Properties

Label 5550.k
Number of curves $1$
Conductor $5550$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 5550.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.k1 5550e1 \([1, 1, 0, -7025, 295125]\) \(-2454365649169/1035763200\) \(-16183800000000\) \([]\) \(24192\) \(1.2424\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5550.k1 has rank \(0\).

Complex multiplication

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

Modular form 5550.2.a.k

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