Base field \(\Q(\sqrt{-19}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 5 \); class number \(1\).
Elliptic curves in class 171.1-c over \(\Q(\sqrt{-19}) \)
Isogeny class 171.1-c contains 2 curves linked by isogenies of degree 5.
Curve label | Weierstrass Coefficients |
---|---|
171.1-c1 | \( \bigl[0\) , \( 1\) , \( 1\) , \( -4390\) , \( -113432\bigr] \) |
171.1-c2 | \( \bigl[0\) , \( 1\) , \( 1\) , \( 20\) , \( -32\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)