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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 4800.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4800.k1 | 4800k2 | \([0, -1, 0, -16833, -518463]\) | \(2060602/729\) | \(186624000000000\) | \([2]\) | \(15360\) | \(1.4395\) | |
4800.k2 | 4800k1 | \([0, -1, 0, 3167, -58463]\) | \(27436/27\) | \(-3456000000000\) | \([2]\) | \(7680\) | \(1.0929\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4800.k have rank \(0\).
Complex multiplication
The elliptic curves in class 4800.k do not have complex multiplication.Modular form 4800.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.