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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 446292.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
446292.b1 | 446292b2 | \([0, 0, 0, -4507167, -3663565850]\) | \(461188987116496/2811467307\) | \(61728933181364773632\) | \([2]\) | \(17694720\) | \(2.6362\) | \(\Gamma_0(N)\)-optimal* |
446292.b2 | 446292b1 | \([0, 0, 0, -4500552, -3674910575]\) | \(7346581704933376/275517\) | \(378080389752912\) | \([2]\) | \(8847360\) | \(2.2896\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 446292.b have rank \(1\).
Complex multiplication
The elliptic curves in class 446292.b do not have complex multiplication.Modular form 446292.2.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.