Properties

Label 5692.a
Number of curves $1$
Conductor $5692$
CM no
Rank $2$

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

Elliptic curves in class 5692.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5692.a1 5692a1 \([0, 1, 0, -18, 25]\) \(-42592000/1423\) \(-22768\) \([]\) \(516\) \(-0.38957\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5692.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 5692.a do not have complex multiplication.

Modular form 5692.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 4 q^{7} + q^{9} - 6 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display