Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4998.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4998.m1 4998m1 \([1, 0, 1, -16047134, 24732961040]\) \(1617840527930521321/623760113664\) \(176196793423506702336\) \([]\) \(282240\) \(2.8504\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4998.m1 has rank \(1\).

Complex multiplication

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

Modular form 4998.2.a.m

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