Properties

Label 189618.r
Number of curves $1$
Conductor $189618$
CM no
Rank $2$

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

Elliptic curves in class 189618.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.r1 189618z1 \([1, 0, 1, -5581, 162242]\) \(-672937149625/10996722\) \(-314077377042\) \([]\) \(288000\) \(1.0061\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 189618.r1 has rank \(2\).

Complex multiplication

The elliptic curves in class 189618.r do not have complex multiplication.

Modular form 189618.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 2q^{7} - q^{8} + q^{9} + q^{11} + q^{12} + 2q^{14} + q^{16} + q^{17} - q^{18} + O(q^{20})\)  Toggle raw display