Base field \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).
Elliptic curves in class 1682.1-b over \(\Q(\sqrt{-2}) \)
Isogeny class 1682.1-b contains 2 curves linked by isogenies of degree 5.
| Curve label | Weierstrass Coefficients |
|---|---|
| 1682.1-b1 | \( \bigl[1\) , \( 1\) , \( 1\) , \( -455\) , \( -3951\bigr] \) |
| 1682.1-b2 | \( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
