Properties

Label 5550.bf
Number of curves $1$
Conductor $5550$
CM no
Rank $1$

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

Elliptic curves in class 5550.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.bf1 5550bh1 \([1, 0, 0, 5062, -71508]\) \(918046641959/674325000\) \(-10536328125000\) \([]\) \(17280\) \(1.1871\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5550.bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5550.bf do not have complex multiplication.

Modular form 5550.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - 3 q^{7} + q^{8} + q^{9} - 5 q^{11} + q^{12} + 2 q^{13} - 3 q^{14} + q^{16} + 7 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display