Elliptic curves in class 12.2-e over 4.4.17428.1
Isogeny class 12.2-e contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 12.2-e1
| \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 4 a - 1\) , \( a^{2} + a - 2\) , \( -3 a^{3} - a^{2} + 11 a - 1\) , \( -29 a^{3} - 42 a^{2} + 78 a + 81\bigr] \)
|
| 12.2-e2
| \( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -16 a^{3} - 7 a^{2} + 82 a + 57\) , \( -208 a^{3} - 109 a^{2} + 1081 a + 816\bigr] \)
|
| 12.2-e3
| \( \bigl[a^{2} + a - 3\) , \( -a^{2} + 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -4644 a^{3} - 6361 a^{2} + 12806 a + 11781\) , \( 332210 a^{3} + 454675 a^{2} - 916288 a - 841506\bigr] \)
|
| 12.2-e4
| \( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 2\) , \( a^{3} - 4 a - 1\) , \( -47 a^{3} - 65 a^{2} + 128 a + 124\) , \( -273 a^{3} - 375 a^{2} + 752 a + 692\bigr] \)
|
| 12.2-e5
| \( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 2\) , \( a^{3} - 4 a - 1\) , \( -382 a^{3} - 525 a^{2} + 1053 a + 974\) , \( 9176 a^{3} + 12558 a^{2} - 25310 a - 23244\bigr] \)
|
| 12.2-e6
| \( \bigl[a^{3} - 3 a - 1\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( 6 a^{3} - 27 a^{2} + 11 a + 28\) , \( -33 a^{3} + 99 a^{2} - 11 a - 96\bigr] \)
|
| 12.2-e7
| \( \bigl[a^{3} - 3 a - 1\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( -14 a^{3} - 47 a^{2} + 81 a + 38\) , \( 71 a^{3} + 111 a^{2} - 243 a - 140\bigr] \)
|
| 12.2-e8
| \( \bigl[1\) , \( a^{3} + a^{2} - 5 a - 5\) , \( 0\) , \( -28 a^{3} + 46 a^{2} + 130 a - 192\) , \( 144 a^{3} - 254 a^{2} - 662 a + 1080\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 12 & 3 & 2 & 4 & 6 & 12 & 4 \\
12 & 1 & 4 & 6 & 12 & 2 & 4 & 3 \\
3 & 4 & 1 & 6 & 12 & 2 & 4 & 12 \\
2 & 6 & 6 & 1 & 2 & 3 & 6 & 2 \\
4 & 12 & 12 & 2 & 1 & 6 & 3 & 4 \\
6 & 2 & 2 & 3 & 6 & 1 & 2 & 6 \\
12 & 4 & 4 & 6 & 3 & 2 & 1 & 12 \\
4 & 3 & 12 & 2 & 4 & 6 & 12 & 1
\end{array}\right)\)
