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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 92400.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.k1 | 92400dj2 | \([0, -1, 0, -347903333, 2497791377037]\) | \(116423188793017446400/91315917\) | \(3652636680000000000\) | \([]\) | \(10560000\) | \(3.3019\) | |
| 92400.k2 | 92400dj1 | \([0, -1, 0, -1080773, -184639443]\) | \(1363413585016606720/644626239703677\) | \(66009726945656524800\) | \([]\) | \(2112000\) | \(2.4972\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.k have rank \(0\).
Complex multiplication
The elliptic curves in class 92400.k do not have complex multiplication.Modular form 92400.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
