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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 53550.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53550.d1 | 53550l2 | \([1, -1, 0, -357, 2601]\) | \(1493271207/56644\) | \(191173500\) | \([2]\) | \(24576\) | \(0.35732\) | |
53550.d2 | 53550l1 | \([1, -1, 0, -57, -99]\) | \(6128487/1904\) | \(6426000\) | \([2]\) | \(12288\) | \(0.010746\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53550.d have rank \(2\).
Complex multiplication
The elliptic curves in class 53550.d do not have complex multiplication.Modular form 53550.2.a.d
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.