Properties

Label 6864.u
Number of curves $1$
Conductor $6864$
CM no
Rank $1$

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

Elliptic curves in class 6864.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6864.u1 6864t1 \([0, 1, 0, -736, -8332]\) \(-10779215329/658944\) \(-2699034624\) \([]\) \(3456\) \(0.56437\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6864.u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6864.u do not have complex multiplication.

Modular form 6864.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 3q^{7} + q^{9} - q^{11} - q^{13} - q^{15} - 4q^{17} + 2q^{19} + O(q^{20})\)  Toggle raw display