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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 115920.ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.ee1 | 115920cs1 | \([0, 0, 0, -66387, 6417234]\) | \(292583028222603/8456021875\) | \(935168371200000\) | \([2]\) | \(552960\) | \(1.6506\) | \(\Gamma_0(N)\)-optimal |
| 115920.ee2 | 115920cs2 | \([0, 0, 0, 15933, 21284226]\) | \(4044759171237/1771943359375\) | \(-195962760000000000\) | \([2]\) | \(1105920\) | \(1.9972\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.ee have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.ee do not have complex multiplication.Modular form 115920.2.a.ee
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.
