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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 283746.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
283746.v1 | 283746v2 | \([1, 1, 1, -52172, 3872165]\) | \(333822098953/53954184\) | \(2538322119916104\) | \([]\) | \(3151872\) | \(1.6780\) | |
283746.v2 | 283746v1 | \([1, 1, 1, -14267, -661273]\) | \(6826561273/7074\) | \(332802562194\) | \([]\) | \(1050624\) | \(1.1286\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 283746.v have rank \(1\).
Complex multiplication
The elliptic curves in class 283746.v do not have complex multiplication.Modular form 283746.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.