Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("gj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162288.gj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162288.gj1 162288cq1 \([0, 0, 0, 64181229, -132809556782]\) \(83228502970940543/69854999176704\) \(-24539923709313415762673664\) \([]\) \(36495360\) \(3.5595\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 162288.gj1 has rank \(1\).

Complex multiplication

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

Modular form 162288.2.a.gj

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