Properties

Label 850.h
Number of curves 11
Conductor 850850
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 850.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
850.h1 850l1 [1,1,1,18,31][1, 1, 1, -18, 31] 5177717/2176-5177717/2176 272000-272000 [][] 112112 0.24929-0.24929 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 850.h1 has rank 11.

Complex multiplication

The elliptic curves in class 850.h do not have complex multiplication.

Modular form 850.2.a.h

sage: E.q_eigenform(10)
 
q+q2q3+q4q6+q82q96q11q123q13+q16q172q187q19+O(q20)q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} - 2 q^{9} - 6 q^{11} - q^{12} - 3 q^{13} + q^{16} - q^{17} - 2 q^{18} - 7 q^{19} + O(q^{20}) Copy content Toggle raw display