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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 4800.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4800.bj1 | 4800o1 | \([0, -1, 0, -1333, 18037]\) | \(131072/9\) | \(18000000000\) | \([2]\) | \(3840\) | \(0.71604\) | \(\Gamma_0(N)\)-optimal |
| 4800.bj2 | 4800o2 | \([0, -1, 0, 1167, 75537]\) | \(5488/81\) | \(-2592000000000\) | \([2]\) | \(7680\) | \(1.0626\) |
Rank
sage: E.rank()
The elliptic curves in class 4800.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 4800.bj do not have complex multiplication.Modular form 4800.2.a.bj
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.
