Properties

Label 82110.g
Number of curves 11
Conductor 8211082110
CM no
Rank 11

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

Elliptic curves in class 82110.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
82110.g1 82110g1 [1,1,0,633,6867][1, 1, 0, -633, -6867] 28119423707929/2562817320-28119423707929/2562817320 2562817320-2562817320 [][] 6912069120 0.548250.54825 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 82110.g1 has rank 11.

Complex multiplication

The elliptic curves in class 82110.g do not have complex multiplication.

Modular form 82110.2.a.g

sage: E.q_eigenform(10)
 
qq2q3+q4q5+q6+q7q8+q9+q10+5q11q122q13q14+q15+q16+q17q18q19+O(q20)q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + 5 q^{11} - q^{12} - 2 q^{13} - q^{14} + q^{15} + q^{16} + q^{17} - q^{18} - q^{19} + O(q^{20}) Copy content Toggle raw display