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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 84150cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.b1 | 84150cw1 | \([1, -1, 0, -32439087, -71130579539]\) | \(-207139083365807493797785/85489525815181312\) | \(-1558046607981679411200\) | \([]\) | \(10699776\) | \(3.0287\) | \(\Gamma_0(N)\)-optimal |
| 84150.b2 | 84150cw2 | \([1, -1, 0, 21726738, -275925373484]\) | \(62235723945184256321015/1840622012131251847168\) | \(-33545336171092064914636800\) | \([]\) | \(32099328\) | \(3.5780\) |
Rank
sage: E.rank()
The elliptic curves in class 84150cw have rank \(0\).
Complex multiplication
The elliptic curves in class 84150cw do not have complex multiplication.Modular form 84150.2.a.cw
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 Cremona 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 Cremona labels.
