Properties

Label 51842n
Number of curves $1$
Conductor $51842$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 51842n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51842.n1 51842n1 \([1, 0, 0, 906695, 152830201]\) \(8947391/6272\) \(-57785247521138442368\) \([]\) \(2225664\) \(2.4804\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51842n1 has rank \(0\).

Complex multiplication

The elliptic curves in class 51842n do not have complex multiplication.

Modular form 51842.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 4 q^{5} + q^{6} + q^{8} - 2 q^{9} - 4 q^{10} + q^{12} - 2 q^{13} - 4 q^{15} + q^{16} + 5 q^{17} - 2 q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display