Properties

Label 5077a
Number of curves 1
Conductor 5077
CM no
Rank 3

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Show commands for: SageMath

sage: E = EllipticCurve("5077.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5077a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5077.a1 5077a1 [0, 0, 1, -7, 6] [] 1984 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5077a1 has rank \(3\).

Modular form 5077.2.a.a

sage: E.q_eigenform(10)
 
\( q - 2q^{2} - 3q^{3} + 2q^{4} - 4q^{5} + 6q^{6} - 4q^{7} + 6q^{9} + 8q^{10} - 6q^{11} - 6q^{12} - 4q^{13} + 8q^{14} + 12q^{15} - 4q^{16} - 4q^{17} - 12q^{18} - 7q^{19} + O(q^{20}) \)