Properties

Label 786j
Number of curves 1
Conductor 786
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("786.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 786j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
786.j1 786j1 [1, 1, 1, -861, 9267] [] 504 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 786j1 has rank \(1\).

Modular form 786.2.a.j

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