Base field \(\Q(\sqrt{2}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).
Elliptic curves in class 89.2-b over \(\Q(\sqrt{2}) \)
Isogeny class 89.2-b contains 2 curves linked by isogenies of degree 3.
Curve label | Weierstrass Coefficients |
---|---|
89.2-b1 | \( \bigl[0\) , \( 1\) , \( a + 1\) , \( -2 a - 3\) , \( a + 1\bigr] \) |
89.2-b2 | \( \bigl[0\) , \( 1\) , \( a + 1\) , \( 18 a - 23\) , \( 59 a - 64\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)