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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 2160.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2160.q1 | 2160v1 | \([0, 0, 0, -2547, -49486]\) | \(-16522921323/4000\) | \(-442368000\) | \([]\) | \(1440\) | \(0.64777\) | \(\Gamma_0(N)\)-optimal |
| 2160.q2 | 2160v2 | \([0, 0, 0, 1053, -174366]\) | \(1601613/163840\) | \(-13209037701120\) | \([]\) | \(4320\) | \(1.1971\) |
Rank
sage: E.rank()
The elliptic curves in class 2160.q have rank \(0\).
Complex multiplication
The elliptic curves in class 2160.q do not have complex multiplication.Modular form 2160.2.a.q
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.
