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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 53958.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53958.o1 | 53958m1 | \([1, 1, 0, -1333, -12455]\) | \(1771561/612\) | \(90597964068\) | \([2]\) | \(95040\) | \(0.80422\) | \(\Gamma_0(N)\)-optimal |
53958.o2 | 53958m2 | \([1, 1, 0, 3957, -81225]\) | \(46268279/46818\) | \(-6930744251202\) | \([2]\) | \(190080\) | \(1.1508\) |
Rank
sage: E.rank()
The elliptic curves in class 53958.o have rank \(1\).
Complex multiplication
The elliptic curves in class 53958.o do not have complex multiplication.Modular form 53958.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.