Properties

Label 8050j
Number of curves $1$
Conductor $8050$
CM no
Rank $1$

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

Elliptic curves in class 8050j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8050.i1 8050j1 \([1, -1, 0, 268, 33946]\) \(84972077055/20040095362\) \(-501002384050\) \([]\) \(8064\) \(0.92419\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8050j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8050j do not have complex multiplication.

Modular form 8050.2.a.j

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