Properties

Label 139.a
Number of curves $1$
Conductor $139$
CM no
Rank $0$

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

Elliptic curves in class 139.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139.a1 139a1 \([1, 1, 0, -3, -4]\) \(-4826809/139\) \(-139\) \([]\) \(6\) \(-0.80932\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 139.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 139.a do not have complex multiplication.

Modular form 139.2.a.a

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