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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 175450.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
175450.bm1 | 175450cz1 | \([1, -1, 0, -3592, -118684]\) | \(-185193/116\) | \(-3210954312500\) | \([]\) | \(617760\) | \(1.1014\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 175450.bm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 175450.bm do not have complex multiplication.Modular form 175450.2.a.bm
sage: E.q_eigenform(10)