Properties

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

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 80223.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80223.g1 80223q1 \([1, 0, 0, 8671, -456114]\) \(595857993887783/1089934767909\) \(-131882106916989\) \([]\) \(240000\) \(1.3941\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 80223.g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 80223.g do not have complex multiplication.

Modular form 80223.2.a.g

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