Base field \(\Q(\sqrt{34}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 34 \); class number \(2\).
Elliptic curves in class 18.2-b over \(\Q(\sqrt{34}) \)
Isogeny class 18.2-b contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 18.2-b1 | \( \bigl[1\) , \( -1\) , \( 0\) , \( 11 a - 64\) , \( 0\bigr] \) |
| 18.2-b2 | \( \bigl[1\) , \( -1\) , \( 0\) , \( -44 a + 256\) , \( 33 a - 192\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
