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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 451770bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
451770.bp1 | 451770bp1 | \([1, 1, 1, 10239, 653199]\) | \(46268279/97680\) | \(-250620155631120\) | \([]\) | \(1838592\) | \(1.4472\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 451770bp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 451770bp do not have complex multiplication.Modular form 451770.2.a.bp
sage: E.q_eigenform(10)