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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 221067.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221067.bf1 | 221067bh1 | \([1, -1, 0, -3034521, 2035484644]\) | \(-289531596860402017/17410522563\) | \(-185827538955919707\) | \([]\) | \(3870720\) | \(2.3747\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 221067.bf1 has rank \(1\).
Complex multiplication
The elliptic curves in class 221067.bf do not have complex multiplication.Modular form 221067.2.a.bf
sage: E.q_eigenform(10)