Properties

Label 53361by
Number of curves $1$
Conductor $53361$
CM no
Rank $0$

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

Elliptic curves in class 53361by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53361.cg1 53361by1 \([0, 0, 1, 195657, -6277329]\) \(45056/27\) \(-496387702582306227\) \([]\) \(1197504\) \(2.0848\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53361by1 has rank \(0\).

Complex multiplication

The elliptic curves in class 53361by do not have complex multiplication.

Modular form 53361.2.a.by

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + 4 q^{5} + 8 q^{10} + 2 q^{13} - 4 q^{16} + 4 q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display