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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 221067bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221067.bi1 | 221067bf1 | \([1, -1, 0, -1847511, 16366811764]\) | \(-36883367257/6098396283\) | \(-115310809763674414242507\) | \([]\) | \(13685760\) | \(3.1045\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 221067bf1 has rank \(1\).
Complex multiplication
The elliptic curves in class 221067bf do not have complex multiplication.Modular form 221067.2.a.bf
sage: E.q_eigenform(10)