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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 160446.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160446.w1 | 160446r4 | \([1, 1, 1, -132074, -18528949]\) | \(143820170742457/5826444\) | \(10321900959084\) | \([2]\) | \(737280\) | \(1.5794\) | |
| 160446.w2 | 160446r3 | \([1, 1, 1, -40114, 2832875]\) | \(4029546653497/351790452\) | \(623218244935572\) | \([2]\) | \(737280\) | \(1.5794\) | |
| 160446.w3 | 160446r2 | \([1, 1, 1, -8654, -262789]\) | \(40459583737/7033104\) | \(12459572755344\) | \([2, 2]\) | \(368640\) | \(1.2328\) | |
| 160446.w4 | 160446r1 | \([1, 1, 1, 1026, -22725]\) | \(67419143/169728\) | \(-300683505408\) | \([2]\) | \(184320\) | \(0.88625\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 160446.w have rank \(1\).
Complex multiplication
The elliptic curves in class 160446.w do not have complex multiplication.Modular form 160446.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
