Properties

Label 66759j
Number of curves $1$
Conductor $66759$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 66759j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66759.g1 66759j1 \([0, 1, 1, 5259, -626128]\) \(55648414859264/621508960611\) \(-179616089616579\) \([]\) \(165888\) \(1.4161\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 66759j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 66759j do not have complex multiplication.

Modular form 66759.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - q^{5} + q^{7} + q^{9} - q^{11} - 2 q^{12} - 6 q^{13} - q^{15} + 4 q^{16} + O(q^{20})\) Copy content Toggle raw display