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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 5544.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5544.e1 | 5544y2 | \([0, 0, 0, -2091, 36790]\) | \(1354435492/539\) | \(402361344\) | \([2]\) | \(3072\) | \(0.61502\) | |
5544.e2 | 5544y1 | \([0, 0, 0, -111, 754]\) | \(-810448/847\) | \(-158070528\) | \([2]\) | \(1536\) | \(0.26845\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5544.e have rank \(1\).
Complex multiplication
The elliptic curves in class 5544.e do not have complex multiplication.Modular form 5544.2.a.e
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.