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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 406503.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
406503.w1 | 406503w1 | \([0, 0, 1, -106671, 5086813]\) | \(207474688/102789\) | \(66503473966539261\) | \([]\) | \(6854400\) | \(1.9210\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 406503.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 406503.w do not have complex multiplication.Modular form 406503.2.a.w
sage: E.q_eigenform(10)