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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 23826.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23826.k1 | 23826e1 | \([1, 1, 0, -4122266, -3271873332]\) | \(-164668416049678897/2902956072984\) | \(-136572125957832578904\) | \([]\) | \(1425600\) | \(2.6608\) | \(\Gamma_0(N)\)-optimal |
23826.k2 | 23826e2 | \([1, 1, 0, 16054024, -15582041922]\) | \(9726437216910146543/7860157321308534\) | \(-369788025979560054848454\) | \([]\) | \(4276800\) | \(3.2101\) |
Rank
sage: E.rank()
The elliptic curves in class 23826.k have rank \(0\).
Complex multiplication
The elliptic curves in class 23826.k do not have complex multiplication.Modular form 23826.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.