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Properties

Label 411840lk
Number of curves $1$
Conductor $411840$
CM no
Rank $2$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("lk1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 411840lk1 has rank \(2\).

Complex multiplication

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

Modular form 411840.2.a.lk

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

Elliptic curves in class 411840lk

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
411840.lk1 411840lk1 \([0, 0, 0, -616217772, 14044629445936]\) \(-135412551115258010417641/367535633653760000000\) \(-70237153377279289589760000000\) \([]\) \(294174720\) \(4.2225\) \(\Gamma_0(N)\)-optimal