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SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 485520.ff
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485520.ff1 | 485520ff2 | \([0, 1, 0, -601896, 178458804]\) | \(1198345620520313/8268750000\) | \(166397414400000000\) | \([2]\) | \(7077888\) | \(2.1380\) | \(\Gamma_0(N)\)-optimal* |
485520.ff2 | 485520ff1 | \([0, 1, 0, -14376, 6197940]\) | \(-16329068153/816480000\) | \(-16430556119040000\) | \([2]\) | \(3538944\) | \(1.7915\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485520.ff have rank \(1\).
Complex multiplication
The elliptic curves in class 485520.ff do not have complex multiplication.Modular form 485520.2.a.ff
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.