Properties

Label 54390.j
Number of curves $1$
Conductor $54390$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 54390.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54390.j1 54390l1 \([1, 1, 0, -8992, -20865536]\) \(-683565019129/1597684769280\) \(-187966015421022720\) \([]\) \(816480\) \(1.9935\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 54390.j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 54390.j do not have complex multiplication.

Modular form 54390.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - 5 q^{11} - q^{12} - 2 q^{13} - q^{15} + q^{16} - q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display