Properties

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

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

Elliptic curves in class 5077a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5077.a1 5077a1 \([0, 0, 1, -7, 6]\) \(37933056/5077\) \(5077\) \([]\) \(1984\) \(-0.56139\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 5077a do not have complex multiplication.

Modular form 5077.2.a.a

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