Properties

Label 55470.f
Number of curves $1$
Conductor $55470$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("55470.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55470.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55470.f1 55470i1 [1, 0, 1, -186659, 1896143582] [] 2451456 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 55470.f1 has rank \(1\).

Modular form 55470.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 2q^{7} - q^{8} + q^{9} + q^{10} - q^{11} + q^{12} + 4q^{13} + 2q^{14} - q^{15} + q^{16} + q^{17} - q^{18} + 5q^{19} + O(q^{20}) \)