Properties

Label 22386q
Number of curves $1$
Conductor $22386$
CM no
Rank $1$

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

Elliptic curves in class 22386q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22386.r1 22386q1 \([1, 1, 1, -165, -657]\) \(496981290961/138211164\) \(138211164\) \([]\) \(9984\) \(0.26930\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 22386q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 22386q do not have complex multiplication.

Modular form 22386.2.a.q

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