Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 5550.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.u1 5550s1 \([1, 0, 1, 78674, -21105952]\) \(137868581419655/572735619072\) \(-223724851200000000\) \([]\) \(64800\) \(2.0117\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5550.u1 has rank \(1\).

Complex multiplication

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

Modular form 5550.2.a.u

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