Properties

Label 259182.df
Number of curves $1$
Conductor $259182$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("df1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 259182.df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.df1 259182df1 \([1, -1, 0, -841275, 405644773]\) \(-421375171921/210567168\) \(-32904831088200056832\) \([]\) \(12570624\) \(2.4501\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 259182.df1 has rank \(1\).

Complex multiplication

The elliptic curves in class 259182.df do not have complex multiplication.

Modular form 259182.2.a.df

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 4q^{5} + q^{7} - q^{8} - 4q^{10} + 2q^{13} - q^{14} + q^{16} + q^{17} - 7q^{19} + O(q^{20})\)  Toggle raw display