Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("786.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 786k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
786.i1 786k1 [1, 1, 1, 10, 11] [] 144 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 786k1 has rank \(1\).

Modular form 786.2.a.i

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