Properties

Label 20339.a
Number of curves $1$
Conductor $20339$
CM no
Rank $1$

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

Elliptic curves in class 20339.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20339.a1 20339e1 \([1, 1, 1, -490, 2934]\) \(7037694889/1771561\) \(3275616289\) \([]\) \(8064\) \(0.53571\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20339.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 20339.a do not have complex multiplication.

Modular form 20339.2.a.a

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