Properties

Label 550.g
Number of curves 11
Conductor 550550
CM no
Rank 00

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 550.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
550.g1 550e1 [1,1,0,367,10541][1, -1, 0, -367, 10541] 2803221/22528-2803221/22528 44000000000-44000000000 [][] 880880 0.725110.72511 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 550.g1 has rank 00.

Complex multiplication

The elliptic curves in class 550.g do not have complex multiplication.

Modular form 550.2.a.g

sage: E.q_eigenform(10)
 
qq2+3q3+q43q6+q7q8+6q9q11+3q12q14+q16+5q176q187q19+O(q20)q - q^{2} + 3 q^{3} + q^{4} - 3 q^{6} + q^{7} - q^{8} + 6 q^{9} - q^{11} + 3 q^{12} - q^{14} + q^{16} + 5 q^{17} - 6 q^{18} - 7 q^{19} + O(q^{20}) Copy content Toggle raw display