Properties

Label 259182be
Number of curves $1$
Conductor $259182$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 259182be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.be1 259182be1 \([1, -1, 0, -53058825, 157258087069]\) \(-12791249261627475241/868557554027856\) \(-1121714260259962957744464\) \([]\) \(41287680\) \(3.3662\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 259182be1 has rank \(1\).

Complex multiplication

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

Modular form 259182.2.a.be

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