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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 197106by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
197106.be1 | 197106by1 | \([1, 0, 1, -36274732, 84569973098]\) | \(-112205650221491190337/745029571313664\) | \(-35050572553503650217984\) | \([]\) | \(34186320\) | \(3.1615\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 197106by1 has rank \(0\).
Complex multiplication
The elliptic curves in class 197106by do not have complex multiplication.Modular form 197106.2.a.by
sage: E.q_eigenform(10)