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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 34650.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
34650.w1 | 34650d1 | \([1, -1, 0, -523167, 145761741]\) | \(37537160298467283/5519360000\) | \(2328480000000000\) | \([2]\) | \(344064\) | \(1.9629\) | \(\Gamma_0(N)\)-optimal |
34650.w2 | 34650d2 | \([1, -1, 0, -475167, 173553741]\) | \(-28124139978713043/14526050000000\) | \(-6128177343750000000\) | \([2]\) | \(688128\) | \(2.3095\) |
Rank
sage: E.rank()
The elliptic curves in class 34650.w have rank \(0\).
Complex multiplication
The elliptic curves in class 34650.w do not have complex multiplication.Modular form 34650.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.