Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("786.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 786a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
786.c1 786a1 [1, 1, 0, -8, 6] [] 40 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 786a1 has rank \(1\).

Modular form 786.2.a.c

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