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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 5850.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5850.bp1 | 5850bl1 | \([1, -1, 1, -80915, 9430067]\) | \(-3214683778008145/238496514048\) | \(-4346598968524800\) | \([]\) | \(30912\) | \(1.7495\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5850.bp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5850.bp do not have complex multiplication.Modular form 5850.2.a.bp
sage: E.q_eigenform(10)