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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 95106.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95106.k1 | 95106h2 | \([1, 0, 1, -27472448, 55421158340]\) | \(1294373635812597347281/2083292441154\) | \(3690679640343221394\) | \([]\) | \(5670000\) | \(2.8270\) | |
95106.k2 | 95106h1 | \([1, 0, 1, -258338, -48058540]\) | \(1076291879750641/60150618144\) | \(106560489229802784\) | \([]\) | \(1134000\) | \(2.0223\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95106.k have rank \(1\).
Complex multiplication
The elliptic curves in class 95106.k do not have complex multiplication.Modular form 95106.2.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.