Properties

Label 73689.u
Number of curves $1$
Conductor $73689$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 73689.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73689.u1 73689n1 \([1, 1, 0, -40797451, 100287457516]\) \(-289531596860402017/17410522563\) \(-451584116241821772363\) \([]\) \(5322240\) \(3.0244\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 73689.u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 73689.u do not have complex multiplication.

Modular form 73689.2.a.u

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