Properties

Label 162288.z
Number of curves $1$
Conductor $162288$
CM no
Rank $1$

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

Elliptic curves in class 162288.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162288.z1 162288gf1 \([0, 0, 0, 21, 266]\) \(756/23\) \(-31159296\) \([]\) \(39936\) \(0.11791\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 162288.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 162288.z do not have complex multiplication.

Modular form 162288.2.a.z

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