Properties

Label 55545n
Number of curves $1$
Conductor $55545$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 55545n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55545.x1 55545n1 \([0, 1, 1, -23429586, 61040931995]\) \(-18163305455448064/10048419997875\) \(-786901670550895176277875\) \([]\) \(12055680\) \(3.2887\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 55545n1 has rank \(0\).

Complex multiplication

The elliptic curves in class 55545n do not have complex multiplication.

Modular form 55545.2.a.n

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