Properties

Label 55473.e
Number of curves $1$
Conductor $55473$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 55473.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55473.e1 55473b1 \([0, -1, 1, -3216313, 2221361481]\) \(-460816384000/29403\) \(-234780756511844763\) \([]\) \(1377600\) \(2.3911\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 55473.e1 has rank \(0\).

Complex multiplication

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

Modular form 55473.2.a.e

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