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Properties

Label 402800r
Number of curves $1$
Conductor $402800$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("r1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 402800r1 has rank \(1\).

Complex multiplication

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

Modular form 402800.2.a.r

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

Elliptic curves in class 402800r

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
402800.r1 402800r1 \([0, 0, 0, 85, 1050]\) \(132651/1007\) \(-515584000\) \([]\) \(77824\) \(0.35325\) \(\Gamma_0(N)\)-optimal