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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 64757b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64757.b2 | 64757b1 | \([1, 0, 0, 2926, 231403]\) | \(4657463/41503\) | \(-24686952291463\) | \([2]\) | \(145152\) | \(1.2511\) | \(\Gamma_0(N)\)-optimal |
64757.b1 | 64757b2 | \([1, 0, 0, -43329, 3200974]\) | \(15124197817/1294139\) | \(769784057815619\) | \([2]\) | \(290304\) | \(1.5976\) |
Rank
sage: E.rank()
The elliptic curves in class 64757b have rank \(1\).
Complex multiplication
The elliptic curves in class 64757b do not have complex multiplication.Modular form 64757.2.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 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.