![Copy content]()
sage:R.<x> = PolynomialRing(QQ); K.<a> = NumberField(R([2, -1, 1]))
![Copy content]()
pari:K = nfinit(Polrev(%s));
![Copy content]()
magma:R<x> := PolynomialRing(Rationals()); K<a> := NumberField(R!%s);
![Copy content]()
oscar:Qx, x = polynomial_ring(QQ); K, a = number_field(Qx(%s))
Generator \(a\), with minimal polynomial
\( x^{2} - x + 2 \); class number \(1\).
![Copy content]()
sage:E = EllipticCurve([K([1,1]),K([1,0]),K([0,0]),K([576,192]),K([6260,-4560])])
E.isogeny_class()
![Copy content]()
sage:E.rank()
![Copy content]()
magma:Rank(E);
The elliptic curves in class 18144.5-a have
rank \( 1 \).
![Copy content]()
sage:E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr}
1 & 8 & 2 & 8 & 4 & 4 \\
8 & 1 & 4 & 4 & 8 & 2 \\
2 & 4 & 1 & 4 & 2 & 2 \\
8 & 4 & 4 & 1 & 8 & 2 \\
4 & 8 & 2 & 8 & 1 & 4 \\
4 & 2 & 2 & 2 & 4 & 1
\end{array}\right)\)
![Copy content]()
sage:E.isogeny_class().graph().plot(edge_labels=True)
Elliptic curves in class 18144.5-a over \(\Q(\sqrt{-7}) \)
![Copy content]()
sage:E.isogeny_class().curves
Isogeny class 18144.5-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 18144.5-a1
| \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 192 a + 576\) , \( -4560 a + 6260\bigr] \)
|
| 18144.5-a2
| \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 21 a - 126\) , \( 106 a - 574\bigr] \)
|
| 18144.5-a3
| \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 12 a + 36\) , \( -60 a + 104\bigr] \)
|
| 18144.5-a4
| \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 69 a - 87\) , \( 345 a - 431\bigr] \)
|
| 18144.5-a5
| \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -3 a - 15\) , \( -29 a - 45\bigr] \)
|
| 18144.5-a6
| \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -21 a + 3\) , \( 39 a - 17\bigr] \)
|
