Properties

Label 4598.k
Number of curves $1$
Conductor $4598$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4598.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4598.k1 4598g1 \([1, -1, 0, -5407, 158285]\) \(-81563625/2432\) \(-521320798592\) \([]\) \(16632\) \(1.0266\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4598.k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 4598.k do not have complex multiplication.

Modular form 4598.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + 3 q^{3} + q^{4} - 3 q^{6} - q^{8} + 6 q^{9} + 3 q^{12} - 7 q^{13} + q^{16} + 7 q^{17} - 6 q^{18} - q^{19} + O(q^{20})\)  Toggle raw display