Properties

Label 8664.n
Number of curves $1$
Conductor $8664$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 8664.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8664.n1 8664m1 \([0, 1, 0, -4129, 429203]\) \(-4434684928/43046721\) \(-75585909590784\) \([]\) \(25600\) \(1.3453\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8664.n1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8664.n do not have complex multiplication.

Modular form 8664.2.a.n

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