Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 53361.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53361.a1 53361cf1 \([0, 0, 1, -15065589, 8797048510]\) \(495616/243\) \(185414209382461098052629\) \([]\) \(9461760\) \(3.1580\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53361.a1 has rank \(0\).

Complex multiplication

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

Modular form 53361.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} - 3 q^{5} + 6 q^{10} - 4 q^{13} - 4 q^{16} - q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display