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SageMath
sage: E = EllipticCurve("dw1")
sage: E.isogeny_class()
Elliptic curves in class 422370.dw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
422370.dw1 | 422370dw6 | [1, -1, 1, -29289803, -61005726943] | [2] | 28311552 | |
422370.dw2 | 422370dw3 | [1, -1, 1, -2745473, 1750254581] | [2] | 14155776 | \(\Gamma_0(N)\)-optimal* |
422370.dw3 | 422370dw4 | [1, -1, 1, -1835753, -947247163] | [2, 2] | 14155776 | |
422370.dw4 | 422370dw5 | [1, -1, 1, -373703, -2415730183] | [2] | 28311552 | |
422370.dw5 | 422370dw2 | [1, -1, 1, -211253, 13807037] | [2, 2] | 7077888 | \(\Gamma_0(N)\)-optimal* |
422370.dw6 | 422370dw1 | [1, -1, 1, 48667, 1642781] | [2] | 3538944 | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 422370.dw have rank \(0\).
Complex multiplication
The elliptic curves in class 422370.dw do not have complex multiplication.Modular form 422370.2.a.dw
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.