Base field \(\Q(\sqrt{53}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 13 \); class number \(1\).
Elliptic curves in class 212.1-c over \(\Q(\sqrt{53}) \)
Isogeny class 212.1-c contains 2 curves linked by isogenies of degree 3.
Curve label | Weierstrass Coefficients |
---|---|
212.1-c1 | \( \bigl[1\) , \( 0\) , \( 0\) , \( -24603\) , \( -1487407\bigr] \) |
212.1-c2 | \( \bigl[1\) , \( 0\) , \( 0\) , \( -283\) , \( -2351\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)