Base field \(\Q(\sqrt{2}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).
Elliptic curves in class 5000.1-c over \(\Q(\sqrt{2}) \)
Isogeny class 5000.1-c contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
5000.1-c1 | \( \bigl[0\) , \( -1\) , \( 0\) , \( -83\) , \( -88\bigr] \) |
5000.1-c2 | \( \bigl[a\) , \( -1\) , \( a\) , \( -178\) , \( 926\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)