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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 450528.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450528.bn1 | 450528bn2 | \([0, 1, 0, -474113, 125421615]\) | \(61162984000/41067\) | \(7913607966830592\) | \([2]\) | \(4193280\) | \(1.9890\) | \(\Gamma_0(N)\)-optimal* |
450528.bn2 | 450528bn1 | \([0, 1, 0, -35498, 1118124]\) | \(1643032000/767637\) | \(2311306173004608\) | \([2]\) | \(2096640\) | \(1.6425\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450528.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 450528.bn do not have complex multiplication.Modular form 450528.2.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.