Isogeny class 51.3-a contains
6 curves linked by isogenies of
degrees dividing 8.
Curve label |
Weierstrass Coefficients |
51.3-a1
| \( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -543 a^{2} - 968 a - 272\) , \( -13153 a^{2} - 24560 a - 6934\bigr] \)
|
51.3-a2
| \( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( 42 a^{2} + 22 a - 82\) , \( -59 a^{2} + 88 a + 322\bigr] \)
|
51.3-a3
| \( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -48 a^{2} - 38 a - 12\) , \( -255 a^{2} - 344 a - 86\bigr] \)
|
51.3-a4
| \( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -3 a^{2} - 8 a - 7\) , \( a^{2} + 4 a + 4\bigr] \)
|
51.3-a5
| \( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -3 a^{2} - 8 a - 2\) , \( 5 a^{2} + 10 a + 2\bigr] \)
|
51.3-a6
| \( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 2\) , \( -273 a^{2} + 412 a + 168\) , \( -3801 a^{2} + 3940 a + 1822\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 2 & 4 & 8 & 4 \\
8 & 1 & 4 & 2 & 4 & 8 \\
2 & 4 & 1 & 2 & 4 & 2 \\
4 & 2 & 2 & 1 & 2 & 4 \\
8 & 4 & 4 & 2 & 1 & 8 \\
4 & 8 & 2 & 4 & 8 & 1
\end{array}\right)\)