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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 46550.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46550.o1 | 46550v2 | \([1, 1, 0, -85775, 10667875]\) | \(-37966934881/4952198\) | \(-9103455351593750\) | \([]\) | \(264000\) | \(1.7955\) | |
46550.o2 | 46550v1 | \([1, 1, 0, -25, -50875]\) | \(-1/608\) | \(-1117665500000\) | \([]\) | \(52800\) | \(0.99074\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46550.o have rank \(1\).
Complex multiplication
The elliptic curves in class 46550.o do not have complex multiplication.Modular form 46550.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.