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Properties

Label 477950x
Number of curves $1$
Conductor $477950$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("x1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 477950x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 477950x do not have complex multiplication.

Modular form 477950.2.a.x

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

Elliptic curves in class 477950x

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
477950.x1 477950x1 \([1, -1, 0, 1633, 35041]\) \(185193/316\) \(-821476562500\) \([]\) \(529920\) \(0.97116\) \(\Gamma_0(N)\)-optimal