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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 27200bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27200.b1 | 27200bp1 | \([0, 0, 0, 500, -50000]\) | \(216/17\) | \(-1088000000000\) | \([]\) | \(79360\) | \(0.98913\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 27200bp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 27200bp do not have complex multiplication.Modular form 27200.2.a.bp
sage: E.q_eigenform(10)