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Properties

Label 402800.x
Number of curves $1$
Conductor $402800$
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 402800.x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 402800.x do not have complex multiplication.

Modular form 402800.2.a.x

Copy content sage:E.q_eigenform(10)
 
\(q + 4 q^{7} - 3 q^{9} + q^{11} - 3 q^{13} + 4 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 402800.x

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
402800.x1 402800x1 \([0, 0, 0, -800, 8875]\) \(-226492416/5035\) \(-1258750000\) \([]\) \(154368\) \(0.53479\) \(\Gamma_0(N)\)-optimal