Properties

Label 83259.h
Number of curves $1$
Conductor $83259$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 83259.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83259.h1 83259j1 \([0, 0, 1, -146334, 27760779]\) \(-950272/363\) \(-132378707522630547\) \([]\) \(584640\) \(1.9950\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 83259.h1 has rank \(1\).

Complex multiplication

The elliptic curves in class 83259.h do not have complex multiplication.

Modular form 83259.2.a.h

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} + 2 q^{5} - 3 q^{7} - q^{11} + 2 q^{13} + 4 q^{16} + 2 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display