Elliptic curves in class 180.1-r over \(\Q(\sqrt{85}) \)
Isogeny class 180.1-r contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 180.1-r1
| \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 147 a - 774\) , \( 7288 a - 37301\bigr] \)
|
| 180.1-r2
| \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -18 a + 81\) , \( -269 a + 1372\bigr] \)
|
| 180.1-r3
| \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 4987 a - 25854\) , \( 65888 a - 337421\bigr] \)
|
| 180.1-r4
| \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 752 a - 3909\) , \( 22453 a - 114926\bigr] \)
|
| 180.1-r5
| \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 202 a - 1059\) , \( -2737 a + 13984\bigr] \)
|
| 180.1-r6
| \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 3667 a - 19014\) , \( 268856 a - 1375733\bigr] \)
|
| 180.1-r7
| \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 3172 a - 16449\) , \( -205399 a + 1050622\bigr] \)
|
| 180.1-r8
| \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 58667 a - 304014\) , \( 16899856 a - 86464733\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\
3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\
4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\
12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\
6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\
2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\
12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\
4 & 12 & 4 & 3 & 6 & 2 & 12 & 1
\end{array}\right)\)
