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SageMath
sage: E = EllipticCurve("cb1")
sage: E.isogeny_class()
Elliptic curves in class 88935.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
88935.cb1 | 88935s2 | [0, -1, 1, -158839886, -14567227396723] | [] | 172800000 | |
88935.cb2 | 88935s1 | [0, -1, 1, -53007236, 173973325217] | [] | 34560000 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88935.cb have rank \(1\).
Complex multiplication
The elliptic curves in class 88935.cb do not have complex multiplication.Modular form 88935.2.a.cb
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.