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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 208725.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
208725.bp1 | 208725bg1 | \([0, 1, 1, 75827, -4407386]\) | \(217732612096/164333367\) | \(-36390822996985875\) | \([]\) | \(1152000\) | \(1.8659\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 208725.bp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 208725.bp do not have complex multiplication.Modular form 208725.2.a.bp
sage: E.q_eigenform(10)