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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 5850.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5850.w1 | 5850q2 | \([1, -1, 0, -2051156367, 35756293724541]\) | \(-134057911417971280740025/1872\) | \(-13327031250000\) | \([]\) | \(1344000\) | \(3.4980\) | |
| 5850.w2 | 5850q1 | \([1, -1, 0, -3197727, 2412033741]\) | \(-198417696411528597145/22989483914821632\) | \(-418983344347624243200\) | \([]\) | \(268800\) | \(2.6933\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5850.w have rank \(1\).
Complex multiplication
The elliptic curves in class 5850.w do not have complex multiplication.Modular form 5850.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
