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SageMath
E = EllipticCurve("kf1")
E.isogeny_class()
Elliptic curves in class 296450.kf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296450.kf1 | 296450kf2 | \([1, 1, 1, -553638, -158661469]\) | \(553463785/512\) | \(17361297800000000\) | \([]\) | \(4665600\) | \(2.0392\) | |
296450.kf2 | 296450kf1 | \([1, 1, 1, -24263, 1209781]\) | \(46585/8\) | \(271270278125000\) | \([]\) | \(1555200\) | \(1.4899\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 296450.kf have rank \(1\).
Complex multiplication
The elliptic curves in class 296450.kf do not have complex multiplication.Modular form 296450.2.a.kf
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.