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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 80223.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80223.p1 | 80223k1 | \([1, 0, 1, 1049188, 608136923]\) | \(595857993887783/1089934767909\) | \(-233637197211967949829\) | \([]\) | \(2640000\) | \(2.5931\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 80223.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 80223.p do not have complex multiplication.Modular form 80223.2.a.p
sage: E.q_eigenform(10)