Properties

Label 5200.j
Number of curves $1$
Conductor $5200$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 5200.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5200.j1 5200y1 \([0, -1, 0, 4792, -1411088]\) \(304175/21632\) \(-865280000000000\) \([]\) \(20160\) \(1.5457\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5200.j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5200.j do not have complex multiplication.

Modular form 5200.2.a.j

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