Base field \(\Q(\sqrt{41}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 10 \); class number \(1\).
Elliptic curves in class 16.4-a over \(\Q(\sqrt{41}) \)
Isogeny class 16.4-a contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 16.4-a1 | \( \bigl[a\) , \( a + 1\) , \( a\) , \( 4 a + 7\) , \( 4 a + 9\bigr] \) |
| 16.4-a2 | \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -a - 3\) , \( -12 a + 41\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
