Properties

Label 73689u
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 73689u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73689.o1 73689u1 \([0, 1, 1, -2220995, -1241532682]\) \(5652299539972096/168301718109\) \(36076967964222676029\) \([]\) \(1552320\) \(2.5295\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 73689.2.a.u

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