Properties

Label 84525.by
Number of curves $1$
Conductor $84525$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 84525.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84525.by1 84525bo1 \([0, 1, 1, 35731617, 184993854644]\) \(2744564518708084736/9629735831296875\) \(-17702012356503844482421875\) \([]\) \(10782720\) \(3.5276\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 84525.by1 has rank \(1\).

Complex multiplication

The elliptic curves in class 84525.by do not have complex multiplication.

Modular form 84525.2.a.by

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + q^{9} + q^{11} - 2 q^{12} + 4 q^{16} + 2 q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display