Properties

Label 83391p
Number of curves $1$
Conductor $83391$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 83391p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83391.q1 83391p1 \([1, 0, 1, 752, 4079]\) \(6869835701/4991679\) \(-34237926261\) \([]\) \(57600\) \(0.70972\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 83391p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 83391p do not have complex multiplication.

Modular form 83391.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + q^{7} - 3 q^{8} + q^{9} + q^{10} - q^{11} - q^{12} - 4 q^{13} + q^{14} + q^{15} - q^{16} + q^{18} + O(q^{20})\) Copy content Toggle raw display