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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 116242.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116242.b1 | 116242i1 | \([1, 0, 1, -50187, 3705830]\) | \(297141543217/45566864\) | \(2143733261287184\) | \([2]\) | \(691200\) | \(1.6654\) | \(\Gamma_0(N)\)-optimal |
116242.b2 | 116242i2 | \([1, 0, 1, 86993, 20441790]\) | \(1547612421263/4729960396\) | \(-222525153924928876\) | \([2]\) | \(1382400\) | \(2.0120\) |
Rank
sage: E.rank()
The elliptic curves in class 116242.b have rank \(1\).
Complex multiplication
The elliptic curves in class 116242.b do not have complex multiplication.Modular form 116242.2.a.b
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.