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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 6864.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6864.n1 | 6864f2 | \([0, -1, 0, -47312, -3238368]\) | \(5718957389087906/1075876263891\) | \(2203394588448768\) | \([2]\) | \(37632\) | \(1.6619\) | |
6864.n2 | 6864f1 | \([0, -1, 0, 5928, -299520]\) | \(22494434350748/50367250791\) | \(-51576064809984\) | \([2]\) | \(18816\) | \(1.3153\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6864.n have rank \(1\).
Complex multiplication
The elliptic curves in class 6864.n do not have complex multiplication.Modular form 6864.2.a.n
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.