Properties

Label 16811.a
Number of curves $1$
Conductor $16811$
CM no
Rank $3$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 16811.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16811.a1 16811a1 \([0, 0, 1, -1, 6]\) \(-110592/16811\) \(-16811\) \([]\) \(4160\) \(-0.50980\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 16811.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 16811.a do not have complex multiplication.

Modular form 16811.2.a.a

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