Properties

Label 82110u
Number of curves 11
Conductor 8211082110
CM no
Rank 22

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 82110u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
82110.s1 82110u1 [1,0,1,46826,13756472][1, 0, 1, 46826, 13756472] 11355289913493692711/8827688329173000011355289913493692711/88276883291730000 88276883291730000-88276883291730000 [][] 11980801198080 1.93311.9331 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 82110u1 has rank 22.

Complex multiplication

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

Modular form 82110.2.a.u

sage: E.q_eigenform(10)
 
qq2+q3+q4q5q6q7q8+q9+q105q11+q12q13+q14q15+q16+q17q187q19+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} - q^{13} + q^{14} - q^{15} + q^{16} + q^{17} - q^{18} - 7 q^{19} + O(q^{20}) Copy content Toggle raw display