Properties

Label 53176.a
Number of curves 11
Conductor 5317653176
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 53176.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53176.a1 53176b1 [0,0,0,15895,771341][0, 0, 0, -15895, -771341] 1149984000/23-1149984000/23 8882625392-8882625392 [][] 110592110592 1.02971.0297 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53176.a1 has rank 11.

Complex multiplication

The elliptic curves in class 53176.a do not have complex multiplication.

Modular form 53176.2.a.a

sage: E.q_eigenform(10)
 
q3q3+2q7+6q95q13+6q19+O(q20)q - 3 q^{3} + 2 q^{7} + 6 q^{9} - 5 q^{13} + 6 q^{19} + O(q^{20}) Copy content Toggle raw display