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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 253253.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 253253.k1 | 253253k3 | \([0, 1, 1, -1794388779, 29255943621790]\) | \(-360675992659311050823073792/56219378022244619\) | \(-99596057548465699480259\) | \([]\) | \(94478400\) | \(3.8173\) | |
| 253253.k2 | 253253k2 | \([0, 1, 1, -19305469, 50818948065]\) | \(-449167881463536812032/369990050199923699\) | \(-655459943322227028124139\) | \([]\) | \(31492800\) | \(3.2680\) | |
| 253253.k3 | 253253k1 | \([0, 1, 1, 1961491, -1132247660]\) | \(471114356703100928/585612268875179\) | \(-1037447856660780984419\) | \([]\) | \(10497600\) | \(2.7187\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 253253.k have rank \(0\).
Complex multiplication
The elliptic curves in class 253253.k do not have complex multiplication.Modular form 253253.2.a.k
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.
