Properties

Label 80223l
Number of curves $1$
Conductor $80223$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 80223l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80223.r1 80223l1 \([0, 1, 1, -209854, -121518809]\) \(-39404941312/222861483\) \(-5780452911779543283\) \([]\) \(2078208\) \(2.2840\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 80223l1 has rank \(1\).

Complex multiplication

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

Modular form 80223.2.a.l

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