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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 4800.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4800.bn1 | 4800bg1 | \([0, 1, 0, -53, 123]\) | \(131072/9\) | \(1152000\) | \([2]\) | \(768\) | \(-0.088679\) | \(\Gamma_0(N)\)-optimal |
4800.bn2 | 4800bg2 | \([0, 1, 0, 47, 623]\) | \(5488/81\) | \(-165888000\) | \([2]\) | \(1536\) | \(0.25789\) |
Rank
sage: E.rank()
The elliptic curves in class 4800.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 4800.bn do not have complex multiplication.Modular form 4800.2.a.bn
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.