Properties

Label 5733.g
Number of curves $1$
Conductor $5733$
CM no
Rank $1$

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

Elliptic curves in class 5733.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5733.g1 5733e1 \([0, 0, 1, 42, -2340]\) \(32768/9477\) \(-2369695419\) \([]\) \(1536\) \(0.47800\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5733.g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5733.g do not have complex multiplication.

Modular form 5733.2.a.g

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - q^{5} + 2 q^{11} - q^{13} + 4 q^{16} + 2 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display