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Label Class Equation Sato-Tate \(\overline{\Q}\)-simple \(\GL_2\) Rank*
12544.a.12544.1 12544.a $y^2 = x^5 + 2x^4 - x^3 - 3x^2 - x$ $E_6$ $0$
12544.b.12544.1 12544.b $y^2 = x^5 - 3x^3 - x^2 + x$ $\mathrm{USp}(4)$ $0$
12544.b.200704.1 12544.b $y^2 = x^5 - 7x^4 + 8x^3 + 15x^2 + 4x$ $\mathrm{USp}(4)$ $0$
12544.b.401408.1 12544.b $y^2 + y = 4x^6 - 4x^5 - 5x^4 - 6x^3 + 7x^2 + 7x + 5$ $\mathrm{USp}(4)$ $0$
12544.c.12544.1 12544.c $y^2 = x^5 - 2x^4 - x^3 + 3x^2 - x$ $E_6$ $0$
12544.d.25088.1 12544.d $y^2 + (x^3 + x^2 + x + 1)y = x^4 - x^3 + x^2 - x$ $E_4$ $2$
12544.e.50176.1 12544.e $y^2 = x^5 + x^4 - 3x^3 - 2x^2 + 2x + 1$ $\mathrm{USp}(4)$ $1$
12544.f.175616.1 12544.f $y^2 + y = 2x^5 - 3x^4 - 3x^3 + 3x^2 + x - 1$ $\mathrm{USp}(4)$ $0$
12544.g.175616.1 12544.g $y^2 + x^3y = x^5 + x^4 - 2x^2 - 4x - 2$ $J(E_4)$ $1$
12544.h.401408.1 12544.h $y^2 = x^5 - x^4 + 4x^3 - x^2 + x$ $\mathrm{SU}(2)\times\mathrm{SU}(2)$ $1$
12544.i.614656.1 12544.i $y^2 = x^5 + 4x^4 - 13x^3 + 9x^2 - x$ $E_3$ $0$
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