Properties

Label 208725.bm
Number of curves $1$
Conductor $208725$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 208725.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
208725.bm1 208725be1 \([0, 1, 1, -342833, 77165369]\) \(-6439567360/1587\) \(-1098229416796875\) \([]\) \(1176000\) \(1.8739\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 208725.bm1 has rank \(1\).

Complex multiplication

The elliptic curves in class 208725.bm do not have complex multiplication.

Modular form 208725.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - 3 q^{7} + q^{9} - 2 q^{12} + 3 q^{13} + 4 q^{16} - q^{19} + O(q^{20})\) Copy content Toggle raw display