Properties

Label 5550c
Number of curves $1$
Conductor $5550$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 5550c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.i1 5550c1 \([1, 1, 0, -260, -1680]\) \(78218787505/2589408\) \(64735200\) \([]\) \(1680\) \(0.27188\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5550c1 has rank \(1\).

Complex multiplication

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

Modular form 5550.2.a.c

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