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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 52325.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52325.g1 | 52325d3 | \([0, -1, 1, -370741483, -2747485524632]\) | \(-360675992659311050823073792/56219378022244619\) | \(-878427781597572171875\) | \([]\) | \(7558272\) | \(3.4230\) | |
| 52325.g2 | 52325d2 | \([0, -1, 1, -3988733, -4771903257]\) | \(-449167881463536812032/369990050199923699\) | \(-5781094534373807796875\) | \([]\) | \(2519424\) | \(2.8737\) | |
| 52325.g3 | 52325d1 | \([0, -1, 1, 405267, 106260618]\) | \(471114356703100928/585612268875179\) | \(-9150191701174671875\) | \([]\) | \(839808\) | \(2.3244\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 52325.g have rank \(0\).
Complex multiplication
The elliptic curves in class 52325.g do not have complex multiplication.Modular form 52325.2.a.g
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
