Isogeny class 79.2-c contains
4 curves linked by isogenies of
degrees dividing 10.
| Curve label |
Weierstrass Coefficients |
| 79.2-c1
| \( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{4} + a^{3} - 5 a^{2} - 2 a + 4\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{5} + 5 a^{4} - 2 a^{3} - 14 a^{2} + 6\) , \( 3 a^{5} + 4 a^{4} - 8 a^{3} - 10 a^{2} + 3 a + 3\bigr] \)
|
| 79.2-c2
| \( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{4} + a^{3} - 5 a^{2} - 2 a + 4\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( 6 a^{5} + 15 a^{4} - 27 a^{3} - 54 a^{2} + 20 a + 16\) , \( -24 a^{5} - 17 a^{4} + 112 a^{3} + 78 a^{2} - 80 a - 16\bigr] \)
|
| 79.2-c3
| \( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{4} + a^{3} - 5 a^{2} - 2 a + 4\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( 66 a^{5} - 60 a^{4} - 292 a^{3} + 256 a^{2} + 250 a - 254\) , \( 536 a^{5} - 544 a^{4} - 2472 a^{3} + 2270 a^{2} + 2330 a - 2043\bigr] \)
|
| 79.2-c4
| \( \bigl[a^{5} - 5 a^{3} + a^{2} + 6 a - 1\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 7 a + 4\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 3\) , \( -374 a^{5} - 33 a^{4} + 1737 a^{3} + 125 a^{2} - 1818 a - 430\) , \( -5000 a^{5} - 11 a^{4} + 24043 a^{3} + 1223 a^{2} - 26468 a - 6156\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 5 & 10 \\
2 & 1 & 10 & 5 \\
5 & 10 & 1 & 2 \\
10 & 5 & 2 & 1
\end{array}\right)\)
