Elliptic curves in class 27.1-c over 4.4.8112.1
Isogeny class 27.1-c contains
12 curves linked by isogenies of
degrees dividing 24.
| Curve label |
Weierstrass Coefficients |
| 27.1-c1
| \( \bigl[a^{3} - 4 a\) , \( a^{2} - 2\) , \( a^{3} - 4 a\) , \( 89 a^{2} - 389\) , \( 626 a^{2} - 2691\bigr] \)
|
| 27.1-c2
| \( \bigl[a^{3} - 4 a\) , \( a^{2} - 2\) , \( a^{3} - 4 a\) , \( 14 a^{2} - 59\) , \( -16 a^{2} + 69\bigr] \)
|
| 27.1-c3
| \( \bigl[a^{3} - 4 a\) , \( a^{2} - 2\) , \( 0\) , \( -12 a^{2} + 8\) , \( -29 a^{2} + 20\bigr] \)
|
| 27.1-c4
| \( \bigl[a^{3} - 4 a\) , \( a^{2} - 2\) , \( 0\) , \( -87 a^{2} + 53\) , \( 538 a^{2} - 385\bigr] \)
|
| 27.1-c5
| \( \bigl[a^{3} - 3 a\) , \( a^{2} - 2\) , \( a^{3} - 4 a\) , \( 103 a^{2} - 443\) , \( -740 a^{2} + 3174\bigr] \)
|
| 27.1-c6
| \( \bigl[a^{3} - 3 a\) , \( a^{2} - 2\) , \( a^{3} - 4 a\) , \( 18 a^{2} - 78\) , \( 34 a^{2} - 156\bigr] \)
|
| 27.1-c7
| \( \bigl[a^{3} - 3 a\) , \( a^{2} - 2\) , \( a^{3} - 4 a\) , \( 3 a^{2} - 8\) , \( 2 a^{2} - 6\bigr] \)
|
| 27.1-c8
| \( \bigl[a^{3} - 3 a\) , \( a^{2} - 2\) , \( a^{3} - 4 a\) , \( -67 a^{2} + 207\) , \( 140 a^{2} - 1026\bigr] \)
|
| 27.1-c9
| \( \bigl[a\) , \( a^{2} - 2\) , \( a^{3} - 3 a\) , \( 69 a^{2} - 133\) , \( 208 a^{2} + 194\bigr] \)
|
| 27.1-c10
| \( \bigl[a\) , \( a^{2} - 2\) , \( a^{3} - 3 a\) , \( -a^{2} + 2\) , \( -1\bigr] \)
|
| 27.1-c11
| \( \bigl[a\) , \( a^{2} - 2\) , \( a^{3} - 3 a\) , \( -16 a^{2} + 7\) , \( 17 a^{2} - 6\bigr] \)
|
| 27.1-c12
| \( \bigl[a\) , \( a^{2} - 2\) , \( a^{3} - 3 a\) , \( -101 a^{2} + 67\) , \( -842 a^{2} + 594\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 2 & 6 & 3 & 24 & 12 & 12 & 24 & 8 & 4 & 4 & 8 \\
2 & 1 & 3 & 6 & 12 & 6 & 6 & 12 & 4 & 2 & 2 & 4 \\
6 & 3 & 1 & 2 & 4 & 2 & 2 & 4 & 12 & 6 & 6 & 12 \\
3 & 6 & 2 & 1 & 8 & 4 & 4 & 8 & 24 & 12 & 12 & 24 \\
24 & 12 & 4 & 8 & 1 & 2 & 8 & 4 & 3 & 24 & 6 & 12 \\
12 & 6 & 2 & 4 & 2 & 1 & 4 & 2 & 6 & 12 & 3 & 6 \\
12 & 6 & 2 & 4 & 8 & 4 & 1 & 8 & 24 & 3 & 12 & 24 \\
24 & 12 & 4 & 8 & 4 & 2 & 8 & 1 & 12 & 24 & 6 & 3 \\
8 & 4 & 12 & 24 & 3 & 6 & 24 & 12 & 1 & 8 & 2 & 4 \\
4 & 2 & 6 & 12 & 24 & 12 & 3 & 24 & 8 & 1 & 4 & 8 \\
4 & 2 & 6 & 12 & 6 & 3 & 12 & 6 & 2 & 4 & 1 & 2 \\
8 & 4 & 12 & 24 & 12 & 6 & 24 & 3 & 4 & 8 & 2 & 1
\end{array}\right)\)
