Properties

Label 18745.a
Number of curves 11
Conductor 1874518745
CM no
Rank 33

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

Elliptic curves in class 18745.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18745.a1 18745a1 [0,1,1,146,636][0, 1, 1, -146, 636] 346540109824/2155675-346540109824/2155675 2155675-2155675 [][] 1097610976 0.0535750.053575 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 18745.a1 has rank 33.

Complex multiplication

The elliptic curves in class 18745.a do not have complex multiplication.

Modular form 18745.2.a.a

sage: E.q_eigenform(10)
 
q2q22q3+2q4q5+4q64q7+q9+2q106q114q124q13+8q14+2q154q166q172q186q19+O(q20)q - 2 q^{2} - 2 q^{3} + 2 q^{4} - q^{5} + 4 q^{6} - 4 q^{7} + q^{9} + 2 q^{10} - 6 q^{11} - 4 q^{12} - 4 q^{13} + 8 q^{14} + 2 q^{15} - 4 q^{16} - 6 q^{17} - 2 q^{18} - 6 q^{19} + O(q^{20}) Copy content Toggle raw display