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Properties

Label 411840.gt
Number of curves $1$
Conductor $411840$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("gt1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 411840.gt1 has rank \(1\).

Complex multiplication

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

Modular form 411840.2.a.gt

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

Elliptic curves in class 411840.gt

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
411840.gt1 411840gt1 \([0, 0, 0, -84588, -9518512]\) \(-9456845543523/57200000\) \(-404855193600000\) \([]\) \(2150400\) \(1.6423\) \(\Gamma_0(N)\)-optimal