Properties

Label 4998.e
Number of curves $1$
Conductor $4998$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4998.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4998.e1 4998b1 \([1, 1, 0, -327492, -72248112]\) \(1617840527930521321/623760113664\) \(1497648032907264\) \([]\) \(40320\) \(1.8774\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4998.e1 has rank \(0\).

Complex multiplication

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

Modular form 4998.2.a.e

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