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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 29040.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29040.p1 | 29040a2 | \([0, -1, 0, -957876, 361157040]\) | \(161019290864/135\) | \(81490672200960\) | \([2]\) | \(304128\) | \(1.9721\) | |
29040.p2 | 29040a1 | \([0, -1, 0, -59451, 5740110]\) | \(-615962624/18225\) | \(-687577546695600\) | \([2]\) | \(152064\) | \(1.6255\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29040.p have rank \(1\).
Complex multiplication
The elliptic curves in class 29040.p do not have complex multiplication.Modular form 29040.2.a.p
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.