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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 149184cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
149184.fe2 | 149184cn1 | \([0, 0, 0, -84684, -9991280]\) | \(-351447414193/22278144\) | \(-4257419618156544\) | \([2]\) | \(737280\) | \(1.7525\) | \(\Gamma_0(N)\)-optimal |
149184.fe1 | 149184cn2 | \([0, 0, 0, -1374924, -620532848]\) | \(1504154129818033/5519808\) | \(1054851735748608\) | \([2]\) | \(1474560\) | \(2.0991\) |
Rank
sage: E.rank()
The elliptic curves in class 149184cn have rank \(0\).
Complex multiplication
The elliptic curves in class 149184cn do not have complex multiplication.Modular form 149184.2.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.