Properties

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

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 4998.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4998.ba1 4998ba1 \([1, 1, 1, 9212930, 137302547003]\) \(15001431500460925919/1421324083670155776\) \(-8193650498865797687640576\) \([]\) \(1330560\) \(3.4599\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4998.ba1 has rank \(1\).

Complex multiplication

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

Modular form 4998.2.a.ba

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