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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 58443.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58443.k1 | 58443n2 | \([0, 1, 1, -85169, 9538139]\) | \(564661380021747712/27978783021\) | \(3385432745541\) | \([]\) | \(186624\) | \(1.4757\) | |
58443.k2 | 58443n1 | \([0, 1, 1, -2009, -14866]\) | \(7414712369152/3571421301\) | \(432141977421\) | \([]\) | \(62208\) | \(0.92636\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58443.k have rank \(1\).
Complex multiplication
The elliptic curves in class 58443.k do not have complex multiplication.Modular form 58443.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.