228064572928}{29} a^{4} - \frac{23238544756608}{29} a^{3} - \frac{20165653546816}{29} a^{2} + \frac{34580410198528}{29} a + \frac{30007755638656}{29} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 6 a + 3\) , \( -a^{4} + 4 a^{2} - 1\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 3\) , \( 2 a^{4} + a^{3} - 10 a^{2} + 11\) , \( 3 a^{5} + 9 a^{4} - 9 a^{3} - 30 a^{2} + 6 a + 17\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+6a+3\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+3\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-1\right){x}^{2}+\left(2a^{4}+a^{3}-10a^{2}+11\right){x}+3a^{5}+9a^{4}-9a^{3}-30a^{2}+6a+17$ |
| 29.3-a4 |
29.3-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{5} \) |
$122.69875$ |
$(a^5+a^4-5a^3-4a^2+5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$2500$ |
\( 1 \) |
$1$ |
$3.174882953$ |
1.91325 |
\( -\frac{9333084346559279257475328}{20511149} a^{5} + \frac{8098918785868051251992576}{20511149} a^{4} + \frac{58303656218014178170587776}{20511149} a^{3} - \frac{50593887546799104218019648}{20511149} a^{2} - \frac{86759652322047479298547712}{20511149} a + \frac{75287123468681894775064448}{20511149} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a + 1\) , \( a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 3 a + 1\) , \( 397 a^{5} - 703 a^{4} - 1285 a^{3} + 2222 a^{2} + 718 a - 1334\) , \( 12286 a^{5} - 23477 a^{4} - 39452 a^{3} + 74822 a^{2} + 22682 a - 43149\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+3a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+3a+1\right){x}^{2}+\left(397a^{5}-703a^{4}-1285a^{3}+2222a^{2}+718a-1334\right){x}+12286a^{5}-23477a^{4}-39452a^{3}+74822a^{2}+22682a-43149$ |
| 29.3-b1 |
29.3-b |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^5+a^4-5a^3-4a^2+5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.027222349$ |
$75000.91466$ |
2.95290 |
\( \frac{3029504}{29} a^{5} - \frac{4780288}{29} a^{4} - \frac{13721984}{29} a^{3} + \frac{21882304}{29} a^{2} + \frac{7840512}{29} a - \frac{13042816}{29} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 6 a + 3\) , \( -a^{4} + 3 a^{2} + a\) , \( a^{4} - 3 a^{2} + a\) , \( 2 a^{4} - 2 a^{3} - 8 a^{2} + 7 a + 8\) , \( 3 a^{5} + 6 a^{4} - 10 a^{3} - 20 a^{2} + 8 a + 12\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+6a+3\right){x}{y}+\left(a^{4}-3a^{2}+a\right){y}={x}^{3}+\left(-a^{4}+3a^{2}+a\right){x}^{2}+\left(2a^{4}-2a^{3}-8a^{2}+7a+8\right){x}+3a^{5}+6a^{4}-10a^{3}-20a^{2}+8a+12$ |
| 29.3-b2 |
29.3-b |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^5+a^4-5a^3-4a^2+5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.013611174$ |
$75000.91466$ |
2.95290 |
\( -\frac{3849088}{841} a^{5} - \frac{6215360}{841} a^{4} + \frac{17899904}{841} a^{3} + \frac{29889984}{841} a^{2} - \frac{10493440}{841} a - \frac{18286592}{841} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( a^{4} - 5 a^{2} + a + 5\) , \( a^{2} - 1\) , \( 2 a^{5} + 4 a^{4} - 9 a^{3} - 19 a^{2} + 6 a + 15\) , \( -3 a^{5} - 3 a^{4} + 15 a^{3} + 12 a^{2} - 13 a - 3\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-5a^{2}+a+5\right){x}^{2}+\left(2a^{5}+4a^{4}-9a^{3}-19a^{2}+6a+15\right){x}-3a^{5}-3a^{4}+15a^{3}+12a^{2}-13a-3$ |
| 29.3-c1 |
29.3-c |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{10} \) |
$122.69875$ |
$(a^5+a^4-5a^3-4a^2+5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$4622.007287$ |
2.22826 |
\( -\frac{835014258814272032979854369152}{420707233300201} a^{5} - \frac{1305681097629273002898348169152}{420707233300201} a^{4} + \frac{3803454846833048030493700214912}{420707233300201} a^{3} + \frac{5947322909367360822472170753216}{420707233300201} a^{2} - \frac{2390592337533999723550389291520}{420707233300201} a - \frac{3738082838237017786881864213248}{420707233300201} \) |
\( \bigl[a^{5} - 4 a^{3} + 3 a + 1\) , \( -a^{5} + a^{4} + 5 a^{3} - 4 a^{2} - 6 a + 3\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( -128 a^{5} - 221 a^{4} + 258 a^{3} + 637 a^{2} + 228 a - 456\) , \( 2676 a^{5} + 4729 a^{4} - 8235 a^{3} - 15201 a^{2} + 3355 a + 10371\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+3a+1\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-4a^{2}-6a+3\right){x}^{2}+\left(-128a^{5}-221a^{4}+258a^{3}+637a^{2}+228a-456\right){x}+2676a^{5}+4729a^{4}-8235a^{3}-15201a^{2}+3355a+10371$ |
| 29.3-c2 |
29.3-c |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^5+a^4-5a^3-4a^2+5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$4622.007287$ |
2.22826 |
\( -\frac{253222784}{841} a^{5} + \frac{233815104}{841} a^{4} + \frac{1044382848}{841} a^{3} - \frac{367451968}{841} a^{2} - \frac{1161980416}{841} a - \frac{306055424}{841} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( a + 1\) , \( a^{5} - 5 a^{3} + 5 a + 1\) , \( -a^{5} + 3 a^{4} + 6 a^{3} - 14 a^{2} - 7 a + 12\) , \( -2 a^{5} + 3 a^{4} + 12 a^{3} - 15 a^{2} - 16 a + 15\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}{y}+\left(a^{5}-5a^{3}+5a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a^{5}+3a^{4}+6a^{3}-14a^{2}-7a+12\right){x}-2a^{5}+3a^{4}+12a^{3}-15a^{2}-16a+15$ |
| 29.3-c3 |
29.3-c |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^5+a^4-5a^3-4a^2+5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$9244.014574$ |
2.22826 |
\( \frac{3719964882176}{29} a^{5} + \frac{3228064572928}{29} a^{4} - \frac{23238544756608}{29} a^{3} - \frac{20165653546816}{29} a^{2} + \frac{34580410198528}{29} a + \frac{30007755638656}{29} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 6 a + 3\) , \( -a^{5} - a^{4} + 4 a^{3} + 4 a^{2} - a - 1\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 3\) , \( -2 a^{5} - a^{4} + 9 a^{3} + 3 a^{2} - 2 a + 4\) , \( -3 a^{5} - 8 a^{4} + 11 a^{3} + 31 a^{2} - 5 a - 19\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+6a+3\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+3\right){y}={x}^{3}+\left(-a^{5}-a^{4}+4a^{3}+4a^{2}-a-1\right){x}^{2}+\left(-2a^{5}-a^{4}+9a^{3}+3a^{2}-2a+4\right){x}-3a^{5}-8a^{4}+11a^{3}+31a^{2}-5a-19$ |
| 29.3-c4 |
29.3-c |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{5} \) |
$122.69875$ |
$(a^5+a^4-5a^3-4a^2+5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$9244.014574$ |
2.22826 |
\( -\frac{9333084346559279257475328}{20511149} a^{5} + \frac{8098918785868051251992576}{20511149} a^{4} + \frac{58303656218014178170587776}{20511149} a^{3} - \frac{50593887546799104218019648}{20511149} a^{2} - \frac{86759652322047479298547712}{20511149} a + \frac{75287123468681894775064448}{20511149} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{5} + 4 a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 396 a^{5} - 707 a^{4} - 1281 a^{3} + 2238 a^{2} + 716 a - 1346\) , \( -11064 a^{5} + 21262 a^{4} + 35504 a^{3} - 67829 a^{2} - 20471 a + 39101\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{5}+4a^{3}-2a+1\right){x}^{2}+\left(396a^{5}-707a^{4}-1281a^{3}+2238a^{2}+716a-1346\right){x}-11064a^{5}+21262a^{4}+35504a^{3}-67829a^{2}-20471a+39101$ |
| 29.3-d1 |
29.3-d |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^5+a^4-5a^3-4a^2+5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.107677395$ |
$22728.25708$ |
3.53954 |
\( \frac{3029504}{29} a^{5} - \frac{4780288}{29} a^{4} - \frac{13721984}{29} a^{3} + \frac{21882304}{29} a^{2} + \frac{7840512}{29} a - \frac{13042816}{29} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 6 a + 3\) , \( -a^{5} - a^{4} + 4 a^{3} + 5 a^{2} - 2 a - 5\) , \( a^{5} - 5 a^{3} + a^{2} + 5 a - 1\) , \( -a^{5} - a^{4} + 5 a^{3} + 6 a^{2} - 4 a - 6\) , \( -2 a^{5} - 4 a^{4} + 7 a^{3} + 14 a^{2} - 4 a - 9\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+6a+3\right){x}{y}+\left(a^{5}-5a^{3}+a^{2}+5a-1\right){y}={x}^{3}+\left(-a^{5}-a^{4}+4a^{3}+5a^{2}-2a-5\right){x}^{2}+\left(-a^{5}-a^{4}+5a^{3}+6a^{2}-4a-6\right){x}-2a^{5}-4a^{4}+7a^{3}+14a^{2}-4a-9$ |
| 29.3-d2 |
29.3-d |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^5+a^4-5a^3-4a^2+5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.053838697$ |
$22728.25708$ |
3.53954 |
\( -\frac{3849088}{841} a^{5} - \frac{6215360}{841} a^{4} + \frac{17899904}{841} a^{3} + \frac{29889984}{841} a^{2} - \frac{10493440}{841} a - \frac{18286592}{841} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 2 a - 4\) , \( a^{5} - 4 a^{3} + a^{2} + 3 a - 2\) , \( 2 a^{5} + 2 a^{4} - 11 a^{3} - 9 a^{2} + 9 a + 5\) , \( 5 a^{5} + 5 a^{4} - 25 a^{3} - 23 a^{2} + 20 a + 11\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}{y}+\left(a^{5}-4a^{3}+a^{2}+3a-2\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+2a-4\right){x}^{2}+\left(2a^{5}+2a^{4}-11a^{3}-9a^{2}+9a+5\right){x}+5a^{5}+5a^{4}-25a^{3}-23a^{2}+20a+11$ |
| 29.4-a1 |
29.4-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29^{10} \) |
$122.69875$ |
$(a^5-a^4-5a^3+4a^2+5a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$6.349765907$ |
1.91325 |
\( \frac{835014258814272032979854369152}{420707233300201} a^{5} - \frac{1305681097629273002898348169152}{420707233300201} a^{4} - \frac{3803454846833048030493700214912}{420707233300201} a^{3} + \frac{5947322909367360822472170753216}{420707233300201} a^{2} + \frac{2390592337533999723550389291520}{420707233300201} a - \frac{3738082838237017786881864213248}{420707233300201} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 6 a + 3\) , \( -a^{5} - a^{4} + 4 a^{3} + 3 a^{2} - a\) , \( a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 3 a\) , \( 3918 a^{5} - 7587 a^{4} - 12536 a^{3} + 24217 a^{2} + 7192 a - 13939\) , \( 374636 a^{5} - 730039 a^{4} - 1198246 a^{3} + 2334446 a^{2} + 689786 a - 1344006\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+6a+3\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+3a\right){y}={x}^{3}+\left(-a^{5}-a^{4}+4a^{3}+3a^{2}-a\right){x}^{2}+\left(3918a^{5}-7587a^{4}-12536a^{3}+24217a^{2}+7192a-13939\right){x}+374636a^{5}-730039a^{4}-1198246a^{3}+2334446a^{2}+689786a-1344006$ |
| 29.4-a2 |
29.4-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^5-a^4-5a^3+4a^2+5a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$99215.09230$ |
1.91325 |
\( \frac{253222784}{841} a^{5} + \frac{233815104}{841} a^{4} - \frac{1044382848}{841} a^{3} - \frac{367451968}{841} a^{2} + \frac{1161980416}{841} a - \frac{306055424}{841} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( a\) , \( a^{3} - 2 a\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 3 a + 10\) , \( -a^{5} - a^{4} + 6 a^{3} + 5 a^{2} - 8 a - 7\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+a{x}^{2}+\left(2a^{4}-a^{3}-10a^{2}+3a+10\right){x}-a^{5}-a^{4}+6a^{3}+5a^{2}-8a-7$ |
| 29.4-a3 |
29.4-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^5-a^4-5a^3+4a^2+5a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$49607.54615$ |
1.91325 |
\( -\frac{3719964882176}{29} a^{5} + \frac{3228064572928}{29} a^{4} + \frac{23238544756608}{29} a^{3} - \frac{20165653546816}{29} a^{2} - \frac{34580410198528}{29} a + \frac{30007755638656}{29} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -a - 1\) , \( a\) , \( 28 a^{5} + 44 a^{4} - 128 a^{3} - 201 a^{2} + 81 a + 127\) , \( -29 a^{5} - 45 a^{4} + 132 a^{3} + 205 a^{2} - 83 a - 129\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(28a^{5}+44a^{4}-128a^{3}-201a^{2}+81a+127\right){x}-29a^{5}-45a^{4}+132a^{3}+205a^{2}-83a-129$ |
| 29.4-a4 |
29.4-a |
$4$ |
$10$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29^{5} \) |
$122.69875$ |
$(a^5-a^4-5a^3+4a^2+5a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$2500$ |
\( 1 \) |
$1$ |
$3.174882953$ |
1.91325 |
\( \frac{9333084346559279257475328}{20511149} a^{5} + \frac{8098918785868051251992576}{20511149} a^{4} - \frac{58303656218014178170587776}{20511149} a^{3} - \frac{50593887546799104218019648}{20511149} a^{2} + \frac{86759652322047479298547712}{20511149} a + \frac{75287123468681894775064448}{20511149} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{5} + a^{4} + 4 a^{3} - 3 a^{2} - 2 a + 1\) , \( a^{5} - 5 a^{3} + a^{2} + 6 a - 1\) , \( -396 a^{5} - 703 a^{4} + 1283 a^{3} + 2223 a^{2} - 718 a - 1335\) , \( -12988 a^{5} - 24969 a^{4} + 41671 a^{3} + 79658 a^{2} - 24015 a - 45928\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{5}-5a^{3}+a^{2}+6a-1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-3a^{2}-2a+1\right){x}^{2}+\left(-396a^{5}-703a^{4}+1283a^{3}+2223a^{2}-718a-1335\right){x}-12988a^{5}-24969a^{4}+41671a^{3}+79658a^{2}-24015a-45928$ |
| 29.4-b1 |
29.4-b |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29 \) |
$122.69875$ |
$(a^5-a^4-5a^3+4a^2+5a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.027222349$ |
$75000.91466$ |
2.95290 |
\( -\frac{3029504}{29} a^{5} - \frac{4780288}{29} a^{4} + \frac{13721984}{29} a^{3} + \frac{21882304}{29} a^{2} - \frac{7840512}{29} a - \frac{13042816}{29} \) |
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -a^{5} + 6 a^{3} + a^{2} - 8 a - 1\) , \( a^{5} - 4 a^{3} + 2 a + 1\) , \( 8 a^{5} + 13 a^{4} - 36 a^{3} - 59 a^{2} + 22 a + 40\) , \( 35 a^{5} + 57 a^{4} - 159 a^{3} - 259 a^{2} + 99 a + 163\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){x}{y}+\left(a^{5}-4a^{3}+2a+1\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+a^{2}-8a-1\right){x}^{2}+\left(8a^{5}+13a^{4}-36a^{3}-59a^{2}+22a+40\right){x}+35a^{5}+57a^{4}-159a^{3}-259a^{2}+99a+163$ |
| 29.4-b2 |
29.4-b |
$2$ |
$2$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29^{2} \) |
$122.69875$ |
$(a^5-a^4-5a^3+4a^2+5a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.013611174$ |
$75000.91466$ |
2.95290 |
\( \frac{3849088}{841} a^{5} - \frac{6215360}{841} a^{4} - \frac{17899904}{841} a^{3} + \frac{29889984}{841} a^{2} + \frac{10493440}{841} a - \frac{18286592}{841} \) |
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 9 a + 3\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 6 a + 2\) , \( 2 a^{5} + 7 a^{4} - 7 a^{3} - 27 a^{2} + 8 a + 21\) , \( 6 a^{5} + 7 a^{4} - 23 a^{3} - 21 a^{2} + 18 a + 12\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+6a+2\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+9a+3\right){x}^{2}+\left(2a^{5}+7a^{4}-7a^{3}-27a^{2}+8a+21\right){x}+6a^{5}+7a^{4}-23a^{3}-21a^{2}+18a+12$ |
*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.
