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Properties

Label 459914.u
Number of curves $1$
Conductor $459914$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("u1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 459914.u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 459914.u do not have complex multiplication.

Modular form 459914.2.a.u

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} - q^{8} - 2 q^{9} - 2 q^{10} - 5 q^{11} + q^{12} - q^{13} + 2 q^{15} + q^{16} + 8 q^{17} + 2 q^{18} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 459914.u

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
459914.u1 459914u1 \([1, 0, 1, -35802905, 82453809148]\) \(-2673465150439/6656\) \(-12636222928361457152\) \([]\) \(36578304\) \(2.9041\) \(\Gamma_0(N)\)-optimal