Properties

Label 4998.bj
Number of curves $1$
Conductor $4998$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 4998.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4998.bj1 4998bq1 \([1, 0, 0, -107997, 13989681]\) \(-1184052061112257/34349180544\) \(-4041146741821056\) \([]\) \(40320\) \(1.7738\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4998.bj1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4998.bj do not have complex multiplication.

Modular form 4998.2.a.bj

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