Properties

Label 6690.f
Number of curves $1$
Conductor $6690$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 6690.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6690.f1 6690e1 \([1, 0, 1, -38, -94]\) \(-5841725401/167250\) \(-167250\) \([]\) \(1080\) \(-0.21806\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6690.f1 has rank \(0\).

Complex multiplication

The elliptic curves in class 6690.f do not have complex multiplication.

Modular form 6690.2.a.f

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