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SageMath
sage: E = EllipticCurve("ct1")
sage: E.isogeny_class()
Elliptic curves in class 152592.ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
152592.ct1 | 152592w1 | [0, 1, 0, -4180192, -3264988300] | [2] | 7741440 | \(\Gamma_0(N)\)-optimal |
152592.ct2 | 152592w2 | [0, 1, 0, -1220832, -7795176588] | [2] | 15482880 |
Rank
sage: E.rank()
The elliptic curves in class 152592.ct have rank \(1\).
Complex multiplication
The elliptic curves in class 152592.ct do not have complex multiplication.Modular form 152592.2.a.ct
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.