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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2277.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2277.a1 | 2277a2 | \([1, -1, 0, -11142, 451957]\) | \(209849322390625/1882056627\) | \(1372019281083\) | \([2]\) | \(2560\) | \(1.1518\) | |
2277.a2 | 2277a1 | \([1, -1, 0, -207, 16744]\) | \(-1349232625/164333367\) | \(-119799024543\) | \([2]\) | \(1280\) | \(0.80522\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2277.a have rank \(0\).
Complex multiplication
The elliptic curves in class 2277.a do not have complex multiplication.Modular form 2277.2.a.a
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.