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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 54450.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54450.bn1 | 54450bv1 | \([1, -1, 0, -27792, 4878616]\) | \(-117649/440\) | \(-8878842286875000\) | \([]\) | \(345600\) | \(1.7459\) | \(\Gamma_0(N)\)-optimal |
54450.bn2 | 54450bv2 | \([1, -1, 0, 244458, -115728134]\) | \(80062991/332750\) | \(-6714624479449218750\) | \([]\) | \(1036800\) | \(2.2952\) |
Rank
sage: E.rank()
The elliptic curves in class 54450.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 54450.bn do not have complex multiplication.Modular form 54450.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.