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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 46800.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.v1 | 46800eg2 | \([0, 0, 0, -32818501875, -2288369979868750]\) | \(-134057911417971280740025/1872\) | \(-54587520000000000\) | \([]\) | \(32256000\) | \(4.1912\) | |
46800.v2 | 46800eg1 | \([0, 0, 0, -51163635, -154318995790]\) | \(-198417696411528597145/22989483914821632\) | \(-1716155778447868900147200\) | \([]\) | \(6451200\) | \(3.3865\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.v have rank \(0\).
Complex multiplication
The elliptic curves in class 46800.v do not have complex multiplication.Modular form 46800.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.