Elliptic curves in class 20.1-a over 3.3.148.1
Isogeny class 20.1-a contains
12 curves linked by isogenies of
degrees dividing 24.
| Curve label |
Weierstrass Coefficients |
| 20.1-a1
| \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( 1292 a^{2} + 1512 a - 596\) , \( 38980968 a^{2} + 45611104 a - 17962864\bigr] \)
|
| 20.1-a2
| \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( -11628 a^{2} - 13608 a + 5354\) , \( -1052486900 a^{2} - 1231500702 a + 484997670\bigr] \)
|
| 20.1-a3
| \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( -56443 a^{2} - 66043 a + 26009\) , \( 13218157 a^{2} + 15466387 a - 6091074\bigr] \)
|
| 20.1-a4
| \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( -516708 a^{2} - 604593 a + 238104\) , \( -366738953 a^{2} - 429116293 a + 168997390\bigr] \)
|
| 20.1-a5
| \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( -898838 a^{2} - 1051718 a + 414194\) , \( 854513176 a^{2} + 999854320 a - 393769180\bigr] \)
|
| 20.1-a6
| \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( -1057168 a^{2} - 1236978 a + 487154\) , \( 532872492 a^{2} + 623506902 a - 245553574\bigr] \)
|
| 20.1-a7
| \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a + 1\) , \( -101641 a^{2} - 118928 a + 46839\) , \( -32483626 a^{2} - 38008652 a + 14968816\bigr] \)
|
| 20.1-a8
| \( \bigl[a^{2} - a - 2\) , \( 0\) , \( a + 1\) , \( -8231946 a^{2} - 9632088 a + 3793374\) , \( -23684559407 a^{2} - 27712982904 a + 10914108517\bigr] \)
|
| 20.1-a9
| \( \bigl[a^{2} - 1\) , \( a^{2} - 3\) , \( 0\) , \( -625 a^{2} - 730 a + 290\) , \( -9146 a^{2} - 10702 a + 4214\bigr] \)
|
| 20.1-a10
| \( \bigl[a^{2} - 1\) , \( a^{2} - 3\) , \( 0\) , \( -43485 a^{2} - 50880 a + 20040\) , \( -9168052 a^{2} - 10727414 a + 4224740\bigr] \)
|
| 20.1-a11
| \( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( -40 a^{2} + 102 a - 30\) , \( -285 a^{2} + 712 a - 203\bigr] \)
|
| 20.1-a12
| \( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( 2 a\) , \( 2 a - 2\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 3 & 2 & 6 & 4 & 12 & 8 & 24 & 4 & 12 & 24 & 8 \\
3 & 1 & 6 & 2 & 12 & 4 & 24 & 8 & 12 & 4 & 8 & 24 \\
2 & 6 & 1 & 3 & 2 & 6 & 4 & 12 & 2 & 6 & 12 & 4 \\
6 & 2 & 3 & 1 & 6 & 2 & 12 & 4 & 6 & 2 & 4 & 12 \\
4 & 12 & 2 & 6 & 1 & 3 & 8 & 24 & 4 & 12 & 24 & 8 \\
12 & 4 & 6 & 2 & 3 & 1 & 24 & 8 & 12 & 4 & 8 & 24 \\
8 & 24 & 4 & 12 & 8 & 24 & 1 & 3 & 2 & 6 & 12 & 4 \\
24 & 8 & 12 & 4 & 24 & 8 & 3 & 1 & 6 & 2 & 4 & 12 \\
4 & 12 & 2 & 6 & 4 & 12 & 2 & 6 & 1 & 3 & 6 & 2 \\
12 & 4 & 6 & 2 & 12 & 4 & 6 & 2 & 3 & 1 & 2 & 6 \\
24 & 8 & 12 & 4 & 24 & 8 & 12 & 4 & 6 & 2 & 1 & 3 \\
8 & 24 & 4 & 12 & 8 & 24 & 4 & 12 & 2 & 6 & 3 & 1
\end{array}\right)\)
