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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 259182.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259182.ba1 | 259182ba2 | \([1, -1, 0, -5796588, -5370180480]\) | \(338332037348241/653072\) | \(41577559590332304\) | \([2]\) | \(7028736\) | \(2.4426\) | |
| 259182.ba2 | 259182ba1 | \([1, -1, 0, -366108, -81979056]\) | \(85242093201/3625216\) | \(230797881807558912\) | \([2]\) | \(3514368\) | \(2.0960\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259182.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 259182.ba do not have complex multiplication.Modular form 259182.2.a.ba
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.
