Base field \(\Q(\sqrt{21}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).
Elliptic curves in class 625.1-c over \(\Q(\sqrt{21}) \)
Isogeny class 625.1-c contains 2 curves linked by isogenies of degree 3.
Curve label | Weierstrass Coefficients |
---|---|
625.1-c1 | \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a + 2\) , \( -a - 2\bigr] \) |
625.1-c2 | \( \bigl[0\) , \( a + 1\) , \( 1\) , \( a + 2\) , \( a - 1\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)