Properties

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

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

Elliptic curves in class 4598.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4598.e1 4598b1 \([1, -1, 0, -45337, -3704277]\) \(-48077951625/38\) \(-8145637478\) \([]\) \(7128\) \(1.2081\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4598.e1 has rank \(0\).

Complex multiplication

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

Modular form 4598.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{7} - q^{8} - 3 q^{9} - q^{13} + 3 q^{14} + q^{16} - 5 q^{17} + 3 q^{18} - q^{19} + O(q^{20})\)  Toggle raw display