Properties

Label 27225.bk
Number of curves $1$
Conductor $27225$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 27225.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27225.bk1 27225bk1 \([1, -1, 0, -318192, 149863841]\) \(-1459161/3125\) \(-7630255090283203125\) \([]\) \(443520\) \(2.3121\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 27225.bk1 has rank \(1\).

Complex multiplication

The elliptic curves in class 27225.bk do not have complex multiplication.

Modular form 27225.2.a.bk

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 3 q^{7} - 3 q^{8} + 4 q^{13} - 3 q^{14} - q^{16} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display