Base field \(\Q(\sqrt{2}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 1458.1-w over \(\Q(\sqrt{2}) \)
Isogeny class 1458.1-w contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 1458.1-w1 | \( \bigl[1\) , \( -1\) , \( 0\) , \( -27 a - 42\) , \( -108 a - 154\bigr] \) |
| 1458.1-w2 | \( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a + 3\) , \( 1\bigr] \) |