Properties

Label 2550.r
Number of curves 11
Conductor 25502550
CM no
Rank 00

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 2550.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2550.r1 2550t1 [1,1,1,3,9][1, 1, 1, -3, -9] 121945/918-121945/918 22950-22950 [][] 360360 0.48024-0.48024 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2550.r1 has rank 00.

Complex multiplication

The elliptic curves in class 2550.r do not have complex multiplication.

Modular form 2550.2.a.r

sage: E.q_eigenform(10)
 
q+q2q3+q4q64q7+q8+q92q11q126q134q14+q16q17+q18+4q19+O(q20)q + q^{2} - q^{3} + q^{4} - q^{6} - 4 q^{7} + q^{8} + q^{9} - 2 q^{11} - q^{12} - 6 q^{13} - 4 q^{14} + q^{16} - q^{17} + q^{18} + 4 q^{19} + O(q^{20}) Copy content Toggle raw display