Properties

Label 40733g
Number of curves $1$
Conductor $40733$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 40733g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40733.k1 40733g1 \([1, -1, 0, -7, 14]\) \(-77625/77\) \(-40733\) \([]\) \(3840\) \(-0.41963\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40733g1 has rank \(1\).

Complex multiplication

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

Modular form 40733.2.a.g

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