Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 53361.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53361.s1 53361bn1 \([1, -1, 1, -171823532, -868965797752]\) \(-30515071121161/85766121\) \(-1576786954169855123108721\) \([]\) \(10948608\) \(3.5154\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53361.s1 has rank \(0\).

Complex multiplication

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

Modular form 53361.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} + 3 q^{8} - q^{10} + 5 q^{13} - q^{16} + 7 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display