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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 25857f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25857.g2 | 25857f1 | \([1, -1, 1, -50225, 4120328]\) | \(3981876625/232713\) | \(818857416853593\) | \([2]\) | \(86016\) | \(1.6151\) | \(\Gamma_0(N)\)-optimal |
25857.g1 | 25857f2 | \([1, -1, 1, -149090, -16997236]\) | \(104154702625/24649677\) | \(86735897154415197\) | \([2]\) | \(172032\) | \(1.9617\) |
Rank
sage: E.rank()
The elliptic curves in class 25857f have rank \(0\).
Complex multiplication
The elliptic curves in class 25857f do not have complex multiplication.Modular form 25857.2.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 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.