![Copy content]()
sage:R.<x> = PolynomialRing(QQ); K.<a> = NumberField(R([1, 0, 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 \(i\), with minimal polynomial
\( x^{2} + 1 \); class number \(1\).
![Copy content]()
sage:E = EllipticCurve([K([0,0]),K([1,1]),K([0,0]),K([-961,-9264]),K([-201179,276097])])
E.isogeny_class()
![Copy content]()
sage:E.rank()
![Copy content]()
magma:Rank(E);
The elliptic curves in class 26000.3-e have
rank \( 0 \).
![Copy content]()
sage:E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr}
1 & 6 & 18 & 2 & 9 & 3 \\
6 & 1 & 3 & 3 & 6 & 2 \\
18 & 3 & 1 & 9 & 2 & 6 \\
2 & 3 & 9 & 1 & 18 & 6 \\
9 & 6 & 2 & 18 & 1 & 3 \\
3 & 2 & 6 & 6 & 3 & 1
\end{array}\right)\)
![Copy content]()
sage:E.isogeny_class().graph().plot(edge_labels=True)
Elliptic curves in class 26000.3-e over \(\Q(\sqrt{-1}) \)
![Copy content]()
sage:E.isogeny_class().curves
Isogeny class 26000.3-e contains
6 curves linked by isogenies of
degrees dividing 18.
| Curve label |
Weierstrass Coefficients |
| 26000.3-e1
| \( \bigl[0\) , \( i + 1\) , \( 0\) , \( -9264 i - 961\) , \( 276097 i - 201179\bigr] \)
|
| 26000.3-e2
| \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 248 i - 201\) , \( -2001 i + 549\bigr] \)
|
| 26000.3-e3
| \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -12 i - 21\) , \( -29 i - 47\bigr] \)
|
| 26000.3-e4
| \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2308 i + 219\) , \( 25771 i + 36553\bigr] \)
|
| 26000.3-e5
| \( \bigl[0\) , \( i + 1\) , \( 0\) , \( 16 i - 1\) , \( -23 i - 19\bigr] \)
|
| 26000.3-e6
| \( \bigl[0\) , \( i + 1\) , \( 0\) , \( -124 i + 19\) , \( 469 i + 25\bigr] \)
|
