Properties

Label 36225.by
Number of curves $1$
Conductor $36225$
CM no
Rank $1$

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

Elliptic curves in class 36225.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36225.by1 36225a1 \([0, 0, 1, -9525, 382781]\) \(-226534772736/18941489\) \(-7990940671875\) \([]\) \(100352\) \(1.2211\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 36225.by1 has rank \(1\).

Complex multiplication

The elliptic curves in class 36225.by do not have complex multiplication.

Modular form 36225.2.a.by

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} - q^{7} - q^{11} - 2 q^{14} - 4 q^{16} + 4 q^{17} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display