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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 92736.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92736.p1 | 92736cq2 | \([0, 0, 0, -15564, 3411056]\) | \(-2181825073/25039686\) | \(-4785158512705536\) | \([]\) | \(552960\) | \(1.6906\) | |
| 92736.p2 | 92736cq1 | \([0, 0, 0, 1716, -120976]\) | \(2924207/34776\) | \(-6645797093376\) | \([]\) | \(184320\) | \(1.1413\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92736.p have rank \(2\).
Complex multiplication
The elliptic curves in class 92736.p do not have complex multiplication.Modular form 92736.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
