Properties

Label 1339.a
Number of curves $1$
Conductor $1339$
CM no
Rank $1$

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

Elliptic curves in class 1339.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1339.a1 1339a1 \([1, 1, 0, -137, -602]\) \(287626699801/38243179\) \(38243179\) \([]\) \(280\) \(0.18272\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1339.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1339.a do not have complex multiplication.

Modular form 1339.2.a.a

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