Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 55473.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55473.a1 55473h1 \([0, -1, 1, -281656, -58836012]\) \(-1469990616218374144/41768190339579\) \(-70212327960832299\) \([]\) \(1230768\) \(2.0125\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 55473.a1 has rank \(0\).

Complex multiplication

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

Modular form 55473.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 4 q^{7} + q^{9} + 2 q^{10} + q^{11} - 2 q^{12} + 6 q^{13} + 8 q^{14} + q^{15} - 4 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display