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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 6534.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6534.m1 | 6534n2 | \([1, -1, 0, -186423, -30923227]\) | \(18868971/8\) | \(303784261540056\) | \([]\) | \(71280\) | \(1.7398\) | |
6534.m2 | 6534n1 | \([1, -1, 0, -6738, 162278]\) | \(8019/2\) | \(8438451709446\) | \([3]\) | \(23760\) | \(1.1905\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6534.m have rank \(1\).
Complex multiplication
The elliptic curves in class 6534.m do not have complex multiplication.Modular form 6534.2.a.m
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.