Base field \(\Q(\sqrt{42}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 42 \); class number \(2\).
Elliptic curves in class 14.1-f over \(\Q(\sqrt{42}) \)
Isogeny class 14.1-f contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 14.1-f1 | \( \bigl[1\) , \( 0\) , \( 1\) , \( 9 a - 59\) , \( 353 a - 2288\bigr] \) |
| 14.1-f2 | \( \bigl[1\) , \( 0\) , \( 1\) , \( -a + 6\) , \( -13 a + 84\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
