Base field \(\Q(\sqrt{77}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 19 \); class number \(1\).
Elliptic curves in class 44.1-e over \(\Q(\sqrt{77}) \)
Isogeny class 44.1-e contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
44.1-e1 | \( \bigl[a\) , \( -1\) , \( a\) , \( 2 a + 3\) , \( 2 a + 5\bigr] \) |
44.1-e2 | \( \bigl[a\) , \( -1\) , \( a\) , \( -8 a - 37\) , \( -24 a - 97\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)