Properties

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

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 208725.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
208725.bp1 208725bg1 \([0, 1, 1, 75827, -4407386]\) \(217732612096/164333367\) \(-36390822996985875\) \([]\) \(1152000\) \(1.8659\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 208725.bp1 has rank \(1\).

Complex multiplication

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

Modular form 208725.2.a.bp

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - q^{7} + q^{9} - 2 q^{12} + 2 q^{13} + 4 q^{16} + 3 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display