Isogeny class 81.1-d contains
16 curves linked by isogenies of
degrees dividing 60.
| Curve label |
Weierstrass Coefficients |
| 81.1-d1
| \( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( 0\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{9}{7}\) , \( -\frac{24}{7} a^{3} + \frac{36}{7} a^{2} + \frac{144}{7} a - \frac{225}{7}\) , \( \frac{40}{7} a^{3} - \frac{60}{7} a^{2} - \frac{240}{7} a + \frac{228}{7}\bigr] \)
|
| 81.1-d2
| \( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{17}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{3}{7}\) , \( -\frac{24}{7} a^{3} + \frac{36}{7} a^{2} + \frac{144}{7} a - \frac{218}{7}\) , \( -\frac{38}{7} a^{3} + \frac{57}{7} a^{2} + \frac{228}{7} a - \frac{232}{7}\bigr] \)
|
| 81.1-d3
| \( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( 0\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( -\frac{471}{7} a^{3} + \frac{969}{7} a^{2} + \frac{3246}{7} a - \frac{4350}{7}\) , \( -\frac{5050}{7} a^{3} + \frac{10746}{7} a^{2} + \frac{33639}{7} a - \frac{44241}{7}\bigr] \)
|
| 81.1-d4
| \( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( 0\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( -\frac{81}{7} a^{3} - \frac{141}{7} a^{2} + \frac{66}{7} a - \frac{300}{7}\) , \( -190 a^{3} - 168 a^{2} + 663 a - 39\bigr] \)
|
| 81.1-d5
| \( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( 0\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( -\frac{6}{7} a^{3} + \frac{9}{7} a^{2} + \frac{36}{7} a - \frac{30}{7}\) , \( -\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{24}{7} a - \frac{27}{7}\bigr] \)
|
| 81.1-d6
| \( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( 0\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{9}{7}\) , \( \frac{465}{7} a^{3} - \frac{435}{7} a^{2} - \frac{3735}{7} a - \frac{615}{7}\) , \( \frac{5050}{7} a^{3} - \frac{4404}{7} a^{2} - \frac{39981}{7} a - \frac{4906}{7}\bigr] \)
|
| 81.1-d7
| \( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( 0\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{9}{7}\) , \( \frac{75}{7} a^{3} - \frac{375}{7} a^{2} + \frac{495}{7} a - \frac{465}{7}\) , \( 190 a^{3} - 738 a^{2} + 243 a + 266\bigr] \)
|
| 81.1-d8
| \( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( 0\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{9}{7}\) , \( 0\) , \( \frac{4}{7} a^{3} - \frac{6}{7} a^{2} - \frac{24}{7} a - \frac{1}{7}\bigr] \)
|
| 81.1-d9
| \( \bigl[\frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{9}{7}\) , \( 0\) , \( -\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( \frac{24}{7} a^{3} - \frac{36}{7} a^{2} - \frac{144}{7} a - \frac{69}{7}\) , \( -\frac{40}{7} a^{3} + \frac{60}{7} a^{2} + \frac{240}{7} a - \frac{32}{7}\bigr] \)
|
| 81.1-d10
| \( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{3}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{17}{7}\) , \( 1\) , \( 4 a^{3} - 6 a^{2} - 24 a - 6\) , \( \frac{64}{7} a^{3} - \frac{96}{7} a^{2} - \frac{384}{7} a - \frac{37}{7}\bigr] \)
|
| 81.1-d11
| \( \bigl[1\) , \( -1\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -\frac{467}{7} a^{3} + \frac{963}{7} a^{2} + \frac{3222}{7} a - \frac{4330}{7}\) , \( \frac{5048}{7} a^{3} - \frac{10743}{7} a^{2} - \frac{33627}{7} a + \frac{44224}{7}\bigr] \)
|
| 81.1-d12
| \( \bigl[1\) , \( -1\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -11 a^{3} - 21 a^{2} + 6 a - 40\) , \( \frac{1328}{7} a^{3} + \frac{1179}{7} a^{2} - \frac{4629}{7} a + \frac{256}{7}\bigr] \)
|
| 81.1-d13
| \( \bigl[1\) , \( -1\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\bigr] \)
|
| 81.1-d14
| \( \bigl[1\) , \( -1\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{3}{7}\) , \( 67 a^{3} - 63 a^{2} - 537 a - 87\) , \( -\frac{5048}{7} a^{3} + \frac{4401}{7} a^{2} + \frac{39969}{7} a + \frac{4902}{7}\bigr] \)
|
| 81.1-d15
| \( \bigl[1\) , \( -1\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{3}{7}\) , \( \frac{79}{7} a^{3} - \frac{381}{7} a^{2} + \frac{471}{7} a - \frac{459}{7}\) , \( -\frac{1328}{7} a^{3} + \frac{5163}{7} a^{2} - \frac{1713}{7} a - \frac{1866}{7}\bigr] \)
|
| 81.1-d16
| \( \bigl[1\) , \( -1\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{3}{7}\) , \( \frac{4}{7} a^{3} - \frac{6}{7} a^{2} - \frac{24}{7} a + \frac{6}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{3}{7}\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrrrrrr}
1 & 15 & 10 & 10 & 10 & 2 & 2 & 2 & 5 & 3 & 6 & 6 & 6 & 30 & 30 & 30 \\
15 & 1 & 6 & 6 & 6 & 30 & 30 & 30 & 3 & 5 & 10 & 10 & 10 & 2 & 2 & 2 \\
10 & 6 & 1 & 4 & 4 & 5 & 20 & 20 & 2 & 30 & 60 & 15 & 60 & 12 & 3 & 12 \\
10 & 6 & 4 & 1 & 4 & 20 & 5 & 20 & 2 & 30 & 15 & 60 & 60 & 3 & 12 & 12 \\
10 & 6 & 4 & 4 & 1 & 20 & 20 & 5 & 2 & 30 & 60 & 60 & 15 & 12 & 12 & 3 \\
2 & 30 & 5 & 20 & 20 & 1 & 4 & 4 & 10 & 6 & 12 & 3 & 12 & 60 & 15 & 60 \\
2 & 30 & 20 & 5 & 20 & 4 & 1 & 4 & 10 & 6 & 3 & 12 & 12 & 15 & 60 & 60 \\
2 & 30 & 20 & 20 & 5 & 4 & 4 & 1 & 10 & 6 & 12 & 12 & 3 & 60 & 60 & 15 \\
5 & 3 & 2 & 2 & 2 & 10 & 10 & 10 & 1 & 15 & 30 & 30 & 30 & 6 & 6 & 6 \\
3 & 5 & 30 & 30 & 30 & 6 & 6 & 6 & 15 & 1 & 2 & 2 & 2 & 10 & 10 & 10 \\
6 & 10 & 60 & 15 & 60 & 12 & 3 & 12 & 30 & 2 & 1 & 4 & 4 & 5 & 20 & 20 \\
6 & 10 & 15 & 60 & 60 & 3 & 12 & 12 & 30 & 2 & 4 & 1 & 4 & 20 & 5 & 20 \\
6 & 10 & 60 & 60 & 15 & 12 & 12 & 3 & 30 & 2 & 4 & 4 & 1 & 20 & 20 & 5 \\
30 & 2 & 12 & 3 & 12 & 60 & 15 & 60 & 6 & 10 & 5 & 20 & 20 & 1 & 4 & 4 \\
30 & 2 & 3 & 12 & 12 & 15 & 60 & 60 & 6 & 10 & 20 & 5 & 20 & 4 & 1 & 4 \\
30 & 2 & 12 & 12 & 3 & 60 & 60 & 15 & 6 & 10 & 20 & 20 & 5 & 4 & 4 & 1
\end{array}\right)\)
