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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2090.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2090.d1 | 2090i1 | \([1, 1, 0, -47, 709]\) | \(-11867954041/222543200\) | \(-222543200\) | \([]\) | \(640\) | \(0.28276\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2090.d1 has rank \(1\).
Complex multiplication
The elliptic curves in class 2090.d do not have complex multiplication.Modular form 2090.2.a.d
sage: E.q_eigenform(10)