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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 17600.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17600.v1 | 17600dj2 | \([0, 1, 0, -8833, 254463]\) | \(595508/121\) | \(15488000000000\) | \([2]\) | \(51200\) | \(1.2466\) | |
17600.v2 | 17600dj1 | \([0, 1, 0, 1167, 24463]\) | \(5488/11\) | \(-352000000000\) | \([2]\) | \(25600\) | \(0.90003\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17600.v have rank \(0\).
Complex multiplication
The elliptic curves in class 17600.v do not have complex multiplication.Modular form 17600.2.a.v
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.