Base field \(\Q(\sqrt{85}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 21 \); class number \(2\).
Elliptic curves in class 4.1-a over \(\Q(\sqrt{85}) \)
Isogeny class 4.1-a contains 2 curves linked by isogenies of degree 5.
| Curve label | Weierstrass Coefficients |
|---|---|
| 4.1-a1 | \( \bigl[a\) , \( 0\) , \( a\) , \( -383 a - 1644\) , \( -9842 a - 40758\bigr] \) |
| 4.1-a2 | \( \bigl[a\) , \( 0\) , \( a\) , \( 2 a + 6\) , \( a + 3\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
