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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 190575.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190575.bf1 | 190575bc1 | \([1, -1, 1, 19645, -186128]\) | \(1382658525/823543\) | \(-499426843348125\) | \([]\) | \(677376\) | \(1.5097\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 190575.bf1 has rank \(1\).
Complex multiplication
The elliptic curves in class 190575.bf do not have complex multiplication.Modular form 190575.2.a.bf
sage: E.q_eigenform(10)