Base field \(\Q(\sqrt{165}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 41 \); class number \(2\).
Elliptic curves in class 1.1-a over \(\Q(\sqrt{165}) \)
Isogeny class 1.1-a contains 2 curves linked by isogenies of degree 11.
Curve label | Weierstrass Coefficients |
---|---|
1.1-a1 | \( \bigl[0\) , \( -1\) , \( 1\) , \( 112 a - 775\) , \( -1715 a + 11872\bigr] \) |
1.1-a2 | \( \bigl[0\) , \( a\) , \( 1\) , \( a + 9\) , \( a + 5\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)