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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 6534.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6534.o1 | 6534m1 | \([1, -1, 0, -55743, 5079597]\) | \(-400478525811/352\) | \(-16836915744\) | \([]\) | \(28800\) | \(1.2623\) | \(\Gamma_0(N)\)-optimal |
6534.o2 | 6534m2 | \([1, -1, 0, -43038, 7445268]\) | \(-20479683819/43614208\) | \(-18775450875101184\) | \([]\) | \(86400\) | \(1.8116\) |
Rank
sage: E.rank()
The elliptic curves in class 6534.o have rank \(1\).
Complex multiplication
The elliptic curves in class 6534.o do not have complex multiplication.Modular form 6534.2.a.o
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.