Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 80223a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80223.i1 80223a1 \([0, -1, 1, 103, 2474]\) \(89915392/2094417\) \(-2787669027\) \([]\) \(51840\) \(0.49260\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 80223a1 has rank \(1\).

Complex multiplication

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

Modular form 80223.2.a.a

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