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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 148225by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148225.by2 | 148225by1 | \([1, 1, 0, -970, -13075]\) | \(-9317\) | \(-10850811125\) | \([]\) | \(69120\) | \(0.66397\) | \(\Gamma_0(N)\)-optimal |
148225.by1 | 148225by2 | \([1, 1, 0, -25178045, 48616918750]\) | \(-162677523113838677\) | \(-10850811125\) | \([]\) | \(2557440\) | \(2.4694\) |
Rank
sage: E.rank()
The elliptic curves in class 148225by have rank \(0\).
Complex multiplication
The elliptic curves in class 148225by do not have complex multiplication.Modular form 148225.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.