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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 34496.cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34496.cw1 | 34496dm2 | \([0, -1, 0, -321505, 70273281]\) | \(1389715708/11\) | \(29090753871872\) | \([2]\) | \(344064\) | \(1.7560\) | |
| 34496.cw2 | 34496dm1 | \([0, -1, 0, -19665, 1151921]\) | \(-1272112/121\) | \(-79999573147648\) | \([2]\) | \(172032\) | \(1.4094\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34496.cw have rank \(0\).
Complex multiplication
The elliptic curves in class 34496.cw do not have complex multiplication.Modular form 34496.2.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 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.
