Properties

Label 55470.b
Number of curves $1$
Conductor $55470$
CM no
Rank $2$

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Show commands for: SageMath
sage: E = EllipticCurve("55470.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55470.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55470.b1 55470a1 [1, 1, 0, -253, -323] [] 36288 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 55470.b1 has rank \(2\).

Modular form 55470.2.a.b

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