Properties

Label 53361t
Number of curves $1$
Conductor $53361$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 53361t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53361.n1 53361t1 \([1, -1, 1, 1066108, -485118840]\) \(17999471/24057\) \(-179105708322652128633\) \([]\) \(2257920\) \(2.5720\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53361t1 has rank \(1\).

Complex multiplication

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

Modular form 53361.2.a.t

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