| 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 |
| 19.1-a1 |
19.1-a |
$2$ |
$5$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$125.26279$ |
$(-a^5+a^4+5a^3-2a^2-4a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$49573.89131$ |
1.80797 |
\( \frac{1118771298}{19} a^{5} - \frac{749521809}{19} a^{4} - \frac{6455647281}{19} a^{3} + \frac{2001366556}{19} a^{2} + \frac{6695505743}{19} a - \frac{2449393965}{19} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 8 a^{2} + a + 5\) , \( 2 a^{5} - 10 a^{3} - 5 a^{2} + 5 a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a - 2\) , \( 3 a^{5} + a^{4} - 16 a^{3} - 11 a^{2} + 13 a + 8\) , \( 2 a^{5} + a^{4} - 10 a^{3} - 7 a^{2} + 8 a + 5\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-8a^{2}+a+5\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a-2\right){y}={x}^{3}+\left(2a^{5}-10a^{3}-5a^{2}+5a+1\right){x}^{2}+\left(3a^{5}+a^{4}-16a^{3}-11a^{2}+13a+8\right){x}+2a^{5}+a^{4}-10a^{3}-7a^{2}+8a+5$ |
| 19.1-a2 |
19.1-a |
$2$ |
$5$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{5} \) |
$125.26279$ |
$(-a^5+a^4+5a^3-2a^2-4a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$3.172729044$ |
1.80797 |
\( -\frac{99880343556017740944784597960130}{2476099} a^{5} + \frac{183964995719273027262624762310885}{2476099} a^{4} + \frac{260445424966168107631811475766858}{2476099} a^{3} - \frac{279941722623219836713618346811774}{2476099} a^{2} - \frac{83670320622112387111597362661086}{2476099} a + \frac{54228158948731844175448026853264}{2476099} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 8 a^{2} + a + 5\) , \( 2 a^{5} - 10 a^{3} - 5 a^{2} + 5 a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a - 2\) , \( 218 a^{5} - 404 a^{4} - 561 a^{3} + 589 a^{2} + 163 a - 102\) , \( 5256 a^{5} - 9733 a^{4} - 13691 a^{3} + 14779 a^{2} + 4372 a - 2857\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-8a^{2}+a+5\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a-2\right){y}={x}^{3}+\left(2a^{5}-10a^{3}-5a^{2}+5a+1\right){x}^{2}+\left(218a^{5}-404a^{4}-561a^{3}+589a^{2}+163a-102\right){x}+5256a^{5}-9733a^{4}-13691a^{3}+14779a^{2}+4372a-2857$ |
| 19.1-b1 |
19.1-b |
$1$ |
$1$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
19.1 |
\( 19 \) |
\( 19^{3} \) |
$125.26279$ |
$(-a^5+a^4+5a^3-2a^2-4a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.001664003$ |
$105898.2268$ |
2.89198 |
\( -\frac{107378990697}{6859} a^{5} + \frac{137809825796}{6859} a^{4} + \frac{466642852265}{6859} a^{3} - \frac{383912333399}{6859} a^{2} - \frac{148160313215}{6859} a + \frac{83157905202}{6859} \) |
\( \bigl[2 a^{5} - 11 a^{3} - 4 a^{2} + 8 a + 1\) , \( -a^{5} + 6 a^{3} + 3 a^{2} - 4 a - 4\) , \( a^{5} - 5 a^{3} - 3 a^{2} + 3 a + 2\) , \( 2 a^{3} + 2 a^{2} - 3 a - 1\) , \( 2 a^{3} + 2 a^{2} - 2 a - 1\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-4a^{2}+8a+1\right){x}{y}+\left(a^{5}-5a^{3}-3a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+3a^{2}-4a-4\right){x}^{2}+\left(2a^{3}+2a^{2}-3a-1\right){x}+2a^{3}+2a^{2}-2a-1$ |
| 23.1-a1 |
23.1-a |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{2} \) |
$127.27309$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.044422120$ |
$19000.37106$ |
2.30867 |
\( \frac{171072801983575}{529} a^{5} - \frac{220100755787912}{529} a^{4} - \frac{743258195022414}{529} a^{3} + \frac{614124610897504}{529} a^{2} + \frac{236314133338785}{529} a - \frac{132966554354377}{529} \) |
\( \bigl[3 a^{5} - 16 a^{3} - 7 a^{2} + 10 a + 4\) , \( -a^{5} + 5 a^{3} + 3 a^{2} - 3 a - 2\) , \( a^{4} - 5 a^{2} - 2 a + 3\) , \( 29 a^{5} + 2 a^{4} - 132 a^{3} - 110 a^{2} + 20 a + 24\) , \( -92 a^{5} - 4 a^{4} + 400 a^{3} + 342 a^{2} - 19 a - 52\bigr] \) |
${y}^2+\left(3a^{5}-16a^{3}-7a^{2}+10a+4\right){x}{y}+\left(a^{4}-5a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{5}+5a^{3}+3a^{2}-3a-2\right){x}^{2}+\left(29a^{5}+2a^{4}-132a^{3}-110a^{2}+20a+24\right){x}-92a^{5}-4a^{4}+400a^{3}+342a^{2}-19a-52$ |
| 23.1-a2 |
23.1-a |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$127.27309$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.022211060$ |
$76001.48424$ |
2.30867 |
\( -\frac{5525257}{23} a^{5} + \frac{7113115}{23} a^{4} + \frac{24002274}{23} a^{3} - \frac{19876729}{23} a^{2} - \frac{7604872}{23} a + \frac{4359839}{23} \) |
\( \bigl[a^{5} - 5 a^{3} - 2 a^{2} + 3 a\) , \( -a^{4} - a^{3} + 6 a^{2} + 4 a - 3\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 4 a - 2\) , \( 2 a^{5} - 2 a^{4} - 14 a^{3} + 10 a^{2} + 20 a - 8\) , \( -4 a^{5} + 2 a^{4} + 21 a^{3} - a^{2} - 16 a + 5\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-2a^{2}+3a\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+4a-2\right){y}={x}^{3}+\left(-a^{4}-a^{3}+6a^{2}+4a-3\right){x}^{2}+\left(2a^{5}-2a^{4}-14a^{3}+10a^{2}+20a-8\right){x}-4a^{5}+2a^{4}+21a^{3}-a^{2}-16a+5$ |
| 23.1-b1 |
23.1-b |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{2} \) |
$127.27309$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.127899790$ |
$7043.795236$ |
2.46421 |
\( -\frac{64587684849520777390}{529} a^{5} - \frac{57138637099073147545}{529} a^{4} + \frac{336977403710038840340}{529} a^{3} + \frac{427288386591293548325}{529} a^{2} - \frac{9517884661720984800}{529} a - \frac{73007849746353821011}{529} \) |
\( \bigl[a^{5} - 5 a^{3} - 3 a^{2} + 2 a + 2\) , \( a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 3 a - 1\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 3 a + 1\) , \( 13 a^{5} + 14 a^{4} - 65 a^{3} - 100 a^{2} - 17 a + 15\) , \( -76 a^{5} - 54 a^{4} + 403 a^{3} + 433 a^{2} - 68 a - 66\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-3a^{2}+2a+2\right){x}{y}+\left(a^{5}-5a^{3}-2a^{2}+3a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+3a-1\right){x}^{2}+\left(13a^{5}+14a^{4}-65a^{3}-100a^{2}-17a+15\right){x}-76a^{5}-54a^{4}+403a^{3}+433a^{2}-68a-66$ |
| 23.1-b2 |
23.1-b |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$127.27309$ |
$(a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.063949895$ |
$28175.18094$ |
2.46421 |
\( -\frac{3165581690}{23} a^{5} - \frac{2800404377}{23} a^{4} + \frac{16516071565}{23} a^{3} + \frac{20941760961}{23} a^{2} - \frac{466899376}{23} a - \frac{3577908365}{23} \) |
\( \bigl[2 a^{5} - 10 a^{3} - 5 a^{2} + 4 a + 3\) , \( 2 a^{5} - 11 a^{3} - 4 a^{2} + 7 a\) , \( 2 a^{5} - 11 a^{3} - 4 a^{2} + 8 a + 2\) , \( 3 a^{5} + 2 a^{4} - 14 a^{3} - 18 a^{2} - 5 a + 4\) , \( -6 a^{5} - 7 a^{4} + 32 a^{3} + 48 a^{2} - 10\bigr] \) |
${y}^2+\left(2a^{5}-10a^{3}-5a^{2}+4a+3\right){x}{y}+\left(2a^{5}-11a^{3}-4a^{2}+8a+2\right){y}={x}^{3}+\left(2a^{5}-11a^{3}-4a^{2}+7a\right){x}^{2}+\left(3a^{5}+2a^{4}-14a^{3}-18a^{2}-5a+4\right){x}-6a^{5}-7a^{4}+32a^{3}+48a^{2}-10$ |
| 25.2-a1 |
25.2-a |
$1$ |
$1$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{3} \) |
$128.16052$ |
$(a^5-5a^3-2a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.010887039$ |
$24509.33712$ |
2.91945 |
\( -1772 a^{5} + 2520 a^{4} + 8288 a^{3} - 8684 a^{2} - 3481 a + 2302 \) |
\( \bigl[3 a^{5} - 16 a^{3} - 7 a^{2} + 9 a + 3\) , \( a^{5} + a^{4} - 6 a^{3} - 7 a^{2} + 2 a + 2\) , \( 3 a^{5} - 16 a^{3} - 7 a^{2} + 9 a + 4\) , \( a^{5} + 3 a^{4} - 7 a^{3} - 16 a^{2} + 3 a + 5\) , \( a^{5} + 2 a^{4} - 7 a^{3} - 12 a^{2} + 5 a + 5\bigr] \) |
${y}^2+\left(3a^{5}-16a^{3}-7a^{2}+9a+3\right){x}{y}+\left(3a^{5}-16a^{3}-7a^{2}+9a+4\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-7a^{2}+2a+2\right){x}^{2}+\left(a^{5}+3a^{4}-7a^{3}-16a^{2}+3a+5\right){x}+a^{5}+2a^{4}-7a^{3}-12a^{2}+5a+5$ |
| 25.2-b1 |
25.2-b |
$2$ |
$5$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{8} \) |
$128.16052$ |
$(a^5-5a^3-2a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.1 |
$1$ |
\( 3 \) |
$0.004467785$ |
$37950.90693$ |
2.78270 |
\( 26024 a^{5} - 44922 a^{4} - 66007 a^{3} + 51212 a^{2} + 20153 a - 8868 \) |
\( \bigl[2 a^{5} - 11 a^{3} - 5 a^{2} + 7 a + 3\) , \( -2 a^{5} + a^{4} + 10 a^{3} - 6 a + 1\) , \( 2 a^{5} - a^{4} - 11 a^{3} + a^{2} + 10 a\) , \( -12 a^{5} - 3 a^{4} + 69 a^{3} + 44 a^{2} - 50 a - 26\) , \( -12 a^{5} - 6 a^{4} + 70 a^{3} + 60 a^{2} - 50 a - 42\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-5a^{2}+7a+3\right){x}{y}+\left(2a^{5}-a^{4}-11a^{3}+a^{2}+10a\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+10a^{3}-6a+1\right){x}^{2}+\left(-12a^{5}-3a^{4}+69a^{3}+44a^{2}-50a-26\right){x}-12a^{5}-6a^{4}+70a^{3}+60a^{2}-50a-42$ |
| 25.2-b2 |
25.2-b |
$2$ |
$5$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{4} \) |
$128.16052$ |
$(a^5-5a^3-2a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.2 |
$1$ |
\( 3 \) |
$0.022338926$ |
$7590.181386$ |
2.78270 |
\( 22798094503678997126 a^{5} + 20168733073579397000 a^{4} - 118945942375550562381 a^{3} - 150823794748457902004 a^{2} + 3359648661605834886 a + 25770248373248219997 \) |
\( \bigl[2 a^{5} - 11 a^{3} - 4 a^{2} + 8 a + 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 6 a\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 4 a - 1\) , \( 13 a^{5} - 6 a^{4} - 85 a^{3} - 10 a^{2} + 59 a - 18\) , \( -28 a^{5} + 16 a^{4} + 196 a^{3} + 53 a^{2} - 103 a + 21\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-4a^{2}+8a+1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+4a-1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-6a\right){x}^{2}+\left(13a^{5}-6a^{4}-85a^{3}-10a^{2}+59a-18\right){x}-28a^{5}+16a^{4}+196a^{3}+53a^{2}-103a+21$ |
| 25.2-c1 |
25.2-c |
$2$ |
$5$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{2} \) |
$128.16052$ |
$(a^5-5a^3-2a^2+3a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$42669.70410$ |
1.55618 |
\( 26024 a^{5} - 44922 a^{4} - 66007 a^{3} + 51212 a^{2} + 20153 a - 8868 \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + a^{2} + 10 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 3 a + 1\) , \( -3 a^{5} + 4 a^{4} + 15 a^{3} - 13 a^{2} - 18 a + 8\) , \( -2 a^{5} + 3 a^{4} + 10 a^{3} - 11 a^{2} - 14 a + 6\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+a^{2}+10a-1\right){x}{y}+\left(a^{5}-5a^{3}-2a^{2}+3a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2\right){x}^{2}+\left(-3a^{5}+4a^{4}+15a^{3}-13a^{2}-18a+8\right){x}-2a^{5}+3a^{4}+10a^{3}-11a^{2}-14a+6$ |
| 25.2-c2 |
25.2-c |
$2$ |
$5$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{10} \) |
$128.16052$ |
$(a^5-5a^3-2a^2+3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$2.730861062$ |
1.55618 |
\( 22798094503678997126 a^{5} + 20168733073579397000 a^{4} - 118945942375550562381 a^{3} - 150823794748457902004 a^{2} + 3359648661605834886 a + 25770248373248219997 \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( -a^{5} + a^{4} + 4 a^{3} - 2 a^{2}\) , \( a^{5} + a^{4} - 6 a^{3} - 7 a^{2} + 3 a + 3\) , \( 121 a^{5} - 71 a^{4} - 571 a^{3} + 57 a^{2} + 137 a - 31\) , \( -4539 a^{5} + 6376 a^{4} + 19518 a^{3} - 18850 a^{2} - 6567 a + 3998\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-7a^{2}+3a+3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+4a^{3}-2a^{2}\right){x}^{2}+\left(121a^{5}-71a^{4}-571a^{3}+57a^{2}+137a-31\right){x}-4539a^{5}+6376a^{4}+19518a^{3}-18850a^{2}-6567a+3998$ |
| 25.2-d1 |
25.2-d |
$1$ |
$1$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{9} \) |
$128.16052$ |
$(a^5-5a^3-2a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.010782128$ |
$24880.59500$ |
2.93512 |
\( -1772 a^{5} + 2520 a^{4} + 8288 a^{3} - 8684 a^{2} - 3481 a + 2302 \) |
\( \bigl[a^{5} - 6 a^{3} - 2 a^{2} + 6 a + 1\) , \( 2 a^{5} - 2 a^{4} - 10 a^{3} + 5 a^{2} + 8 a - 1\) , \( a^{5} - 5 a^{3} - 3 a^{2} + 3 a + 3\) , \( 12 a^{5} + 3 a^{4} - 69 a^{3} - 44 a^{2} + 51 a + 32\) , \( 88 a^{5} + 32 a^{4} - 515 a^{3} - 365 a^{2} + 389 a + 232\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-2a^{2}+6a+1\right){x}{y}+\left(a^{5}-5a^{3}-3a^{2}+3a+3\right){y}={x}^{3}+\left(2a^{5}-2a^{4}-10a^{3}+5a^{2}+8a-1\right){x}^{2}+\left(12a^{5}+3a^{4}-69a^{3}-44a^{2}+51a+32\right){x}+88a^{5}+32a^{4}-515a^{3}-365a^{2}+389a+232$ |
| 35.1-a1 |
35.1-a |
$1$ |
$1$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5 \cdot 7^{7} \) |
$131.80492$ |
$(a^5-5a^3-2a^2+3a+1), (a^5-a^4-5a^3+3a^2+4a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.002481949$ |
$38040.36254$ |
3.61548 |
\( -\frac{1061449588}{4117715} a^{5} - \frac{682394064}{4117715} a^{4} + \frac{6960636471}{4117715} a^{3} + \frac{597012252}{588245} a^{2} - \frac{3657536166}{4117715} a - \frac{2083912286}{4117715} \) |
\( \bigl[3 a^{5} - a^{4} - 16 a^{3} - 2 a^{2} + 12 a + 2\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 7 a^{2} + 2 a - 3\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 3 a\) , \( 8 a^{5} - 7 a^{4} - 39 a^{3} + 13 a^{2} + 22 a + 1\) , \( 7 a^{5} - 7 a^{4} - 33 a^{3} + 15 a^{2} + 16 a\bigr] \) |
${y}^2+\left(3a^{5}-a^{4}-16a^{3}-2a^{2}+12a+2\right){x}{y}+\left(a^{5}-5a^{3}-2a^{2}+3a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+7a^{2}+2a-3\right){x}^{2}+\left(8a^{5}-7a^{4}-39a^{3}+13a^{2}+22a+1\right){x}+7a^{5}-7a^{4}-33a^{3}+15a^{2}+16a$ |
| 35.1-b1 |
35.1-b |
$4$ |
$4$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5^{2} \cdot 7^{3} \) |
$131.80492$ |
$(a^5-5a^3-2a^2+3a+1), (a^5-a^4-5a^3+3a^2+4a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13690.32267$ |
1.56028 |
\( \frac{87765413}{8575} a^{5} - \frac{31840806}{8575} a^{4} - \frac{499320406}{8575} a^{3} - \frac{440222}{1225} a^{2} + \frac{450658326}{8575} a - \frac{81846074}{8575} \) |
\( \bigl[2 a^{5} - 11 a^{3} - 5 a^{2} + 7 a + 4\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 3 a + 1\) , \( 3 a^{5} - 16 a^{3} - 7 a^{2} + 10 a + 4\) , \( a^{4} - 5 a^{2} - a + 1\) , \( -a^{3} - a^{2} + 4 a + 2\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-5a^{2}+7a+4\right){x}{y}+\left(3a^{5}-16a^{3}-7a^{2}+10a+4\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-3a+1\right){x}^{2}+\left(a^{4}-5a^{2}-a+1\right){x}-a^{3}-a^{2}+4a+2$ |
| 35.1-b2 |
35.1-b |
$4$ |
$4$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{4} \cdot 7^{6} \) |
$131.80492$ |
$(a^5-5a^3-2a^2+3a+1), (a^5-a^4-5a^3+3a^2+4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$6845.161336$ |
1.56028 |
\( -\frac{18188830969244913}{73530625} a^{5} + \frac{9703468871901706}{73530625} a^{4} + \frac{103823232715854756}{73530625} a^{3} - \frac{2678264504132803}{10504375} a^{2} - \frac{98871979437774776}{73530625} a + \frac{34233915826271024}{73530625} \) |
\( \bigl[2 a^{5} - 11 a^{3} - 5 a^{2} + 7 a + 4\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 3 a + 1\) , \( 3 a^{5} - 16 a^{3} - 7 a^{2} + 10 a + 4\) , \( 15 a^{5} + a^{4} - 70 a^{3} - 55 a^{2} + 14 a + 6\) , \( -22 a^{5} - 48 a^{4} + 142 a^{3} + 237 a^{2} + a - 37\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-5a^{2}+7a+4\right){x}{y}+\left(3a^{5}-16a^{3}-7a^{2}+10a+4\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-3a+1\right){x}^{2}+\left(15a^{5}+a^{4}-70a^{3}-55a^{2}+14a+6\right){x}-22a^{5}-48a^{4}+142a^{3}+237a^{2}+a-37$ |
| 35.1-b3 |
35.1-b |
$4$ |
$4$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5^{2} \cdot 7^{12} \) |
$131.80492$ |
$(a^5-5a^3-2a^2+3a+1), (a^5-a^4-5a^3+3a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$106.9556458$ |
1.56028 |
\( -\frac{5264522614282998874472391}{346032180025} a^{5} + \frac{9696637222961801868697742}{346032180025} a^{4} + \frac{13727225612359621146372892}{346032180025} a^{3} - \frac{2107869676718645458420171}{49433168575} a^{2} - \frac{4409993792554692498777657}{346032180025} a + \frac{2858221933664796913212668}{346032180025} \) |
\( \bigl[2 a^{5} - 10 a^{3} - 5 a^{2} + 5 a + 3\) , \( a^{3} - 2 a - 1\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 5 a + 2\) , \( 51 a^{5} - 3 a^{4} - 261 a^{3} - 94 a^{2} + 146 a - 31\) , \( -112 a^{5} - 11 a^{4} + 695 a^{3} + 174 a^{2} - 533 a + 135\bigr] \) |
${y}^2+\left(2a^{5}-10a^{3}-5a^{2}+5a+3\right){x}{y}+\left(a^{5}-6a^{3}-2a^{2}+5a+2\right){y}={x}^{3}+\left(a^{3}-2a-1\right){x}^{2}+\left(51a^{5}-3a^{4}-261a^{3}-94a^{2}+146a-31\right){x}-112a^{5}-11a^{4}+695a^{3}+174a^{2}-533a+135$ |
| 35.1-b4 |
35.1-b |
$4$ |
$4$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{8} \cdot 7^{3} \) |
$131.80492$ |
$(a^5-5a^3-2a^2+3a+1), (a^5-a^4-5a^3+3a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3422.580668$ |
1.56028 |
\( -\frac{30270413430239222287235959}{133984375} a^{5} + \frac{16027934427212101348939758}{133984375} a^{4} + \frac{173135789732515796324370908}{133984375} a^{3} - \frac{4447594013376724556449979}{19140625} a^{2} - \frac{165137558779338445042080393}{133984375} a + \frac{57168681782221940000417132}{133984375} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( 3 a^{5} - a^{4} - 16 a^{3} - 2 a^{2} + 10 a + 2\) , \( 0\) , \( -141 a^{5} - 13 a^{4} + 786 a^{3} + 400 a^{2} - 546 a - 294\) , \( -1163 a^{5} - 435 a^{4} + 6814 a^{3} + 4877 a^{2} - 5140 a - 3087\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}={x}^{3}+\left(3a^{5}-a^{4}-16a^{3}-2a^{2}+10a+2\right){x}^{2}+\left(-141a^{5}-13a^{4}+786a^{3}+400a^{2}-546a-294\right){x}-1163a^{5}-435a^{4}+6814a^{3}+4877a^{2}-5140a-3087$ |
| 35.1-c1 |
35.1-c |
$1$ |
$1$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{5} \cdot 7 \) |
$131.80492$ |
$(a^5-5a^3-2a^2+3a+1), (a^5-a^4-5a^3+3a^2+4a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.001204682$ |
$108679.6889$ |
3.58114 |
\( -\frac{2112158548}{21875} a^{5} - \frac{441784674}{21875} a^{4} + \frac{12902961251}{21875} a^{3} + \frac{1037503262}{3125} a^{2} - \frac{12724949171}{21875} a - \frac{7146961746}{21875} \) |
\( \bigl[2 a^{5} - 11 a^{3} - 4 a^{2} + 7 a + 2\) , \( -a^{4} - a^{3} + 6 a^{2} + 5 a - 2\) , \( a^{5} + a^{4} - 5 a^{3} - 8 a^{2} + a + 4\) , \( -a^{5} - a^{4} + 4 a^{3} + 8 a^{2} - 2\) , \( -a^{5} + a^{4} + 7 a^{3} - a^{2} - 7 a + 2\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-4a^{2}+7a+2\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-8a^{2}+a+4\right){y}={x}^{3}+\left(-a^{4}-a^{3}+6a^{2}+5a-2\right){x}^{2}+\left(-a^{5}-a^{4}+4a^{3}+8a^{2}-2\right){x}-a^{5}+a^{4}+7a^{3}-a^{2}-7a+2$ |
| 41.1-a1 |
41.1-a |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{3} \) |
$133.55432$ |
$(-a^5+2a^4+5a^3-8a^2-6a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12089.60166$ |
2.75570 |
\( \frac{457591040305}{68921} a^{5} + \frac{1100170980571}{68921} a^{4} - \frac{111914302505}{68921} a^{3} - \frac{1194071542265}{68921} a^{2} - \frac{113715440657}{68921} a + \frac{190682849753}{68921} \) |
\( \bigl[2 a^{5} - 11 a^{3} - 5 a^{2} + 7 a + 4\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 5 a + 2\) , \( 1\) , \( -31 a^{5} + 56 a^{4} + 120 a^{3} - 186 a^{2} - 14 a + 55\) , \( 59 a^{5} - 58 a^{4} - 272 a^{3} + 128 a^{2} + 111 a - 11\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-5a^{2}+7a+4\right){x}{y}+{y}={x}^{3}+\left(a^{5}-6a^{3}-2a^{2}+5a+2\right){x}^{2}+\left(-31a^{5}+56a^{4}+120a^{3}-186a^{2}-14a+55\right){x}+59a^{5}-58a^{4}-272a^{3}+128a^{2}+111a-11$ |
| 41.1-a2 |
41.1-a |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{6} \) |
$133.55432$ |
$(-a^5+2a^4+5a^3-8a^2-6a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1511.200207$ |
2.75570 |
\( -\frac{5267792387404773815}{4750104241} a^{5} + \frac{10727333588369067893}{4750104241} a^{4} + \frac{12233177973615040191}{4750104241} a^{3} - \frac{18006167602751945494}{4750104241} a^{2} - \frac{2749339989409868256}{4750104241} a + \frac{4357428283329805232}{4750104241} \) |
\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + a^{2} + 10 a\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 7 a - 3\) , \( 3 a^{5} - a^{4} - 16 a^{3} - 2 a^{2} + 12 a + 2\) , \( 410 a^{5} - 520 a^{4} - 1784 a^{3} + 1437 a^{2} + 560 a - 319\) , \( 3878 a^{5} - 4954 a^{4} - 16862 a^{3} + 13755 a^{2} + 5331 a - 2988\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-11a^{3}+a^{2}+10a\right){x}{y}+\left(3a^{5}-a^{4}-16a^{3}-2a^{2}+12a+2\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+7a-3\right){x}^{2}+\left(410a^{5}-520a^{4}-1784a^{3}+1437a^{2}+560a-319\right){x}+3878a^{5}-4954a^{4}-16862a^{3}+13755a^{2}+5331a-2988$ |
| 41.1-b1 |
41.1-b |
$1$ |
$1$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{3} \) |
$133.55432$ |
$(-a^5+2a^4+5a^3-8a^2-6a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.884186071$ |
$272.5577325$ |
3.95507 |
\( \frac{53605985045}{68921} a^{5} + \frac{29898078880}{68921} a^{4} - \frac{257628147848}{68921} a^{3} - \frac{280481519488}{68921} a^{2} + \frac{17982743468}{68921} a + \frac{45514357148}{68921} \) |
\( \bigl[3 a^{5} - 16 a^{3} - 7 a^{2} + 9 a + 3\) , \( a^{2} - a - 1\) , \( a\) , \( -2 a^{5} - 3 a^{4} + 13 a^{3} + 20 a^{2} - 11 a - 10\) , \( 96 a^{5} + 36 a^{4} - 562 a^{3} - 403 a^{2} + 422 a + 254\bigr] \) |
${y}^2+\left(3a^{5}-16a^{3}-7a^{2}+9a+3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-2a^{5}-3a^{4}+13a^{3}+20a^{2}-11a-10\right){x}+96a^{5}+36a^{4}-562a^{3}-403a^{2}+422a+254$ |
| 41.1-c1 |
41.1-c |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$133.55432$ |
$(-a^5+2a^4+5a^3-8a^2-6a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$8274.923949$ |
1.88618 |
\( \frac{13862760}{41} a^{5} + \frac{3688160}{41} a^{4} - \frac{40793921}{41} a^{3} + \frac{4883426}{41} a^{2} + \frac{9205608}{41} a - \frac{2161525}{41} \) |
\( \bigl[a + 1\) , \( -a^{5} - 2 a^{4} + 6 a^{3} + 13 a^{2} - a - 6\) , \( 2 a^{5} - 10 a^{3} - 5 a^{2} + 5 a + 3\) , \( -2 a^{5} - a^{4} + 10 a^{3} + 9 a^{2} + 2 a\) , \( -4 a^{5} + 2 a^{4} + 20 a^{3} - 10 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(2a^{5}-10a^{3}-5a^{2}+5a+3\right){y}={x}^{3}+\left(-a^{5}-2a^{4}+6a^{3}+13a^{2}-a-6\right){x}^{2}+\left(-2a^{5}-a^{4}+10a^{3}+9a^{2}+2a\right){x}-4a^{5}+2a^{4}+20a^{3}-10a-2$ |
| 41.1-c2 |
41.1-c |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{2} \) |
$133.55432$ |
$(-a^5+2a^4+5a^3-8a^2-6a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1034.365493$ |
1.88618 |
\( \frac{3550541504028148}{1681} a^{5} + \frac{8530239957871129}{1681} a^{4} - \frac{836167754409012}{1681} a^{3} - \frac{9198510337648498}{1681} a^{2} - \frac{867825842472881}{1681} a + \frac{1472553665080339}{1681} \) |
\( \bigl[2 a^{5} - 10 a^{3} - 5 a^{2} + 5 a + 2\) , \( 3 a^{5} - a^{4} - 16 a^{3} - 2 a^{2} + 11 a\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 5 a + 1\) , \( 11 a^{4} - 6 a^{3} - 46 a^{2} - 3 a + 12\) , \( -19 a^{5} + 56 a^{4} + 37 a^{3} - 144 a^{2} - 22 a + 28\bigr] \) |
${y}^2+\left(2a^{5}-10a^{3}-5a^{2}+5a+2\right){x}{y}+\left(a^{5}-6a^{3}-2a^{2}+5a+1\right){y}={x}^{3}+\left(3a^{5}-a^{4}-16a^{3}-2a^{2}+11a\right){x}^{2}+\left(11a^{4}-6a^{3}-46a^{2}-3a+12\right){x}-19a^{5}+56a^{4}+37a^{3}-144a^{2}-22a+28$ |
| 41.1-d1 |
41.1-d |
$4$ |
$10$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{2} \) |
$133.55432$ |
$(-a^5+2a^4+5a^3-8a^2-6a+5)$ |
$1$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$0.891643569$ |
$25811.74461$ |
2.51808 |
\( \frac{47765524309708283288}{1681} a^{5} - \frac{61454610039812849664}{1681} a^{4} - \frac{207526305290305700761}{1681} a^{3} + \frac{171470064606982249005}{1681} a^{2} + \frac{65981604235912703951}{1681} a - \frac{37125698314724310603}{1681} \) |
\( \bigl[2 a^{5} - a^{4} - 10 a^{3} + 7 a + 1\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 5 a + 1\) , \( 2 a^{5} - a^{4} - 10 a^{3} + 7 a + 1\) , \( 18 a^{5} + 22 a^{4} - 94 a^{3} - 150 a^{2} - 14 a + 23\) , \( -90 a^{5} - 79 a^{4} + 470 a^{3} + 591 a^{2} - 17 a - 101\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-10a^{3}+7a+1\right){x}{y}+\left(2a^{5}-a^{4}-10a^{3}+7a+1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-5a+1\right){x}^{2}+\left(18a^{5}+22a^{4}-94a^{3}-150a^{2}-14a+23\right){x}-90a^{5}-79a^{4}+470a^{3}+591a^{2}-17a-101$ |
| 41.1-d2 |
41.1-d |
$4$ |
$10$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$133.55432$ |
$(-a^5+2a^4+5a^3-8a^2-6a+5)$ |
$1$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 1 \) |
$0.445821784$ |
$103246.9784$ |
2.51808 |
\( \frac{2923104726}{41} a^{5} - \frac{3760871287}{41} a^{4} - \frac{12699940098}{41} a^{3} + \frac{10493621237}{41} a^{2} + \frac{4037769085}{41} a - \frac{2271991590}{41} \) |
\( \bigl[2 a^{5} - 11 a^{3} - 5 a^{2} + 7 a + 4\) , \( a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 4 a\) , \( 2 a^{5} - 11 a^{3} - 4 a^{2} + 7 a + 1\) , \( 5 a^{5} - 28 a^{3} - 12 a^{2} + 20 a + 9\) , \( 6 a^{5} + a^{4} - 34 a^{3} - 19 a^{2} + 24 a + 12\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-5a^{2}+7a+4\right){x}{y}+\left(2a^{5}-11a^{3}-4a^{2}+7a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+4a\right){x}^{2}+\left(5a^{5}-28a^{3}-12a^{2}+20a+9\right){x}+6a^{5}+a^{4}-34a^{3}-19a^{2}+24a+12$ |
| 41.1-d3 |
41.1-d |
$4$ |
$10$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{5} \) |
$133.55432$ |
$(-a^5+2a^4+5a^3-8a^2-6a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 5 \) |
$2.229108924$ |
$6.607806621$ |
2.51808 |
\( -\frac{51589187305351644437794}{115856201} a^{5} + \frac{28450442159784808678664}{115856201} a^{4} + \frac{297184534237618843847953}{115856201} a^{3} - \frac{54467674353691223695563}{115856201} a^{2} - \frac{283641203023771664024853}{115856201} a + \frac{98322419594743346373311}{115856201} \) |
\( \bigl[2 a^{5} - 11 a^{3} - 5 a^{2} + 7 a + 4\) , \( a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 4 a\) , \( 2 a^{5} - 11 a^{3} - 4 a^{2} + 7 a + 1\) , \( 215 a^{5} - 185 a^{4} - 1258 a^{3} + 423 a^{2} + 1215 a - 546\) , \( 2231 a^{5} - 2104 a^{4} - 13527 a^{3} + 5065 a^{2} + 13368 a - 6360\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-5a^{2}+7a+4\right){x}{y}+\left(2a^{5}-11a^{3}-4a^{2}+7a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+4a\right){x}^{2}+\left(215a^{5}-185a^{4}-1258a^{3}+423a^{2}+1215a-546\right){x}+2231a^{5}-2104a^{4}-13527a^{3}+5065a^{2}+13368a-6360$ |
| 41.1-d4 |
41.1-d |
$4$ |
$10$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{10} \) |
$133.55432$ |
$(-a^5+2a^4+5a^3-8a^2-6a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2 \cdot 5 \) |
$4.458217849$ |
$1.651951655$ |
2.51808 |
\( -\frac{21180060645091193193650944412424784104}{13422659310152401} a^{5} + \frac{39010576326790926299836970328483348193}{13422659310152401} a^{4} + \frac{55228583514967651803394766823468805189}{13422659310152401} a^{3} - \frac{59362858105143809110780711242176719172}{13422659310152401} a^{2} - \frac{17742654879424394280388256255733481076}{13422659310152401} a + \frac{11499316624983036162314272796652678500}{13422659310152401} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 8 a^{2} + a + 5\) , \( a^{5} - 5 a^{3} - 3 a^{2} + a + 1\) , \( 2 a^{5} - 10 a^{3} - 5 a^{2} + 4 a + 2\) , \( 5075 a^{5} - 3249 a^{4} - 28077 a^{3} + 6737 a^{2} + 26526 a - 10075\) , \( 271569 a^{5} - 157277 a^{4} - 1525871 a^{3} + 306662 a^{2} + 1443648 a - 511515\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-8a^{2}+a+5\right){x}{y}+\left(2a^{5}-10a^{3}-5a^{2}+4a+2\right){y}={x}^{3}+\left(a^{5}-5a^{3}-3a^{2}+a+1\right){x}^{2}+\left(5075a^{5}-3249a^{4}-28077a^{3}+6737a^{2}+26526a-10075\right){x}+271569a^{5}-157277a^{4}-1525871a^{3}+306662a^{2}+1443648a-511515$ |
| 47.1-a1 |
47.1-a |
$4$ |
$4$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( 47^{3} \) |
$135.08302$ |
$(a^3-a^2-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$297.5217858$ |
1.08507 |
\( -\frac{371778363159277920452}{103823} a^{5} - \frac{331084489603497256734}{103823} a^{4} + \frac{1940580263525274860952}{103823} a^{3} + \frac{2469815274283196336045}{103823} a^{2} - \frac{53543792530662170151}{103823} a - \frac{422164576453658766553}{103823} \) |
\( \bigl[a^{5} - 5 a^{3} - 2 a^{2} + 2 a\) , \( 2 a^{5} - 11 a^{3} - 4 a^{2} + 6 a + 2\) , \( 3 a^{5} - 16 a^{3} - 7 a^{2} + 10 a + 4\) , \( 188 a^{5} - 121 a^{4} - 1031 a^{3} + 208 a^{2} + 950 a - 330\) , \( -565 a^{5} + 128 a^{4} + 3668 a^{3} - 347 a^{2} - 3728 a + 1246\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-2a^{2}+2a\right){x}{y}+\left(3a^{5}-16a^{3}-7a^{2}+10a+4\right){y}={x}^{3}+\left(2a^{5}-11a^{3}-4a^{2}+6a+2\right){x}^{2}+\left(188a^{5}-121a^{4}-1031a^{3}+208a^{2}+950a-330\right){x}-565a^{5}+128a^{4}+3668a^{3}-347a^{2}-3728a+1246$ |
| 47.1-a2 |
47.1-a |
$4$ |
$4$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( 47^{6} \) |
$135.08302$ |
$(a^3-a^2-4a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$2380.174287$ |
1.08507 |
\( -\frac{240093819861854332}{10779215329} a^{5} - \frac{243065332851483291}{10779215329} a^{4} + \frac{1264923127803656222}{10779215329} a^{3} + \frac{1732323145623585931}{10779215329} a^{2} - \frac{17537373660297246}{10779215329} a - \frac{297245605291917211}{10779215329} \) |
\( \bigl[3 a^{5} - 16 a^{3} - 7 a^{2} + 10 a + 3\) , \( -3 a^{5} + 16 a^{3} + 7 a^{2} - 10 a - 2\) , \( a^{5} - 5 a^{3} - 2 a^{2} + 2 a\) , \( -173 a^{5} + 218 a^{4} + 753 a^{3} - 599 a^{2} - 240 a + 129\) , \( 2011 a^{5} - 2591 a^{4} - 8737 a^{3} + 7238 a^{2} + 2781 a - 1572\bigr] \) |
${y}^2+\left(3a^{5}-16a^{3}-7a^{2}+10a+3\right){x}{y}+\left(a^{5}-5a^{3}-2a^{2}+2a\right){y}={x}^{3}+\left(-3a^{5}+16a^{3}+7a^{2}-10a-2\right){x}^{2}+\left(-173a^{5}+218a^{4}+753a^{3}-599a^{2}-240a+129\right){x}+2011a^{5}-2591a^{4}-8737a^{3}+7238a^{2}+2781a-1572$ |
| 47.1-a3 |
47.1-a |
$4$ |
$4$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{3} \) |
$135.08302$ |
$(a^3-a^2-4a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$19041.39429$ |
1.08507 |
\( -\frac{229154682}{103823} a^{5} - \frac{47713549}{103823} a^{4} + \frac{1028570145}{103823} a^{3} + \frac{915587017}{103823} a^{2} + \frac{137213024}{103823} a - \frac{37242017}{103823} \) |
\( \bigl[3 a^{5} - a^{4} - 16 a^{3} - 2 a^{2} + 11 a + 1\) , \( a^{5} - 6 a^{3} - 3 a^{2} + 5 a + 2\) , \( a^{4} - 5 a^{2} - 2 a + 2\) , \( -4 a^{5} + 3 a^{4} + 21 a^{3} - 4 a^{2} - 14 a\) , \( -2 a^{5} - 8 a^{4} + 17 a^{3} + 43 a^{2} - 19 a - 25\bigr] \) |
${y}^2+\left(3a^{5}-a^{4}-16a^{3}-2a^{2}+11a+1\right){x}{y}+\left(a^{4}-5a^{2}-2a+2\right){y}={x}^{3}+\left(a^{5}-6a^{3}-3a^{2}+5a+2\right){x}^{2}+\left(-4a^{5}+3a^{4}+21a^{3}-4a^{2}-14a\right){x}-2a^{5}-8a^{4}+17a^{3}+43a^{2}-19a-25$ |
| 47.1-a4 |
47.1-a |
$4$ |
$4$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
47.1 |
\( 47 \) |
\( - 47^{12} \) |
$135.08302$ |
$(a^3-a^2-4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$37.19022323$ |
1.08507 |
\( -\frac{179797038334127903842266740228}{116191483108948578241} a^{5} + \frac{97344675635827469373143458690}{116191483108948578241} a^{4} + \frac{1032377759624194727882300689688}{116191483108948578241} a^{3} - \frac{187583451101160421787450415171}{116191483108948578241} a^{2} - \frac{985041379735734342349754329175}{116191483108948578241} a + \frac{341253866097337239080542420775}{116191483108948578241} \) |
\( \bigl[a^{5} - 6 a^{3} - 2 a^{2} + 5 a + 1\) , \( 2 a^{5} - a^{4} - 11 a^{3} + a^{2} + 10 a - 2\) , \( a^{5} + a^{4} - 6 a^{3} - 7 a^{2} + 3 a + 4\) , \( -26 a^{5} + 9 a^{4} + 144 a^{3} + 19 a^{2} - 122 a - 42\) , \( -1026 a^{5} - 399 a^{4} + 6045 a^{3} + 4372 a^{2} - 4662 a - 2812\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-2a^{2}+5a+1\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-7a^{2}+3a+4\right){y}={x}^{3}+\left(2a^{5}-a^{4}-11a^{3}+a^{2}+10a-2\right){x}^{2}+\left(-26a^{5}+9a^{4}+144a^{3}+19a^{2}-122a-42\right){x}-1026a^{5}-399a^{4}+6045a^{3}+4372a^{2}-4662a-2812$ |
| 49.1-a1 |
49.1-a |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$135.55294$ |
$(a^5-a^4-5a^3+3a^2+4a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.410444871$ |
$3937.946248$ |
4.42104 |
\( -16235 a^{5} - 49063 a^{4} - 17262 a^{3} + 40280 a^{2} + 21028 a + 719 \) |
\( \bigl[3 a^{5} - 16 a^{3} - 7 a^{2} + 10 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 2\) , \( 0\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 6 a + 3\) , \( 0\bigr] \) |
${y}^2+\left(3a^{5}-16a^{3}-7a^{2}+10a+3\right){x}{y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a-2\right){x}^{2}+\left(a^{5}-6a^{3}-2a^{2}+6a+3\right){x}$ |
| 49.1-a2 |
49.1-a |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{3} \) |
$135.55294$ |
$(a^5-a^4-5a^3+3a^2+4a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.820889743$ |
$1968.973124$ |
4.42104 |
\( 58652360717 a^{5} + 140590710784 a^{4} - 14966063178 a^{3} - 152855248918 a^{2} - 14091878346 a + 24561844979 \) |
\( \bigl[3 a^{5} - 16 a^{3} - 7 a^{2} + 10 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 2\) , \( 0\) , \( -4 a^{5} + 24 a^{3} + 8 a^{2} - 24 a - 12\) , \( -21 a^{5} - a^{4} + 120 a^{3} + 56 a^{2} - 106 a - 55\bigr] \) |
${y}^2+\left(3a^{5}-16a^{3}-7a^{2}+10a+3\right){x}{y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a-2\right){x}^{2}+\left(-4a^{5}+24a^{3}+8a^{2}-24a-12\right){x}-21a^{5}-a^{4}+120a^{3}+56a^{2}-106a-55$ |
| 49.1-b1 |
49.1-b |
$1$ |
$1$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{8} \) |
$135.55294$ |
$(a^5-a^4-5a^3+3a^2+4a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$1939.871435$ |
1.76869 |
\( -15077 a^{5} - 22981 a^{4} + 113959 a^{3} + 118358 a^{2} - 94266 a - 64664 \) |
\( \bigl[a\) , \( -2 a^{5} + 10 a^{3} + 5 a^{2} - 3 a - 3\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 5 a + 1\) , \( a^{5} - 5 a^{4} - 3 a^{3} + 21 a^{2} + 5 a - 3\) , \( -17 a^{5} + 15 a^{4} + 77 a^{3} - 29 a^{2} - 21 a + 6\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-6a^{3}-2a^{2}+5a+1\right){y}={x}^{3}+\left(-2a^{5}+10a^{3}+5a^{2}-3a-3\right){x}^{2}+\left(a^{5}-5a^{4}-3a^{3}+21a^{2}+5a-3\right){x}-17a^{5}+15a^{4}+77a^{3}-29a^{2}-21a+6$ |
| 49.1-c1 |
49.1-c |
$1$ |
$1$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{2} \) |
$135.55294$ |
$(a^5-a^4-5a^3+3a^2+4a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.043406515$ |
$13989.29688$ |
3.32186 |
\( -15077 a^{5} - 22981 a^{4} + 113959 a^{3} + 118358 a^{2} - 94266 a - 64664 \) |
\( \bigl[a^{4} - 5 a^{2} - 2 a + 3\) , \( -2 a^{5} + 11 a^{3} + 4 a^{2} - 7 a\) , \( 2 a^{5} - 11 a^{3} - 5 a^{2} + 8 a + 4\) , \( -12 a^{5} - 3 a^{4} + 69 a^{3} + 41 a^{2} - 50 a - 19\) , \( -16 a^{5} - 5 a^{4} + 93 a^{3} + 61 a^{2} - 69 a - 35\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-2a+3\right){x}{y}+\left(2a^{5}-11a^{3}-5a^{2}+8a+4\right){y}={x}^{3}+\left(-2a^{5}+11a^{3}+4a^{2}-7a\right){x}^{2}+\left(-12a^{5}-3a^{4}+69a^{3}+41a^{2}-50a-19\right){x}-16a^{5}-5a^{4}+93a^{3}+61a^{2}-69a-35$ |
| 49.1-d1 |
49.1-d |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{9} \) |
$135.55294$ |
$(a^5-a^4-5a^3+3a^2+4a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.123746574$ |
$10026.21915$ |
3.39368 |
\( -16235 a^{5} - 49063 a^{4} - 17262 a^{3} + 40280 a^{2} + 21028 a + 719 \) |
\( \bigl[a^{5} - 6 a^{3} - 2 a^{2} + 6 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 5 a + 1\) , \( 2 a^{5} - a^{4} - 11 a^{3} - a^{2} + 8 a + 3\) , \( 2 a^{2} + 5 a + 2\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-2a^{2}+6a+2\right){x}{y}+\left(a^{5}-6a^{3}-2a^{2}+5a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+2a+2\right){x}^{2}+\left(2a^{5}-a^{4}-11a^{3}-a^{2}+8a+3\right){x}+2a^{2}+5a+2$ |
| 49.1-d2 |
49.1-d |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{9} \) |
$135.55294$ |
$(a^5-a^4-5a^3+3a^2+4a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.247493149$ |
$5013.109576$ |
3.39368 |
\( 58652360717 a^{5} + 140590710784 a^{4} - 14966063178 a^{3} - 152855248918 a^{2} - 14091878346 a + 24561844979 \) |
\( \bigl[a^{5} - 6 a^{3} - 2 a^{2} + 6 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 5 a + 1\) , \( 7 a^{5} + 4 a^{4} - 46 a^{3} - 51 a^{2} + 13 a + 8\) , \( -a^{5} + 57 a^{3} + 102 a^{2} - 2 a - 17\bigr] \) |
${y}^2+\left(a^{5}-6a^{3}-2a^{2}+6a+2\right){x}{y}+\left(a^{5}-6a^{3}-2a^{2}+5a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+2a+2\right){x}^{2}+\left(7a^{5}+4a^{4}-46a^{3}-51a^{2}+13a+8\right){x}-a^{5}+57a^{3}+102a^{2}-2a-17$ |
| 59.1-a1 |
59.1-a |
$2$ |
$5$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
59.1 |
\( 59 \) |
\( - 59^{15} \) |
$137.66713$ |
$(-a^5+7a^3+a^2-9a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$2500$ |
\( 1 \) |
$1$ |
$1.061992371$ |
2.42070 |
\( -\frac{925407288142548678467119022213032747485084148}{365409786560616989860302899} a^{5} - \frac{818677915886865767293977448190681193732449907}{365409786560616989860302899} a^{4} + \frac{4828185838787453339089957196919479220016209416}{365409786560616989860302899} a^{3} + \frac{6122154526448547457142220948047009220182792847}{365409786560616989860302899} a^{2} - \frac{136371505644163515712935614990330697640845872}{365409786560616989860302899} a - \frac{1046050751248991924827249304037232696742761327}{365409786560616989860302899} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 4 a - 1\) , \( 3 a^{5} - 16 a^{3} - 7 a^{2} + 9 a + 2\) , \( a^{5} + a^{4} - 6 a^{3} - 7 a^{2} + 3 a + 3\) , \( -442 a^{5} + 28 a^{4} + 464 a^{3} - 254 a^{2} + 119 a - 65\) , \( -24434 a^{5} - 13656 a^{4} + 32194 a^{3} + 6414 a^{2} - 6934 a + 309\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+4a-1\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-7a^{2}+3a+3\right){y}={x}^{3}+\left(3a^{5}-16a^{3}-7a^{2}+9a+2\right){x}^{2}+\left(-442a^{5}+28a^{4}+464a^{3}-254a^{2}+119a-65\right){x}-24434a^{5}-13656a^{4}+32194a^{3}+6414a^{2}-6934a+309$ |
| 59.1-a2 |
59.1-a |
$2$ |
$5$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
59.1 |
\( 59 \) |
\( - 59^{3} \) |
$137.66713$ |
$(-a^5+7a^3+a^2-9a-1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$16593.63079$ |
2.42070 |
\( -\frac{423667917050043863480}{205379} a^{5} + \frac{224328976446122374268}{205379} a^{4} + \frac{2423227005555206521140}{205379} a^{3} - \frac{435744667243090033449}{205379} a^{2} - \frac{2311283990296103639894}{205379} a + \frac{800139610350127076946}{205379} \) |
\( \bigl[a\) , \( a^{4} - 5 a^{2} - a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 4 a - 1\) , \( 24 a^{5} - 20 a^{4} - 108 a^{3} + 33 a^{2} + 28 a - 9\) , \( -20 a^{5} + 39 a^{4} + 79 a^{3} - 129 a^{2} - 33 a + 26\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+4a-1\right){y}={x}^{3}+\left(a^{4}-5a^{2}-a+1\right){x}^{2}+\left(24a^{5}-20a^{4}-108a^{3}+33a^{2}+28a-9\right){x}-20a^{5}+39a^{4}+79a^{3}-129a^{2}-33a+26$ |
| 59.1-b1 |
59.1-b |
$1$ |
$1$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
59.1 |
\( 59 \) |
\( -59 \) |
$137.66713$ |
$(-a^5+7a^3+a^2-9a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1238.043155$ |
1.12879 |
\( \frac{12328094877615}{59} a^{5} - \frac{22706546070578}{59} a^{4} - \frac{32146429710909}{59} a^{3} + \frac{34552818333256}{59} a^{2} + \frac{10327320671213}{59} a - \frac{6693306180611}{59} \) |
\( \bigl[a\) , \( -2 a^{5} + a^{4} + 11 a^{3} - a^{2} - 9 a\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 6 a + 2\) , \( 3 a^{5} - 15 a^{3} - 8 a^{2} + 5 a + 2\) , \( -13 a^{5} - 13 a^{4} + 68 a^{3} + 94 a^{2} + a - 21\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-6a^{3}-2a^{2}+6a+2\right){y}={x}^{3}+\left(-2a^{5}+a^{4}+11a^{3}-a^{2}-9a\right){x}^{2}+\left(3a^{5}-15a^{3}-8a^{2}+5a+2\right){x}-13a^{5}-13a^{4}+68a^{3}+94a^{2}+a-21$ |
| 59.1-c1 |
59.1-c |
$1$ |
$1$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
59.1 |
\( 59 \) |
\( -59 \) |
$137.66713$ |
$(-a^5+7a^3+a^2-9a-1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.000959870$ |
$134075.0973$ |
4.22418 |
\( -\frac{985145}{59} a^{5} + \frac{1245966}{59} a^{4} + \frac{4322482}{59} a^{3} - \frac{3446676}{59} a^{2} - \frac{1425253}{59} a + \frac{838216}{59} \) |
\( \bigl[a + 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 7 a + 1\) , \( a\) , \( -a^{5} + 3 a^{4} + 5 a^{3} - 12 a^{2} - 6 a + 4\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 12 a^{2} + a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-7a+1\right){x}^{2}+\left(-a^{5}+3a^{4}+5a^{3}-12a^{2}-6a+4\right){x}+a^{5}-3a^{4}-3a^{3}+12a^{2}+a-2$ |
| 61.1-a1 |
61.1-a |
$1$ |
$1$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
61.1 |
\( 61 \) |
\( -61 \) |
$138.05011$ |
$(2a^5-11a^3-5a^2+7a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.088678770$ |
$7231.423800$ |
3.50812 |
\( \frac{37892}{61} a^{5} + \frac{19314}{61} a^{4} - \frac{251227}{61} a^{3} - \frac{126919}{61} a^{2} + \frac{209067}{61} a + \frac{44233}{61} \) |
\( \bigl[2 a^{5} - 11 a^{3} - 4 a^{2} + 7 a + 2\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 9 a^{2} + 8 a - 4\) , \( 2 a^{5} - a^{4} - 10 a^{3} + 7 a\) , \( -a^{5} - 2 a^{4} + 5 a^{3} + 13 a^{2} - 2 a + 1\) , \( 4 a^{5} - 5 a^{4} - 20 a^{3} + 15 a^{2} + 15 a - 3\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-4a^{2}+7a+2\right){x}{y}+\left(2a^{5}-a^{4}-10a^{3}+7a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-6a^{3}+9a^{2}+8a-4\right){x}^{2}+\left(-a^{5}-2a^{4}+5a^{3}+13a^{2}-2a+1\right){x}+4a^{5}-5a^{4}-20a^{3}+15a^{2}+15a-3$ |
| 73.1-a1 |
73.1-a |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
73.1 |
\( 73 \) |
\( 73 \) |
$140.13163$ |
$(2a^5-a^4-11a^3+2a^2+8a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$10060.87430$ |
2.29327 |
\( -\frac{1939698596560}{73} a^{5} - \frac{733988208371}{73} a^{4} + \frac{13343215424150}{73} a^{3} + \frac{15436315173189}{73} a^{2} - \frac{539312160784}{73} a - \frac{2655561761244}{73} \) |
\( \bigl[a^{5} - 5 a^{3} - 3 a^{2} + 2 a + 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 4 a + 2\) , \( a^{5} + a^{4} - 6 a^{3} - 7 a^{2} + 4 a + 4\) , \( -a^{5} + 3 a^{4} + 4 a^{3} - 11 a^{2} - 4 a + 7\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} - 5 a + 3\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-3a^{2}+2a+3\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-7a^{2}+4a+4\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-4a+2\right){x}^{2}+\left(-a^{5}+3a^{4}+4a^{3}-11a^{2}-4a+7\right){x}+a^{5}-2a^{4}-3a^{3}+5a^{2}-5a+3$ |
| 73.1-a2 |
73.1-a |
$2$ |
$2$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
73.1 |
\( 73 \) |
\( - 73^{2} \) |
$140.13163$ |
$(2a^5-a^4-11a^3+2a^2+8a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5030.437153$ |
2.29327 |
\( \frac{58913469545655284086039582}{5329} a^{5} + \frac{141245851847712373776581738}{5329} a^{4} - \frac{14841948810663561884636012}{5329} a^{3} - \frac{153410715076829944127936139}{5329} a^{2} - \frac{14323477748980300686468291}{5329} a + \frac{24572735046753627901621406}{5329} \) |
\( \bigl[a^{5} - 5 a^{3} - 3 a^{2} + 2 a + 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 4 a + 2\) , \( a^{5} + a^{4} - 6 a^{3} - 7 a^{2} + 4 a + 4\) , \( -26 a^{5} + 18 a^{4} + 124 a^{3} - 16 a^{2} - 49 a - 28\) , \( 90 a^{5} - 135 a^{4} - 372 a^{3} + 411 a^{2} + 82 a - 103\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}-3a^{2}+2a+3\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-7a^{2}+4a+4\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-4a+2\right){x}^{2}+\left(-26a^{5}+18a^{4}+124a^{3}-16a^{2}-49a-28\right){x}+90a^{5}-135a^{4}-372a^{3}+411a^{2}+82a-103$ |
| 79.1-a1 |
79.1-a |
$1$ |
$1$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( 79 \) |
$141.05707$ |
$(-2a^5+11a^3+4a^2-6a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$2447.408659$ |
2.23144 |
\( -\frac{2248311}{79} a^{5} + \frac{344041}{79} a^{4} + \frac{12225319}{79} a^{3} + \frac{3867560}{79} a^{2} - \frac{8350654}{79} a - \frac{3874311}{79} \) |
\( \bigl[2 a^{5} - 11 a^{3} - 4 a^{2} + 7 a + 2\) , \( -a^{5} + 2 a^{4} + 6 a^{3} - 9 a^{2} - 9 a + 5\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 4 a - 2\) , \( -4 a^{5} + 2 a^{4} + 22 a^{3} - 4 a^{2} - 16 a + 10\) , \( -2 a^{5} + 2 a^{4} + 12 a^{3} - 8 a^{2} - 14 a + 7\bigr] \) |
${y}^2+\left(2a^{5}-11a^{3}-4a^{2}+7a+2\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+4a-2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+6a^{3}-9a^{2}-9a+5\right){x}^{2}+\left(-4a^{5}+2a^{4}+22a^{3}-4a^{2}-16a+10\right){x}-2a^{5}+2a^{4}+12a^{3}-8a^{2}-14a+7$ |
| 79.1-b1 |
79.1-b |
$4$ |
$4$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$141.05707$ |
$(-2a^5+11a^3+4a^2-6a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$9274.112539$ |
0.528484 |
\( -\frac{42493493458943}{79} a^{5} - \frac{37592500430321}{79} a^{4} + \frac{221704158630257}{79} a^{3} + \frac{281120792800266}{79} a^{2} - \frac{6263132963312}{79} a - \frac{48033797897110}{79} \) |
\( \bigl[a + 1\) , \( a^{5} + 2 a^{4} - 6 a^{3} - 13 a^{2} + 2 a + 7\) , \( a^{5} - 5 a^{3} - 3 a^{2} + 2 a + 3\) , \( 4 a^{5} - 12 a^{4} - 23 a^{3} + 56 a^{2} + 33 a - 50\) , \( -77 a^{5} - 6 a^{4} + 449 a^{3} + 196 a^{2} - 365 a - 95\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}-5a^{3}-3a^{2}+2a+3\right){y}={x}^{3}+\left(a^{5}+2a^{4}-6a^{3}-13a^{2}+2a+7\right){x}^{2}+\left(4a^{5}-12a^{4}-23a^{3}+56a^{2}+33a-50\right){x}-77a^{5}-6a^{4}+449a^{3}+196a^{2}-365a-95$ |
| 79.1-b2 |
79.1-b |
$4$ |
$4$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( 79^{2} \) |
$141.05707$ |
$(-2a^5+11a^3+4a^2-6a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$1159.264067$ |
0.528484 |
\( \frac{3696701976527687}{79} a^{5} + \frac{1411203466392681}{79} a^{4} - \frac{21662343237280084}{79} a^{3} - \frac{15658239757079252}{79} a^{2} + \frac{16320248792066697}{79} a + \frac{9947604397412480}{79} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a - 1\) , \( -a^{2} - a + 2\) , \( a^{5} + a^{4} - 6 a^{3} - 7 a^{2} + 4 a + 3\) , \( 116 a^{5} + 13 a^{4} - 634 a^{3} - 283 a^{2} + 334 a - 78\) , \( -749 a^{5} - 190 a^{4} + 4082 a^{3} + 2404 a^{2} - 1925 a + 114\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a-1\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-7a^{2}+4a+3\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(116a^{5}+13a^{4}-634a^{3}-283a^{2}+334a-78\right){x}-749a^{5}-190a^{4}+4082a^{3}+2404a^{2}-1925a+114$ |
| 79.1-b3 |
79.1-b |
$4$ |
$4$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$141.05707$ |
$(-2a^5+11a^3+4a^2-6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$144.9080084$ |
0.528484 |
\( -\frac{26951863235275985299090423}{79} a^{5} + \frac{14287136160179458673302170}{79} a^{4} + \frac{154116176470654981294076067}{79} a^{3} - \frac{27742206053302057320259358}{79} a^{2} - \frac{146976129229509794251793322}{79} a + \frac{50884571595768286934026297}{79} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a - 1\) , \( -a^{2} - a + 2\) , \( a^{5} + a^{4} - 6 a^{3} - 7 a^{2} + 4 a + 3\) , \( 1121 a^{5} - 502 a^{4} - 6379 a^{3} + 662 a^{2} + 5774 a - 1948\) , \( -24813 a^{5} + 12783 a^{4} + 141816 a^{3} - 23621 a^{2} - 134134 a + 46081\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a-1\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-7a^{2}+4a+3\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(1121a^{5}-502a^{4}-6379a^{3}+662a^{2}+5774a-1948\right){x}-24813a^{5}+12783a^{4}+141816a^{3}-23621a^{2}-134134a+46081$ |
| 79.1-b4 |
79.1-b |
$4$ |
$4$ |
6.6.1202933.1 |
$6$ |
$[6, 0]$ |
79.1 |
\( 79 \) |
\( 79^{4} \) |
$141.05707$ |
$(-2a^5+11a^3+4a^2-6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$18.11350105$ |
0.528484 |
\( \frac{47536589105638094205645029777721}{6241} a^{5} + \frac{17862072931637200441983533525626}{6241} a^{4} - \frac{278507785738548973123999486534221}{6241} a^{3} - \frac{199723647975433489571480345720254}{6241} a^{2} + \frac{210172535397471797846841721450870}{6241} a + \frac{126509801658902332225961666267705}{6241} \) |
\( \bigl[2 a^{5} - a^{4} - 10 a^{3} + 7 a\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 8 a^{2} + 6 a - 5\) , \( 2 a^{5} - 10 a^{3} - 5 a^{2} + 5 a + 2\) , \( -9 a^{5} + 259 a^{4} - 14 a^{3} - 1223 a^{2} - 324 a + 145\) , \( -4638 a^{5} - 1054 a^{4} + 23193 a^{3} + 16199 a^{2} - 3190 a - 2881\bigr] \) |
${y}^2+\left(2a^{5}-a^{4}-10a^{3}+7a\right){x}{y}+\left(2a^{5}-10a^{3}-5a^{2}+5a+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+8a^{2}+6a-5\right){x}^{2}+\left(-9a^{5}+259a^{4}-14a^{3}-1223a^{2}-324a+145\right){x}-4638a^{5}-1054a^{4}+23193a^{3}+16199a^{2}-3190a-2881$ |
*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.
