Base field \(\Q(\sqrt{53}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 13 \); class number \(1\).
Elliptic curves in class 1764.1-l over \(\Q(\sqrt{53}) \)
Isogeny class 1764.1-l contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
1764.1-l1 | \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -8\) , \( -14 a - 20\bigr] \) |
1764.1-l2 | \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)