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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 259182.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259182.w1 | 259182w2 | \([1, -1, 0, -60085053, 179278024261]\) | \(18575453384550358633/352517816448\) | \(455265468444413354112\) | \([2]\) | \(23224320\) | \(3.0876\) | |
259182.w2 | 259182w1 | \([1, -1, 0, -3631293, 2995513285]\) | \(-4100379159705193/626805817344\) | \(-809499635882640654336\) | \([2]\) | \(11612160\) | \(2.7411\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259182.w have rank \(0\).
Complex multiplication
The elliptic curves in class 259182.w do not have complex multiplication.Modular form 259182.2.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.