Properties

Label 27584q
Number of curves $1$
Conductor $27584$
CM no
Rank $2$

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

Elliptic curves in class 27584q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27584.q1 27584q1 \([0, 1, 0, 63, 191]\) \(415292/431\) \(-28246016\) \([]\) \(5120\) \(0.11648\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 27584q1 has rank \(2\).

Complex multiplication

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

Modular form 27584.2.a.q

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