Properties

Label 489762be
Number of curves $1$
Conductor $489762$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 489762be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
489762.be1 489762be1 \([1, -1, 0, 62462115, 193290163717]\) \(1294412885063448427199/1524386354090213376\) \(-31739201022535355905081344\) \([]\) \(125411328\) \(3.5796\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 489762be1 has rank \(0\).

Complex multiplication

The elliptic curves in class 489762be do not have complex multiplication.

Modular form 489762.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + 4 q^{11} + q^{14} + q^{16} + 6 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display