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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 84525.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84525.by1 | 84525bo1 | \([0, 1, 1, 35731617, 184993854644]\) | \(2744564518708084736/9629735831296875\) | \(-17702012356503844482421875\) | \([]\) | \(10782720\) | \(3.5276\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 84525.by1 has rank \(1\).
Complex multiplication
The elliptic curves in class 84525.by do not have complex multiplication.Modular form 84525.2.a.by
sage: E.q_eigenform(10)