Base field \(\Q(\sqrt{-1}) \)
Generator \(i\), with minimal polynomial \( x^{2} + 1 \); class number \(1\).
Elliptic curves in class 40000.3-CMc over \(\Q(\sqrt{-1}) \)
Isogeny class 40000.3-CMc contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
40000.3-CMc1 | \( \bigl[0\) , \( 0\) , \( 0\) , \( -25\) , \( 0\bigr] \) |
40000.3-CMc2 | \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 68\) , \( 253 i\bigr] \) |
Rank
Rank: \( 2 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)