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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 93600cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93600.m2 | 93600cn1 | \([0, 0, 0, -44625, 3625000]\) | \(107850176/117\) | \(10661625000000\) | \([2]\) | \(286720\) | \(1.4154\) | \(\Gamma_0(N)\)-optimal |
93600.m1 | 93600cn2 | \([0, 0, 0, -55875, 1656250]\) | \(26463592/13689\) | \(9979281000000000\) | \([2]\) | \(573440\) | \(1.7620\) |
Rank
sage: E.rank()
The elliptic curves in class 93600cn have rank \(0\).
Complex multiplication
The elliptic curves in class 93600cn do not have complex multiplication.Modular form 93600.2.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.