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| Label | Class | Equation | Sato-Tate | \(\overline{\Q}\)-simple | \(\GL_2\) | Rank* |
|---|---|---|---|---|---|---|
| 249.a.249.1 | 249.a | \(y^2 + (x^3 + 1)y = x^2 + x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 249.a.6723.1 | 249.a | \(y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 277.a.277.1 | 277.a | \(y^2 + (x^3 + x^2 + x + 1)y = -x^2 - x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 277.a.277.2 | 277.a | \(y^2 + y = x^5 - 9x^4 + 14x^3 - 19x^2 + 11x - 6\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 295.a.295.1 | 295.a | \(y^2 + (x^3 + 1)y = -x^2\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 295.a.295.2 | 295.a | \(y^2 + (x^2 + x + 1)y = x^5 - 40x^3 + 22x^2 + 389x - 608\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 349.a.349.1 | 349.a | \(y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 353.a.353.1 | 353.a | \(y^2 + (x^3 + x + 1)y = x^2\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 363.a.11979.1 | 363.a | \(y^2 + (x^2 + 1)y = x^5 + 2x^3 + 4x^2 + 2x\) | $G_{3,3}$ | ✓ | 0 | |
| 363.a.43923.1 | 363.a | \(y^2 + x^2y = 11x^5 - 13x^4 - 7x^3 + 10x^2 + x - 2\) | $G_{3,3}$ | ✓ | 0 | |
| 388.a.776.1 | 388.a | \(y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 389.a.389.1 | 389.a | \(y^2 + (x^3 + x)y = x^5 - 2x^4 - 8x^3 + 16x + 7\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 389.a.389.2 | 389.a | \(y^2 + (x + 1)y = x^5 + 2x^4 + 2x^3 + x^2\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 394.a.394.1 | 394.a | \(y^2 + (x^3 + x)y = 2x^5 + x^4 - 12x^3 + 17x - 9\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 394.a.3152.1 | 394.a | \(y^2 + (x + 1)y = -x^5\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 427.a.2989.1 | 427.a | \(y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 461.a.461.1 | 461.a | \(y^2 + x^3y = x^5 - 3x^3 + 3x - 2\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 461.a.461.2 | 461.a | \(y^2 + y = x^5 - x^4 - 39x^3 + 10x^2 + 272x - 306\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 464.a.464.1 | 464.a | \(y^2 + (x + 1)y = -x^6 - 2x^5 - 2x^4 - x^3\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 464.a.29696.1 | 464.a | \(y^2 + (x + 1)y = 8x^5 + 3x^4 - 4x^3 - 2x^2\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 464.a.29696.2 | 464.a | \(y^2 + xy = 4x^5 + 33x^4 + 72x^3 + 16x^2 + x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 472.a.944.1 | 472.a | \(y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 472.a.60416.1 | 472.a | \(y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 523.a.523.1 | 523.a | \(y^2 + (x + 1)y = x^5 - x^4 - x^3\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 523.a.523.2 | 523.a | \(y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 529.a.529.1 | 529.a | \(y^2 + (x^3 + x + 1)y = -x^5\) | $G_{3,3}$ | ✓ | ✓ | 0 |
| 555.a.8325.1 | 555.a | \(y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 574.a.293888.1 | 574.a | \(y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 587.a.587.1 | 587.a | \(y^2 + (x^3 + x + 1)y = -x^2 - x\) | $\mathrm{USp}(4)$ | ✓ | 1 | |
| 597.a.597.1 | 597.a | \(y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 600.a.18000.1 | 600.a | \(y^2 + xy = 10x^5 - 18x^4 + 8x^3 + x^2 - x\) | $G_{3,3}$ | ✓ | 0 | |
| 600.a.96000.1 | 600.a | \(y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2\) | $G_{3,3}$ | ✓ | 0 | |
| 603.a.603.1 | 603.a | \(y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 603.a.603.2 | 603.a | \(y^2 + (x^2 + 1)y = x^5 - x^3 + x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 604.a.9664.1 | 604.a | \(y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 604.a.9664.2 | 604.a | \(y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 644.b.14812.1 | 644.b | \(y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 688.a.2752.1 | 688.a | \(y^2 + y = 2x^5 - 5x^4 + 4x^3 - x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 688.a.704512.2 | 688.a | \(y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 688.a.704512.1 | 688.a | \(y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 691.a.691.1 | 691.a | \(y^2 + (x + 1)y = x^5 - x^3 - x^2\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 704.a.45056.1 | 704.a | \(y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 708.a.2832.1 | 708.a | \(y^2 + (x^2 + x + 1)y = x^5\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 708.a.19116.1 | 708.a | \(y^2 + (x^3 + 1)y = -x^5 + 4x^2 + 4x - 1\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 708.a.181248.1 | 708.a | \(y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 709.a.709.1 | 709.a | \(y^2 + xy = x^5 - 2x^2 + x\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 713.a.713.1 | 713.a | \(y^2 + (x^3 + x + 1)y = -x^5 - x\) | $\mathrm{USp}(4)$ | ✓ | 1 | |
| 713.b.713.1 | 713.b | \(y^2 + (x^3 + x + 1)y = -x^4\) | $\mathrm{USp}(4)$ | ✓ | 0 | |
| 726.a.1452.1 | 726.a | \(y^2 + (x^2 + 1)y = 2x^5 + 2x^4 + 6x^3 - 2x^2 - x\) | $G_{3,3}$ | ✓ | 0 | |
| 731.a.12427.1 | 731.a | \(y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3\) | $\mathrm{USp}(4)$ | ✓ | 0 |