Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4598.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4598.c1 4598j1 \([1, 1, 0, -32914, -3211468]\) \(-18396908233/9961472\) \(-2135329991032832\) \([]\) \(20064\) \(1.6452\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4598.c1 has rank \(1\).

Complex multiplication

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

Modular form 4598.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} + 3 q^{7} - q^{8} - 2 q^{9} - 2 q^{10} - q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + q^{16} - 2 q^{17} + 2 q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display