Properties

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

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

Elliptic curves in class 73689.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73689.a1 73689i1 \([1, 1, 1, -337169, -75500710]\) \(-289531596860402017/17410522563\) \(-254907460844883\) \([]\) \(483840\) \(1.8254\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 73689.a1 has rank \(1\).

Complex multiplication

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

Modular form 73689.2.a.a

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