Properties

Label 85176.by
Number of curves $1$
Conductor $85176$
CM no
Rank $1$

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

Elliptic curves in class 85176.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.by1 85176d1 \([0, 0, 0, -118131, -15629458]\) \(-683064198/91\) \(-24288193972224\) \([]\) \(322560\) \(1.5878\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 85176.by1 has rank \(1\).

Complex multiplication

The elliptic curves in class 85176.by do not have complex multiplication.

Modular form 85176.2.a.by

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