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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 64680cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64680.bz1 | 64680cn1 | \([0, 1, 0, -5896, -173440]\) | \(188183524/3465\) | \(417437475840\) | \([2]\) | \(110592\) | \(1.0244\) | \(\Gamma_0(N)\)-optimal |
64680.bz2 | 64680cn2 | \([0, 1, 0, -16, -498016]\) | \(-2/444675\) | \(-107142285465600\) | \([2]\) | \(221184\) | \(1.3710\) |
Rank
sage: E.rank()
The elliptic curves in class 64680cn have rank \(0\).
Complex multiplication
The elliptic curves in class 64680cn do not have complex multiplication.Modular form 64680.2.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 Cremona 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 Cremona labels.