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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 47040.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47040.bk1 | 47040m4 | \([0, -1, 0, -1171361, -487569375]\) | \(5763259856089/5670\) | \(174868353515520\) | \([2]\) | \(589824\) | \(2.0263\) | |
47040.bk2 | 47040m2 | \([0, -1, 0, -73761, -7479135]\) | \(1439069689/44100\) | \(1360087194009600\) | \([2, 2]\) | \(294912\) | \(1.6797\) | |
47040.bk3 | 47040m1 | \([0, -1, 0, -11041, 285601]\) | \(4826809/1680\) | \(51812845486080\) | \([2]\) | \(147456\) | \(1.3331\) | \(\Gamma_0(N)\)-optimal |
47040.bk4 | 47040m3 | \([0, -1, 0, 20319, -25335519]\) | \(30080231/9003750\) | \(-277684468776960000\) | \([2]\) | \(589824\) | \(2.0263\) |
Rank
sage: E.rank()
The elliptic curves in class 47040.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 47040.bk do not have complex multiplication.Modular form 47040.2.a.bk
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.