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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 53900bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53900.k1 | 53900bf1 | \([0, -1, 0, -15108, -712088]\) | \(-20261200/77\) | \(-1449435680000\) | \([]\) | \(82944\) | \(1.1926\) | \(\Gamma_0(N)\)-optimal |
| 53900.k2 | 53900bf2 | \([0, -1, 0, 33892, -3769688]\) | \(228714800/456533\) | \(-8593704146720000\) | \([]\) | \(248832\) | \(1.7420\) |
Rank
sage: E.rank()
The elliptic curves in class 53900bf have rank \(0\).
Complex multiplication
The elliptic curves in class 53900bf do not have complex multiplication.Modular form 53900.2.a.bf
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
