Properties

Label 4704.h
Number of curves 11
Conductor 47044704
CM no
Rank 11

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

Elliptic curves in class 4704.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4704.h1 4704b1 [0,1,0,653,6693][0, -1, 0, -653, 6693] 3136000/27-3136000/27 265531392-265531392 [][] 17281728 0.441430.44143 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4704.h1 has rank 11.

Complex multiplication

The elliptic curves in class 4704.h do not have complex multiplication.

Modular form 4704.2.a.h

sage: E.q_eigenform(10)
 
qq3+q92q11+5q132q173q19+O(q20)q - q^{3} + q^{9} - 2 q^{11} + 5 q^{13} - 2 q^{17} - 3 q^{19} + O(q^{20}) Copy content Toggle raw display