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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 29435.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29435.f1 | 29435a2 | \([1, 1, 0, -133, -588]\) | \(10793861/1225\) | \(29876525\) | \([2]\) | \(8960\) | \(0.16687\) | |
29435.f2 | 29435a1 | \([1, 1, 0, 12, -37]\) | \(6859/35\) | \(-853615\) | \([2]\) | \(4480\) | \(-0.17970\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29435.f have rank \(0\).
Complex multiplication
The elliptic curves in class 29435.f do not have complex multiplication.Modular form 29435.2.a.f
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.