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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 388080.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.by1 | 388080by2 | \([0, 0, 0, -639095583, 6217881062218]\) | \(1314817350433665559504/190690249278375\) | \(4186819326241093870944000\) | \([2]\) | \(123863040\) | \(3.7394\) | |
388080.by2 | 388080by1 | \([0, 0, 0, -36303708, 115577794843]\) | \(-3856034557002072064/1973796785296875\) | \(-2708558302674924834750000\) | \([2]\) | \(61931520\) | \(3.3929\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388080.by have rank \(0\).
Complex multiplication
The elliptic curves in class 388080.by do not have complex multiplication.Modular form 388080.2.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.