Properties

Label 27225z
Number of curves $1$
Conductor $27225$
CM no
Rank $1$

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

Elliptic curves in class 27225z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27225.q1 27225z1 \([1, -1, 1, -5105, 759322]\) \(-675/11\) \(-239728741745625\) \([]\) \(69120\) \(1.4405\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 27225z1 has rank \(1\).

Complex multiplication

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

Modular form 27225.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 3 q^{7} + 3 q^{8} - 2 q^{13} - 3 q^{14} - q^{16} - 3 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display