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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 235950.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235950.w1 | 235950w1 | \([1, 1, 0, -2125, -87875]\) | \(-561712921/1404000\) | \(-2654437500000\) | \([]\) | \(414720\) | \(1.0718\) | \(\Gamma_0(N)\)-optimal |
235950.w2 | 235950w2 | \([1, 1, 0, 18500, 1954000]\) | \(370336757879/1079869440\) | \(-2041628160000000\) | \([]\) | \(1244160\) | \(1.6211\) |
Rank
sage: E.rank()
The elliptic curves in class 235950.w have rank \(1\).
Complex multiplication
The elliptic curves in class 235950.w do not have complex multiplication.Modular form 235950.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.