Properties

Label 284592.hn
Number of curves $1$
Conductor $284592$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("hn1")
 
E.isogeny_class()
 

Elliptic curves in class 284592.hn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
284592.hn1 284592hn1 \([0, 1, 0, -1543516, 799449671]\) \(-91625216/9261\) \(-41105532002042060784\) \([]\) \(7299072\) \(2.5036\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 284592.hn1 has rank \(1\).

Complex multiplication

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

Modular form 284592.2.a.hn

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} - q^{13} - q^{15} + 8 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display