Properties

Label 83.a
Number of curves $1$
Conductor $83$
CM no
Rank $1$

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

Elliptic curves in class 83.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83.a1 83a1 \([1, 1, 1, 1, 0]\) \(103823/83\) \(-83\) \([]\) \(2\) \(-0.94387\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 83.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 83.a do not have complex multiplication.

Modular form 83.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} - 2 q^{9} + 2 q^{10} + 3 q^{11} + q^{12} - 6 q^{13} + 3 q^{14} + 2 q^{15} - q^{16} + 5 q^{17} + 2 q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display