Base field \(\Q(\sqrt{2}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).
Elliptic curves in class 1800.1-e over \(\Q(\sqrt{2}) \)
Isogeny class 1800.1-e contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
1800.1-e1 | \( \bigl[a\) , \( a\) , \( a\) , \( 3 a\) , \( -4 a - 2\bigr] \) |
1800.1-e2 | \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -13\) , \( -9 a - 2\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)