Properties

Label 25751a
Number of curves 11
Conductor 2575125751
CM no
Rank 33

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

Elliptic curves in class 25751a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25751.a1 25751a1 [1,0,0,39,94][1, 0, 0, -39, 94] 6570725617/283261-6570725617/283261 283261-283261 [][] 34563456 0.18802-0.18802 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 25751a1 has rank 33.

Complex multiplication

The elliptic curves in class 25751a do not have complex multiplication.

Modular form 25751.2.a.a

sage: E.q_eigenform(10)
 
qq22q3q42q5+2q63q7+3q8+q9+2q10q11+2q125q13+3q14+4q15q166q17q188q19+O(q20)q - q^{2} - 2 q^{3} - q^{4} - 2 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + q^{9} + 2 q^{10} - q^{11} + 2 q^{12} - 5 q^{13} + 3 q^{14} + 4 q^{15} - q^{16} - 6 q^{17} - q^{18} - 8 q^{19} + O(q^{20}) Copy content Toggle raw display