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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 134640.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
134640.o1 | 134640bx2 | \([0, 0, 0, -26741163, -53225351462]\) | \(708234550511150304361/23696640000\) | \(70757787893760000\) | \([2]\) | \(5406720\) | \(2.7328\) | |
134640.o2 | 134640bx1 | \([0, 0, 0, -1673643, -829221158]\) | \(173629978755828841/1000026931200\) | \(2986064416132300800\) | \([2]\) | \(2703360\) | \(2.3862\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 134640.o have rank \(0\).
Complex multiplication
The elliptic curves in class 134640.o do not have complex multiplication.Modular form 134640.2.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.