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SageMath
E = EllipticCurve("fp1")
E.isogeny_class()
Elliptic curves in class 485520.fp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485520.fp1 | 485520fp2 | \([0, 1, 0, -249915736, -1450011075436]\) | \(17460273607244690041/918397653311250\) | \(90799664030672385438720000\) | \([2]\) | \(212336640\) | \(3.7379\) | \(\Gamma_0(N)\)-optimal* |
485520.fp2 | 485520fp1 | \([0, 1, 0, 10184264, -90104235436]\) | \(1181569139409959/36161310937500\) | \(-3575177780774342400000000\) | \([2]\) | \(106168320\) | \(3.3914\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485520.fp have rank \(0\).
Complex multiplication
The elliptic curves in class 485520.fp do not have complex multiplication.Modular form 485520.2.a.fp
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.