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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2736k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2736.r2 | 2736k1 | \([0, 0, 0, -459, 378]\) | \(132651/76\) | \(6127239168\) | \([2]\) | \(1152\) | \(0.56769\) | \(\Gamma_0(N)\)-optimal |
2736.r1 | 2736k2 | \([0, 0, 0, -4779, -126630]\) | \(149721291/722\) | \(58208772096\) | \([2]\) | \(2304\) | \(0.91427\) |
Rank
sage: E.rank()
The elliptic curves in class 2736k have rank \(1\).
Complex multiplication
The elliptic curves in class 2736k do not have complex multiplication.Modular form 2736.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.