Properties

Label 389.a
Number of curves 11
Conductor 389389
CM no
Rank 22

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

Elliptic curves in class 389.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
389.a1 389a1 [0,1,1,2,0][0, 1, 1, -2, 0] 1404928/3891404928/389 389389 [][] 4040 0.79564-0.79564 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 389.a1 has rank 22.

Complex multiplication

The elliptic curves in class 389.a do not have complex multiplication.

Modular form 389.2.a.a

sage: E.q_eigenform(10)
 
q2q22q3+2q43q5+4q65q7+q9+6q104q114q123q13+10q14+6q154q166q172q18+5q19+O(q20)q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} + q^{9} + 6 q^{10} - 4 q^{11} - 4 q^{12} - 3 q^{13} + 10 q^{14} + 6 q^{15} - 4 q^{16} - 6 q^{17} - 2 q^{18} + 5 q^{19} + O(q^{20}) Copy content Toggle raw display