Properties

Label 139650.bf
Number of curves $1$
Conductor $139650$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 139650.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.bf1 139650jp1 \([1, 1, 0, -9825, 392085]\) \(-727890625/49248\) \(-7097622991200\) \([]\) \(403200\) \(1.2175\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 139650.bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 139650.bf do not have complex multiplication.

Modular form 139650.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{12} - 3 q^{13} + q^{16} - 6 q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display