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SageMath
E = EllipticCurve("iz1")
E.isogeny_class()
Elliptic curves in class 169050iz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169050.k1 | 169050iz1 | \([1, 1, 0, -422650, 106052500]\) | \(-222564427157569/1144627200\) | \(-42941404800000000\) | \([]\) | \(2396160\) | \(2.0378\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 169050iz1 has rank \(0\).
Complex multiplication
The elliptic curves in class 169050iz do not have complex multiplication.Modular form 169050.2.a.iz
sage: E.q_eigenform(10)