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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 187200.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187200.by1 | 187200cx2 | \([0, 0, 0, -1920, -32290]\) | \(671088640/2197\) | \(2562580800\) | \([]\) | \(155520\) | \(0.67076\) | |
187200.by2 | 187200cx1 | \([0, 0, 0, -120, 470]\) | \(163840/13\) | \(15163200\) | \([]\) | \(51840\) | \(0.12146\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 187200.by have rank \(0\).
Complex multiplication
The elliptic curves in class 187200.by do not have complex multiplication.Modular form 187200.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.