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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 27200.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27200.bf1 | 27200bg1 | \([0, -1, 0, -8, -38]\) | \(-1600/17\) | \(-680000\) | \([]\) | \(3456\) | \(-0.19874\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 27200.bf1 has rank \(0\).
Complex multiplication
The elliptic curves in class 27200.bf do not have complex multiplication.Modular form 27200.2.a.bf
sage: E.q_eigenform(10)