Base field \(\Q(\sqrt{2}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 1458.1-m over \(\Q(\sqrt{2}) \)
Isogeny class 1458.1-m contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 1458.1-m1 | \( \bigl[1\) , \( -1\) , \( a\) , \( -14 a - 15\) , \( -27 a - 33\bigr] \) |
| 1458.1-m2 | \( \bigl[1\) , \( -1\) , \( a\) , \( a\) , \( -a\bigr] \) |