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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 176890.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176890.by1 | 176890el2 | \([1, 1, 0, -177258, 28652198]\) | \(-5452947409/250\) | \(-28239290070250\) | \([]\) | \(1292760\) | \(1.6566\) | |
176890.by2 | 176890el1 | \([1, 1, 0, -368, 102152]\) | \(-49/40\) | \(-4518286411240\) | \([]\) | \(430920\) | \(1.1073\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176890.by have rank \(0\).
Complex multiplication
The elliptic curves in class 176890.by do not have complex multiplication.Modular form 176890.2.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.