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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 41650.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41650.c1 | 41650o2 | \([1, 0, 1, -857526, -305098552]\) | \(37936442980801/88817792\) | \(163270693922000000\) | \([2]\) | \(860160\) | \(2.1831\) | |
41650.c2 | 41650o1 | \([1, 0, 1, -73526, -906552]\) | \(23912763841/13647872\) | \(25088413952000000\) | \([2]\) | \(430080\) | \(1.8365\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41650.c have rank \(0\).
Complex multiplication
The elliptic curves in class 41650.c do not have complex multiplication.Modular form 41650.2.a.c
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.