Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("786.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 786c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
786.e1 786c1 [1, 1, 0, 1217, 6622405] [] 12960 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 786c1 has rank \(1\).

Modular form 786.2.a.e

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