Properties

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

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 259182bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.bg1 259182bg1 \([1, -1, 0, 169680, -3816928]\) \(15494117157/9143008\) \(-318813353252390304\) \([]\) \(3240000\) \(2.0480\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 259182bg1 has rank \(1\).

Complex multiplication

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

Modular form 259182.2.a.bg

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + 5 q^{13} + q^{14} + q^{16} + q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display