Properties

Label 47937f
Number of curves 11
Conductor 4793747937
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 47937f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47937.f1 47937f1 [0,1,1,1962,36155][0, 1, 1, -1962, 36155] 1404928/171-1404928/171 101714787891-101714787891 [][] 100352100352 0.847100.84710 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47937f1 has rank 11.

Complex multiplication

The elliptic curves in class 47937f do not have complex multiplication.

Modular form 47937.2.a.f

sage: E.q_eigenform(10)
 
q+2q2+q3+2q43q5+2q65q7+q96q10q11+2q12+2q1310q143q154q16+q17+2q18+q19+O(q20)q + 2 q^{2} + q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} + q^{9} - 6 q^{10} - q^{11} + 2 q^{12} + 2 q^{13} - 10 q^{14} - 3 q^{15} - 4 q^{16} + q^{17} + 2 q^{18} + q^{19} + O(q^{20}) Copy content Toggle raw display