Properties

Label 27584.z
Number of curves $1$
Conductor $27584$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 27584.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27584.z1 27584j1 \([0, 1, 0, -129, 8159]\) \(-912673/110336\) \(-28923920384\) \([]\) \(24576\) \(0.68679\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 27584.z1 has rank \(0\).

Complex multiplication

The elliptic curves in class 27584.z do not have complex multiplication.

Modular form 27584.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{3} + 3 q^{5} + 2 q^{7} - 2 q^{9} - 5 q^{11} + 6 q^{13} + 3 q^{15} - 6 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display