Properties

Label 162288.r
Number of curves $1$
Conductor $162288$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 162288.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162288.r1 162288et1 \([0, 0, 0, -173019, 39329066]\) \(-3261064466/1917027\) \(-336723905827362816\) \([]\) \(1843200\) \(2.0657\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 162288.r1 has rank \(2\).

Complex multiplication

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

Modular form 162288.2.a.r

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