Base field \(\Q(\sqrt{11}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).
Elliptic curves in class 121.1-c over \(\Q(\sqrt{11}) \)
Isogeny class 121.1-c contains 2 curves linked by isogenies of degree 11.
Curve label | Weierstrass Coefficients |
---|---|
121.1-c1 | \( \bigl[0\) , \( -1\) , \( 1\) , \( -7\) , \( 10\bigr] \) |
121.1-c2 | \( \bigl[0\) , \( 1\) , \( a\) , \( -7\) , \( -13\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)