Properties

Label 284592kf
Number of curves $1$
Conductor $284592$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("kf1")
 
E.isogeny_class()
 

Elliptic curves in class 284592kf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
284592.kf1 284592kf1 \([0, 1, 0, 61588476, -847157900877]\) \(5820759945472/73222472421\) \(-325002557323189473214387824\) \([]\) \(85155840\) \(3.7680\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 284592kf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 284592kf do not have complex multiplication.

Modular form 284592.2.a.kf

sage: E.q_eigenform(10)
 
\(q + q^{3} + 3 q^{5} + q^{9} - 3 q^{13} + 3 q^{15} + 4 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display