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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 47025.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47025.w1 | 47025q2 | \([0, 0, 1, -6764250, 6771386281]\) | \(-3004935183806464000/2037123\) | \(-23204104171875\) | \([]\) | \(622080\) | \(2.3142\) | |
| 47025.w2 | 47025q1 | \([0, 0, 1, -81750, 9698656]\) | \(-5304438784000/497763387\) | \(-5669836080046875\) | \([]\) | \(207360\) | \(1.7649\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47025.w have rank \(1\).
Complex multiplication
The elliptic curves in class 47025.w do not have complex multiplication.Modular form 47025.2.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.
