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Properties

Label 411840cs
Number of curves $1$
Conductor $411840$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cs1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 411840cs1 has rank \(1\).

Complex multiplication

The elliptic curves in class 411840cs do not have complex multiplication.

Modular form 411840.2.a.cs

Copy content sage:E.q_eigenform(10)
 
\(q - q^{5} - q^{7} + q^{11} - q^{13} - 5 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 411840cs

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
411840.cs1 411840cs1 \([0, 0, 0, 15252, -26192]\) \(2053225511/1189760\) \(-227366676725760\) \([]\) \(1290240\) \(1.4443\) \(\Gamma_0(N)\)-optimal