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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 52272.cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52272.cv1 | 52272cd3 | \([0, 0, 0, -238491, -59439798]\) | \(-1167051/512\) | \(-658142326092201984\) | \([]\) | \(583200\) | \(2.1262\) | |
| 52272.cv2 | 52272cd1 | \([0, 0, 0, -6171, 189002]\) | \(-132651/2\) | \(-391840948224\) | \([]\) | \(64800\) | \(1.0276\) | \(\Gamma_0(N)\)-optimal |
| 52272.cv3 | 52272cd2 | \([0, 0, 0, 22869, 934362]\) | \(9261/8\) | \(-1142608205021184\) | \([]\) | \(194400\) | \(1.5769\) |
Rank
sage: E.rank()
The elliptic curves in class 52272.cv have rank \(1\).
Complex multiplication
The elliptic curves in class 52272.cv do not have complex multiplication.Modular form 52272.2.a.cv
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
