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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 289578.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
289578.d1 | 289578d2 | \([1, 0, 1, -248691, -47753084]\) | \(70470585447625/4518018\) | \(109053971218242\) | \([2]\) | \(1769472\) | \(1.7513\) | |
289578.d2 | 289578d1 | \([1, 0, 1, -14601, -841448]\) | \(-14260515625/4382748\) | \(-105788882259612\) | \([2]\) | \(884736\) | \(1.4047\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 289578.d have rank \(0\).
Complex multiplication
The elliptic curves in class 289578.d do not have complex multiplication.Modular form 289578.2.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.