Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 27584.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27584.a1 27584bd1 \([0, 0, 0, -4, 64]\) \(-1728/431\) \(-1765376\) \([]\) \(12032\) \(-0.12211\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 27584.2.a.a

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