Base field \(\Q(\sqrt{53}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 13 \); class number \(1\).
Elliptic curves in class 17.2-a over \(\Q(\sqrt{53}) \)
Isogeny class 17.2-a contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 17.2-a1 | \( \bigl[1\) , \( -1\) , \( 0\) , \( a - 4\) , \( 0\bigr] \) |
| 17.2-a2 | \( \bigl[1\) , \( -1\) , \( 0\) , \( -4 a + 16\) , \( 3 a - 12\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
