Properties

Label 27584.a
Number of curves 1
Conductor 27584
CM no
Rank 3

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Show commands for: SageMath

sage: E = EllipticCurve("27584.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 27584.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27584.a1 27584bd1 [0, 0, 0, -4, 64] [] 12032 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 27584.a1 has rank \(3\).

Modular form 27584.2.a.a

sage: E.q_eigenform(10)
 
\( q - 3q^{3} - 3q^{5} - 4q^{7} + 6q^{9} - 5q^{11} - 4q^{13} + 9q^{15} - 6q^{17} - 7q^{19} + O(q^{20}) \)