Base field \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).
Elliptic curves in class 1458.3-a over \(\Q(\sqrt{-2}) \)
Isogeny class 1458.3-a contains 2 curves linked by isogenies of degree 3.
Curve label | Weierstrass Coefficients |
---|---|
1458.3-a1 | \( \bigl[1\) , \( -1\) , \( a\) , \( a\) , \( -a\bigr] \) |
1458.3-a2 | \( \bigl[1\) , \( -1\) , \( a\) , \( -14 a - 15\) , \( -27 a - 5\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)