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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 458640.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
458640.v1 | 458640v2 | \([0, 0, 0, -16671123, 25881698178]\) | \(216092050322508/3016755625\) | \(7153517112270721920000\) | \([2]\) | \(39813120\) | \(2.9988\) | \(\Gamma_0(N)\)-optimal* |
458640.v2 | 458640v1 | \([0, 0, 0, -133623, 1085370678]\) | \(-445090032/858203125\) | \(-508756053159900000000\) | \([2]\) | \(19906560\) | \(2.6522\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 458640.v have rank \(1\).
Complex multiplication
The elliptic curves in class 458640.v do not have complex multiplication.Modular form 458640.2.a.v
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.