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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 200277.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200277.w1 | 200277w1 | \([1, -1, 0, -25263567, -48839419310]\) | \(350662100640625/246071287\) | \(1251353002642581797343\) | \([]\) | \(14688000\) | \(2.9845\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 200277.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 200277.w do not have complex multiplication.Modular form 200277.2.a.w
sage: E.q_eigenform(10)