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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 44880.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44880.f1 | 44880bb2 | \([0, -1, 0, -5956, 133900]\) | \(91289479134544/23464596375\) | \(6006936672000\) | \([2]\) | \(80640\) | \(1.1613\) | |
44880.f2 | 44880bb1 | \([0, -1, 0, 919, 12900]\) | \(5358924087296/7810171875\) | \(-124962750000\) | \([2]\) | \(40320\) | \(0.81476\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44880.f have rank \(0\).
Complex multiplication
The elliptic curves in class 44880.f do not have complex multiplication.Modular form 44880.2.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.