Properties

Label 55473p
Number of curves $1$
Conductor $55473$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 55473p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55473.g1 55473p1 \([0, 1, 1, -19051, 1010452]\) \(-270622818304/1449459\) \(-4095824713299\) \([]\) \(141120\) \(1.2646\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 55473p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 55473p do not have complex multiplication.

Modular form 55473.2.a.p

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