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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 267410.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
267410.o1 | 267410o1 | \([1, -1, 0, -2140, -16560]\) | \(611960049/282880\) | \(501139175680\) | \([2]\) | \(327680\) | \(0.93967\) | \(\Gamma_0(N)\)-optimal |
267410.o2 | 267410o2 | \([1, -1, 0, 7540, -130784]\) | \(26757728271/19536400\) | \(-34609924320400\) | \([2]\) | \(655360\) | \(1.2862\) |
Rank
sage: E.rank()
The elliptic curves in class 267410.o have rank \(1\).
Complex multiplication
The elliptic curves in class 267410.o do not have complex multiplication.Modular form 267410.2.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.