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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 18150.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18150.k1 | 18150e2 | \([1, 1, 0, -43464775, -80555859875]\) | \(2711280982499089/732421875000\) | \(2453142711639404296875000\) | \([]\) | \(3421440\) | \(3.3880\) | |
18150.k2 | 18150e1 | \([1, 1, 0, -15513775, 23505713125]\) | \(123286270205329/43200000\) | \(144692244675000000000\) | \([]\) | \(1140480\) | \(2.8387\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18150.k have rank \(0\).
Complex multiplication
The elliptic curves in class 18150.k do not have complex multiplication.Modular form 18150.2.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.