Properties

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

Related objects

Downloads

Learn more

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

Elliptic curves in class 6864.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6864.q1 6864ba1 \([0, 1, 0, -9152, -7614156]\) \(-20699471212993/6097712265216\) \(-24976229438324736\) \([]\) \(63360\) \(1.8256\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6864.q1 has rank \(1\).

Complex multiplication

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

Modular form 6864.2.a.q

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