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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 239343.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
239343.c1 | 239343c2 | \([1, 0, 0, -118235, 5227716]\) | \(3885442650361/1996623837\) | \(93932927437265397\) | \([2]\) | \(3981312\) | \(1.9490\) | |
239343.c2 | 239343c1 | \([1, 0, 0, -94770, 11211291]\) | \(2000852317801/2094417\) | \(98533692946377\) | \([2]\) | \(1990656\) | \(1.6024\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 239343.c have rank \(1\).
Complex multiplication
The elliptic curves in class 239343.c do not have complex multiplication.Modular form 239343.2.a.c
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.