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SageMath
E = EllipticCurve("ki1")
E.isogeny_class()
Elliptic curves in class 221760.ki
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221760.ki1 | 221760fs1 | \([0, 0, 0, -137472, -19618664]\) | \(10392086293512192/1684375\) | \(46569600000\) | \([2]\) | \(798720\) | \(1.4489\) | \(\Gamma_0(N)\)-optimal |
221760.ki2 | 221760fs2 | \([0, 0, 0, -137052, -19744496]\) | \(-643570518871152/8271484375\) | \(-3659040000000000\) | \([2]\) | \(1597440\) | \(1.7955\) |
Rank
sage: E.rank()
The elliptic curves in class 221760.ki have rank \(0\).
Complex multiplication
The elliptic curves in class 221760.ki do not have complex multiplication.Modular form 221760.2.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.