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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 76050eq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76050.ef2 | 76050eq1 | \([1, -1, 1, -1997105, 1143788897]\) | \(-16022066761/998400\) | \(-54892402671600000000\) | \([2]\) | \(2580480\) | \(2.5418\) | \(\Gamma_0(N)\)-optimal |
| 76050.ef1 | 76050eq2 | \([1, -1, 1, -32417105, 71048948897]\) | \(68523370149961/243360\) | \(13380023151202500000\) | \([2]\) | \(5160960\) | \(2.8883\) |
Rank
sage: E.rank()
The elliptic curves in class 76050eq have rank \(1\).
Complex multiplication
The elliptic curves in class 76050eq do not have complex multiplication.Modular form 76050.2.a.eq
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
