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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 6566.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6566.p1 | 6566o1 | \([1, -1, 1, -18801, -984287]\) | \(18212205591/68608\) | \(2768580269056\) | \([]\) | \(49280\) | \(1.2467\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6566.p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 6566.p do not have complex multiplication.Modular form 6566.2.a.p
sage: E.q_eigenform(10)