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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 418950fq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418950.fq2 | 418950fq1 | \([1, -1, 0, 890958, 223452116]\) | \(2161700757/1848320\) | \(-66876990510960000000\) | \([2]\) | \(16588800\) | \(2.4917\) | \(\Gamma_0(N)\)-optimal* |
418950.fq1 | 418950fq2 | \([1, -1, 0, -4401042, 1975104116]\) | \(260549802603/104256800\) | \(3772280246008837500000\) | \([2]\) | \(33177600\) | \(2.8383\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 418950fq have rank \(0\).
Complex multiplication
The elliptic curves in class 418950fq do not have complex multiplication.Modular form 418950.2.a.fq
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 Cremona 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 Cremona labels.