Properties

Label 22218.q
Number of curves $1$
Conductor $22218$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 22218.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22218.q1 22218w1 \([1, 1, 1, 518, -7033]\) \(54922367/112896\) \(-31592929536\) \([]\) \(18432\) \(0.69906\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 22218.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 22218.q do not have complex multiplication.

Modular form 22218.2.a.q

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