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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 388080.ep
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.ep1 | 388080ep2 | \([0, 0, 0, -354963, 4966738]\) | \(4829379946327/2784375000\) | \(2851736025600000000\) | \([2]\) | \(7077888\) | \(2.2308\) | |
388080.ep2 | 388080ep1 | \([0, 0, 0, 88557, 620242]\) | \(74991286313/43560000\) | \(-44613825822720000\) | \([2]\) | \(3538944\) | \(1.8842\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388080.ep have rank \(1\).
Complex multiplication
The elliptic curves in class 388080.ep do not have complex multiplication.Modular form 388080.2.a.ep
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.