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SageMath
E = EllipticCurve("ki1")
E.isogeny_class()
Elliptic curves in class 114240.ki
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
114240.ki1 | 114240ex2 | \([0, 1, 0, -33185, 1703103]\) | \(15417797707369/4080067320\) | \(1069565167534080\) | \([2]\) | \(442368\) | \(1.5924\) | |
114240.ki2 | 114240ex1 | \([0, 1, 0, 5215, 174783]\) | \(59822347031/83966400\) | \(-22011287961600\) | \([2]\) | \(221184\) | \(1.2458\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 114240.ki have rank \(1\).
Complex multiplication
The elliptic curves in class 114240.ki do not have complex multiplication.Modular form 114240.2.a.ki
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.