Properties

Label 4600.e
Number of curves $1$
Conductor $4600$
CM no
Rank $1$

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

Elliptic curves in class 4600.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4600.e1 4600c1 \([0, -1, 0, -15208, -733588]\) \(-19450850/529\) \(-10580000000000\) \([]\) \(9120\) \(1.2806\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4600.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4600.e do not have complex multiplication.

Modular form 4600.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} - 2 q^{9} + 3 q^{11} + 2 q^{13} + q^{17} - q^{19} + O(q^{20})\)  Toggle raw display