Elliptic curves in class 704.3-q over 4.4.2777.1
Isogeny class 704.3-q contains
12 curves linked by isogenies of
degrees dividing 24.
| Curve label |
Weierstrass Coefficients |
| 704.3-q1
| \( \bigl[a^{2} - a - 2\) , \( a^{3} - 5 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 678 a^{3} - 1671 a^{2} - 249 a + 958\) , \( -157478 a^{3} + 395491 a^{2} + 32545 a - 207862\bigr] \)
|
| 704.3-q2
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + a - 2\) , \( a\) , \( -108 a^{3} - 94 a^{2} + 1028 a - 848\) , \( 1989 a^{3} + 506 a^{2} - 19238 a + 13851\bigr] \)
|
| 704.3-q3
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + a - 2\) , \( a\) , \( -8 a^{3} + 16 a^{2} + 18 a - 28\) , \( 3 a^{3} - 2 a^{2} - 12 a - 1\bigr] \)
|
| 704.3-q4
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + a - 2\) , \( a\) , \( 57 a^{3} - 64 a^{2} - 187 a + 42\) , \( 75 a^{3} + 34 a^{2} - 355 a - 343\bigr] \)
|
| 704.3-q5
| \( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a\) , \( -240 a^{3} + 57 a^{2} + 978 a + 521\) , \( 812 a^{3} - 197 a^{2} - 3322 a - 1776\bigr] \)
|
| 704.3-q6
| \( \bigl[a^{3} - 4 a\) , \( -a^{3} + 3 a\) , \( a^{2} - a - 2\) , \( 398 a^{3} - 48 a^{2} - 1694 a - 1084\) , \( -7179 a^{3} + 1133 a^{2} + 29808 a + 17744\bigr] \)
|
| 704.3-q7
| \( \bigl[a^{3} - 4 a\) , \( -a^{3} + 3 a\) , \( a^{2} - a - 2\) , \( 88 a^{3} + 127 a^{2} - 399 a - 594\) , \( -18184 a^{3} + 3633 a^{2} + 74417 a + 41570\bigr] \)
|
| 704.3-q8
| \( \bigl[a^{3} - 4 a\) , \( -a^{3} + 3 a\) , \( a^{2} - a - 2\) , \( -92 a^{3} + 122 a^{2} + 281 a - 174\) , \( 175 a^{3} + 692 a^{2} - 1295 a - 2930\bigr] \)
|
| 704.3-q9
| \( \bigl[a^{3} - 4 a\) , \( -a^{3} + 3 a\) , \( a^{2} - a - 2\) , \( 28 a^{3} - 3 a^{2} - 129 a - 94\) , \( 224 a^{3} - 15 a^{2} - 907 a - 566\bigr] \)
|
| 704.3-q10
| \( \bigl[a^{3} - 3 a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 4 a\) , \( -142 a^{3} - 219 a^{2} + 49 a + 74\) , \( -3940 a^{3} - 5396 a^{2} + 3018 a + 3316\bigr] \)
|
| 704.3-q11
| \( \bigl[a\) , \( a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( 27 a^{3} + a^{2} - 122 a - 77\) , \( -103 a^{3} - 32 a^{2} + 512 a + 327\bigr] \)
|
| 704.3-q12
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{2} - 3\) , \( a^{2} - 2\) , \( 3 a^{2} + 2 a - 2\) , \( 3 a^{3} + a^{2} - 5 a + 1\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 8 & 12 & 24 & 8 & 2 & 4 & 12 & 6 & 4 & 3 & 24 \\
8 & 1 & 6 & 3 & 4 & 4 & 8 & 24 & 12 & 2 & 24 & 12 \\
12 & 6 & 1 & 2 & 6 & 6 & 12 & 4 & 2 & 3 & 4 & 2 \\
24 & 3 & 2 & 1 & 12 & 12 & 24 & 8 & 4 & 6 & 8 & 4 \\
8 & 4 & 6 & 12 & 1 & 4 & 8 & 24 & 12 & 2 & 24 & 3 \\
2 & 4 & 6 & 12 & 4 & 1 & 2 & 6 & 3 & 2 & 6 & 12 \\
4 & 8 & 12 & 24 & 8 & 2 & 1 & 3 & 6 & 4 & 12 & 24 \\
12 & 24 & 4 & 8 & 24 & 6 & 3 & 1 & 2 & 12 & 4 & 8 \\
6 & 12 & 2 & 4 & 12 & 3 & 6 & 2 & 1 & 6 & 2 & 4 \\
4 & 2 & 3 & 6 & 2 & 2 & 4 & 12 & 6 & 1 & 12 & 6 \\
3 & 24 & 4 & 8 & 24 & 6 & 12 & 4 & 2 & 12 & 1 & 8 \\
24 & 12 & 2 & 4 & 3 & 12 & 24 & 8 & 4 & 6 & 8 & 1
\end{array}\right)\)
