Properties

Label 249690.h
Number of curves 11
Conductor 249690249690
CM no
Rank 11

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

Elliptic curves in class 249690.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249690.h1 249690h1 [1,1,0,221797,36890509][1, 1, 0, -221797, 36890509] 1206684612015266606041/1074505958400000001206684612015266606041/107450595840000000 107450595840000000107450595840000000 [][] 31046403104640 2.00792.0079 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 249690.h1 has rank 11.

Complex multiplication

The elliptic curves in class 249690.h do not have complex multiplication.

Modular form 249690.2.a.h

sage: E.q_eigenform(10)
 
qq2q3+q4+q5+q6q7q8+q9q103q11q12q13+q14q15+q16+4q17q18+q19+O(q20)q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - 3 q^{11} - q^{12} - q^{13} + q^{14} - q^{15} + q^{16} + 4 q^{17} - q^{18} + q^{19} + O(q^{20}) Copy content Toggle raw display