Properties

Label 2166.c
Number of curves $1$
Conductor $2166$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2166.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2166.c1 2166e1 \([1, 0, 1, 87, 412]\) \(205083359/314928\) \(-113689008\) \([]\) \(1296\) \(0.23106\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2166.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2166.c do not have complex multiplication.

Modular form 2166.2.a.c

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