Properties

Label 66759.f
Number of curves $1$
Conductor $66759$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 66759.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66759.f1 66759b1 \([0, -1, 1, 1519755, -3085284346]\) \(55648414859264/621508960611\) \(-4335495756630359156451\) \([]\) \(2820096\) \(2.8327\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 66759.f1 has rank \(1\).

Complex multiplication

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

Modular form 66759.2.a.f

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