Properties

Label 257600.dw
Number of curves $1$
Conductor $257600$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("dw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 257600.dw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.dw1 257600dw1 \([0, 0, 0, 428500, -2176830000]\) \(84972077055/20040095362\) \(-2052105765068800000000\) \([]\) \(7741440\) \(2.7686\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257600.dw1 has rank \(1\).

Complex multiplication

The elliptic curves in class 257600.dw do not have complex multiplication.

Modular form 257600.2.a.dw

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