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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 19350.cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19350.cn1 | 19350bs2 | \([1, -1, 1, -4880, -89253]\) | \(30459021867/9245000\) | \(3900234375000\) | \([2]\) | \(36864\) | \(1.1210\) | |
19350.cn2 | 19350bs1 | \([1, -1, 1, -1880, 30747]\) | \(1740992427/68800\) | \(29025000000\) | \([2]\) | \(18432\) | \(0.77445\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19350.cn have rank \(1\).
Complex multiplication
The elliptic curves in class 19350.cn do not have complex multiplication.Modular form 19350.2.a.cn
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.