Base field \(\Q(\sqrt{57}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 4.3-a over \(\Q(\sqrt{57}) \)
Isogeny class 4.3-a contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 4.3-a1 | \( \bigl[0\) , \( -a - 1\) , \( a\) , \( a + 5\) , \( -10\bigr] \) |
| 4.3-a2 | \( \bigl[0\) , \( a + 1\) , \( a\) , \( a + 5\) , \( -17423 a - 57062\bigr] \) |