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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 51600.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51600.by1 | 51600bv1 | \([0, -1, 0, -9008, -319488]\) | \(1263214441/29025\) | \(1857600000000\) | \([2]\) | \(110592\) | \(1.1405\) | \(\Gamma_0(N)\)-optimal |
51600.by2 | 51600bv2 | \([0, -1, 0, 992, -999488]\) | \(1685159/6739605\) | \(-431334720000000\) | \([2]\) | \(221184\) | \(1.4871\) |
Rank
sage: E.rank()
The elliptic curves in class 51600.by have rank \(0\).
Complex multiplication
The elliptic curves in class 51600.by do not have complex multiplication.Modular form 51600.2.a.by
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.