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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 202800.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
202800.e1 | 202800de2 | \([0, -1, 0, -9526248, -11277886608]\) | \(38686490446661/141927552\) | \(350749278894882816000\) | \([2]\) | \(14450688\) | \(2.8027\) | |
202800.e2 | 202800de1 | \([0, -1, 0, -873448, 5364592]\) | \(29819839301/17252352\) | \(42636189647241216000\) | \([2]\) | \(7225344\) | \(2.4561\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202800.e have rank \(1\).
Complex multiplication
The elliptic curves in class 202800.e do not have complex multiplication.Modular form 202800.2.a.e
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.