## Results (1-50 of 2698 matches)

Label Class Conductor Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Equation
294.a.294.1 294.a $$2 \cdot 3 \cdot 7^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = x^4 + x^2$
294.a.8232.1 294.a $$2 \cdot 3 \cdot 7^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14$
336.a.172032.1 336.a $$2^{4} \cdot 3 \cdot 7$$ $0$ $\Z/2\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56$
360.a.6480.1 360.a $$2^{3} \cdot 3^{2} \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$
448.a.448.2 448.a $$2^{6} \cdot 7$$ $0$ $\Z/12\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + (x^3 + x)y = -2x^4 + 7$
448.a.448.1 448.a $$2^{6} \cdot 7$$ $0$ $\Z/6\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + (x^3 + x)y = x^4 - 7$
450.a.2700.1 450.a $$2 \cdot 3^{2} \cdot 5^{2}$$ $0$ $\Z/24\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$
450.a.36450.1 450.a $$2 \cdot 3^{2} \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = x^5 - 4x^4 - 9x^3 + 28x^2 - 6x - 16$
476.a.952.1 476.a $$2^{2} \cdot 7 \cdot 17$$ $0$ $\Z/3\Z\oplus\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54$
484.a.1936.1 484.a $$2^{2} \cdot 11^{2}$$ $0$ $\Z/15\Z$ $$\Q \times \Q$$ $y^2 + y = x^6 + 2x^4 + x^2$
504.a.27216.1 504.a $$2^{3} \cdot 3^{2} \cdot 7$$ $0$ $\Z/4\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21$
578.a.2312.1 578.a $$2 \cdot 17^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x$
588.a.18816.1 588.a $$2^{2} \cdot 3 \cdot 7^{2}$$ $0$ $\Z/24\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8$
600.b.30000.1 600.b $$2^{3} \cdot 3 \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = x^4 + x^2 - 3$
600.b.450000.1 600.b $$2^{3} \cdot 3 \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45$
630.a.34020.1 630.a $$2 \cdot 3^{2} \cdot 5 \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = 3x^5 + 10x^4 - 23x^2 - 6x + 15$
640.a.81920.1 640.a $$2^{7} \cdot 5$$ $0$ $\Z/12\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + x^3y = 3x^4 + 13x^2 + 20$
640.a.81920.2 640.a $$2^{7} \cdot 5$$ $0$ $\Z/12\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + x^3y = -3x^4 + 13x^2 - 20$
644.a.2576.1 644.a $$2^{2} \cdot 7 \cdot 23$$ $0$ $\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = -5x^6 + 11x^5 - 20x^4 + 20x^3 - 20x^2 + 11x - 5$
644.a.659456.1 644.a $$2^{2} \cdot 7 \cdot 23$$ $0$ $\Z/2\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3$
672.a.172032.1 672.a $$2^{5} \cdot 3 \cdot 7$$ $0$ $\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -x^6 - 16x^4 - 75x^2 + 56$
676.a.5408.1 676.a $$2^{2} \cdot 13^{2}$$ $0$ $\Z/21\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x^2 + x)y = x^3 + 3x^2 + 3x + 1$
676.a.562432.1 676.a $$2^{2} \cdot 13^{2}$$ $0$ $\Z/21\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x$
686.a.686.1 686.a $$2 \cdot 7^{3}$$ $0$ $\Z/6\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$
720.a.6480.1 720.a $$2^{4} \cdot 3^{2} \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5$
720.b.116640.1 720.b $$2^{4} \cdot 3^{2} \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90$
784.a.1568.1 784.a $$2^{4} \cdot 7^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -2x^4 + 3x^2 - 2$
784.a.43904.1 784.a $$2^{4} \cdot 7^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = 4x^4 + 27x^2 + 56$
784.b.12544.1 784.b $$2^{4} \cdot 7^{2}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -1$
800.a.1600.1 800.a $$2^{5} \cdot 5^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^2$
800.a.8000.1 800.a $$2^{5} \cdot 5^{2}$$ $0$ $\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x^2 + x + 1)y = -x^6 + 2x^4 + 4x^3 + 2x^2 - 1$
800.a.409600.1 800.a $$2^{5} \cdot 5^{2}$$ $0$ $\Z/24\Z$ $$\Q \times \Q$$ $y^2 = x^6 - 2x^2 + 1$
816.b.52224.1 816.b $$2^{4} \cdot 3 \cdot 17$$ $0$ $\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -x^6 - 12x^4 - 27x^2 - 17$
847.a.847.1 847.a $$7 \cdot 11^{2}$$ $1$ $\Z/5\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2$
847.d.847.1 847.d $$7 \cdot 11^{2}$$ $0$ $\Z/3\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x^2 + x + 1)y = -12x^6 - 15x^5 + 9x^4 + 31x^3 + 9x^2 - 15x - 12$
847.d.456533.1 847.d $$7 \cdot 11^{2}$$ $0$ $\Z/15\Z$ $$\Q \times \Q$$ $y^2 + y = -x^6 - 9x^5 - 22x^4 + 3x^3 + 37x^2 - 24x + 4$
864.a.1728.1 864.a $$2^{5} \cdot 3^{3}$$ $0$ $\Z/12\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^2$
864.a.221184.1 864.a $$2^{5} \cdot 3^{3}$$ $0$ $\Z/12\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + x^3y = x^5 - 4x^4 - 6x^3 + 33x^2 - 36x + 12$
864.a.442368.1 864.a $$2^{5} \cdot 3^{3}$$ $0$ $\Z/12\Z$ $$\mathsf{CM} \times \Q$$ $y^2 = x^6 - 4x^4 + 6x^2 - 3$
882.a.63504.1 882.a $$2 \cdot 3^{2} \cdot 7^{2}$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = x^5 + x^4 + x^3 + 3x^2 + 3x + 1$
930.a.930.1 930.a $$2 \cdot 3 \cdot 5 \cdot 31$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15$
936.a.1872.1 936.a $$2^{3} \cdot 3^{2} \cdot 13$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -x^6 - 9x^4 - 32x^2 - 39$
960.a.245760.1 960.a $$2^{6} \cdot 3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 = 2x^5 + x^4 + 4x^3 + x^2 + 2x$
960.a.368640.1 960.a $$2^{6} \cdot 3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 = x^5 + 13x^4 + 44x^3 + 13x^2 + x$
960.a.983040.1 960.a $$2^{6} \cdot 3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 = x^5 - 2x^4 - x^3 - 2x^2 + x$
968.a.1936.1 968.a $$2^{3} \cdot 11^{2}$$ $1$ $\Z/5\Z$ $$\Q \times \Q$$ $y^2 + y = x^6 - x^4$
968.a.234256.1 968.a $$2^{3} \cdot 11^{2}$$ $1$ $\Z/5\Z$ $$\Q \times \Q$$ $y^2 + x^3y = 6x^4 + 47x^2 + 121$
980.a.7840.1 980.a $$2^{2} \cdot 5 \cdot 7^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x + 1)y = -x^6 + 3x^5 - 3x^4 - x$
980.a.878080.1 980.a $$2^{2} \cdot 5 \cdot 7^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = -x^6 + x^5 - 4x^4 + 2x^3 - 4x^2 + x - 1$
990.a.8910.1 990.a $$2 \cdot 3^{2} \cdot 5 \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = 3x^5 + 4x^4 + 7x^3 + 4x^2 + 3x$