Properties

Label 52983.l
Number of curves $1$
Conductor $52983$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 52983.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52983.l1 52983e1 \([1, -1, 0, -9809973, -10744808652]\) \(170295687079857398473/17163597526568829\) \(10522812843966556802781\) \([]\) \(5491200\) \(2.9618\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 52983.l1 has rank \(1\).

Complex multiplication

The elliptic curves in class 52983.l do not have complex multiplication.

Modular form 52983.2.a.l

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