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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 119952.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 119952.bz1 | 119952l2 | \([0, 0, 0, -254751, 48942670]\) | \(2248430329584/28647703\) | \(23296022394027264\) | \([2]\) | \(1032192\) | \(1.9494\) | |
| 119952.bz2 | 119952l1 | \([0, 0, 0, -2646, 2000719]\) | \(-40310784/34000561\) | \(-1728057024470448\) | \([2]\) | \(516096\) | \(1.6028\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 119952.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 119952.bz do not have complex multiplication.Modular form 119952.2.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.
