Properties

Label 80223.p
Number of curves $1$
Conductor $80223$
CM no
Rank $1$

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Show commands: 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)
 
\(q + q^{2} + q^{3} - q^{4} + 3 q^{5} + q^{6} - 2 q^{7} - 3 q^{8} + q^{9} + 3 q^{10} - q^{12} - q^{13} - 2 q^{14} + 3 q^{15} - q^{16} - q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display