Properties

Label 52983.b
Number of curves $1$
Conductor $52983$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 52983.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52983.b1 52983k1 \([1, -1, 1, -242366, 47691546]\) \(-4317433/189\) \(-68924451024179541\) \([]\) \(417600\) \(1.9963\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 52983.b1 has rank \(0\).

Complex multiplication

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

Modular form 52983.2.a.b

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