Properties

Label 38640.u
Number of curves $1$
Conductor $38640$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38640.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.u1 38640bn1 \([0, -1, 0, 466699, 275969085]\) \(2744564518708084736/9629735831296875\) \(-39443397964992000000\) \([]\) \(673920\) \(2.4431\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 38640.u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 38640.u do not have complex multiplication.

Modular form 38640.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} - q^{11} + q^{15} + 2q^{17} + 3q^{19} + O(q^{20})\)  Toggle raw display