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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 426888.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
426888.by1 | 426888by2 | \([0, 0, 0, -5923071, -5546875950]\) | \(21882096/7\) | \(7351460851466882304\) | \([2]\) | \(12902400\) | \(2.5949\) | \(\Gamma_0(N)\)-optimal* |
426888.by2 | 426888by1 | \([0, 0, 0, -320166, -110937519]\) | \(-55296/49\) | \(-3216264122516761008\) | \([2]\) | \(6451200\) | \(2.2483\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 426888.by have rank \(1\).
Complex multiplication
The elliptic curves in class 426888.by do not have complex multiplication.Modular form 426888.2.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.