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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 468270.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
468270.bz1 | 468270bz2 | \([1, -1, 0, -212559, -25957387]\) | \(30459021867/9245000\) | \(322369777081935000\) | \([2]\) | \(6451200\) | \(2.0646\) | |
468270.bz2 | 468270bz1 | \([1, -1, 0, -81879, 8725085]\) | \(1740992427/68800\) | \(2399030899214400\) | \([2]\) | \(3225600\) | \(1.7180\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 468270.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 468270.bz do not have complex multiplication.Modular form 468270.2.a.bz
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.