Properties

Label 40733.a
Number of curves $1$
Conductor $40733$
CM no
Rank $1$

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

Elliptic curves in class 40733.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40733.a1 40733e1 \([1, 0, 0, -21699591, 38984528554]\) \(-14429645772301489/34179505129\) \(-2676630723068983006249\) \([]\) \(2627520\) \(2.9915\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40733.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 40733.a do not have complex multiplication.

Modular form 40733.2.a.a

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