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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 69828.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69828.w1 | 69828bd1 | \([0, 1, 0, -16007716, 52750061396]\) | \(-22628157757264/46877879169\) | \(-939789543835662210941184\) | \([]\) | \(8107776\) | \(3.2891\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 69828.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 69828.w do not have complex multiplication.Modular form 69828.2.a.w
sage: E.q_eigenform(10)