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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 57498.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57498.o1 | 57498n2 | \([1, 1, 1, -19768, 699449]\) | \(16865845211125/5489031744\) | \(278035924928832\) | \([2]\) | \(186624\) | \(1.4748\) | |
57498.o2 | 57498n1 | \([1, 1, 1, -7928, -266695]\) | \(1087959899125/37933056\) | \(1921423085568\) | \([2]\) | \(93312\) | \(1.1282\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57498.o have rank \(1\).
Complex multiplication
The elliptic curves in class 57498.o do not have complex multiplication.Modular form 57498.2.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.