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SageMath
sage: E = EllipticCurve("w1")
sage: E.isogeny_class()
Elliptic curves in class 221067.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221067.w1 | 221067v1 | \([0, 0, 1, -264, -10112]\) | \(-23068672/487403\) | \(-42993331227\) | \([]\) | \(144000\) | \(0.72122\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 221067.w1 has rank \(2\).
Complex multiplication
The elliptic curves in class 221067.w do not have complex multiplication.Modular form 221067.2.a.w
sage: E.q_eigenform(10)