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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 52983.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52983.k1 | 52983b2 | \([1, -1, 0, -268857, -53092422]\) | \(4956477625/52983\) | \(22974817008059847\) | \([2]\) | \(430080\) | \(1.9552\) | |
52983.k2 | 52983b1 | \([1, -1, 0, -3942, -2069793]\) | \(-15625/4263\) | \(-1848548494901367\) | \([2]\) | \(215040\) | \(1.6086\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 52983.k have rank \(1\).
Complex multiplication
The elliptic curves in class 52983.k do not have complex multiplication.Modular form 52983.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.