## Results (1-50 of 56695 matches)

Label Class Conductor Discriminant Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Equation
336.a.172032.1 336.a $$2^{4} \cdot 3 \cdot 7$$ $$- 2^{13} \cdot 3 \cdot 7$$ $0$ $\Z/2\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56$
400.a.409600.1 400.a $$2^{4} \cdot 5^{2}$$ $$- 2^{14} \cdot 5^{2}$$ $0$ $\Z/3\Z\oplus\Z/6\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^6 + 4x^4 + 4x^2 + 1$
574.a.293888.1 574.a $$2 \cdot 7 \cdot 41$$ $$- 2^{10} \cdot 7 \cdot 41$$ $0$ $\Z/2\Z\oplus\Z/10\Z$ $$\Q$$ $y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1$
576.b.147456.1 576.b $$2^{6} \cdot 3^{2}$$ $$- 2^{14} \cdot 3^{2}$$ $0$ $\Z/4\Z\oplus\Z/4\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^6 + 2x^4 + 2x^2 + 1$
600.b.450000.1 600.b $$2^{3} \cdot 3 \cdot 5^{2}$$ $$2^{4} \cdot 3^{2} \cdot 5^{5}$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45$
644.a.659456.1 644.a $$2^{2} \cdot 7 \cdot 23$$ $$2^{12} \cdot 7 \cdot 23$$ $0$ $\Z/2\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3$
672.a.172032.1 672.a $$2^{5} \cdot 3 \cdot 7$$ $$2^{13} \cdot 3 \cdot 7$$ $0$ $\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -x^6 - 16x^4 - 75x^2 + 56$
676.a.562432.1 676.a $$2^{2} \cdot 13^{2}$$ $$2^{8} \cdot 13^{3}$$ $0$ $\Z/21\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x$
688.a.704512.2 688.a $$2^{4} \cdot 43$$ $$- 2^{14} \cdot 43$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1$
688.a.704512.1 688.a $$2^{4} \cdot 43$$ $$2^{14} \cdot 43$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1$
708.a.181248.1 708.a $$2^{2} \cdot 3 \cdot 59$$ $$- 2^{10} \cdot 3 \cdot 59$$ $0$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36$
720.b.116640.1 720.b $$2^{4} \cdot 3^{2} \cdot 5$$ $$2^{5} \cdot 3^{6} \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90$
784.c.614656.1 784.c $$2^{4} \cdot 7^{2}$$ $$2^{8} \cdot 7^{4}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x$
800.a.409600.1 800.a $$2^{5} \cdot 5^{2}$$ $$- 2^{14} \cdot 5^{2}$$ $0$ $\Z/24\Z$ $$\Q \times \Q$$ $y^2 = x^6 - 2x^2 + 1$
810.a.196830.1 810.a $$2 \cdot 3^{4} \cdot 5$$ $$- 2 \cdot 3^{9} \cdot 5$$ $0$ $\Z/2\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + (x + 1)y = x^5 + 15x^4 + 20x^3 - 297x^2 + 94x - 8$
830.a.830000.1 830.a $$2 \cdot 5 \cdot 83$$ $$- 2^{4} \cdot 5^{4} \cdot 83$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q$$ $y^2 + (x^2 + x)y = x^5 - 2x^4 + 16x^3 + 8x^2 + x$
847.d.456533.1 847.d $$7 \cdot 11^{2}$$ $$7^{3} \cdot 11^{3}$$ $0$ $\Z/15\Z$ $$\Q \times \Q$$ $y^2 + y = -x^6 - 9x^5 - 22x^4 + 3x^3 + 37x^2 - 24x + 4$
864.a.221184.1 864.a $$2^{5} \cdot 3^{3}$$ $$- 2^{13} \cdot 3^{3}$$ $0$ $\Z/12\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + x^3y = x^5 - 4x^4 - 6x^3 + 33x^2 - 36x + 12$
864.a.442368.1 864.a $$2^{5} \cdot 3^{3}$$ $$2^{14} \cdot 3^{3}$$ $0$ $\Z/12\Z$ $$\mathsf{CM} \times \Q$$ $y^2 = x^6 - 4x^4 + 6x^2 - 3$
880.a.225280.1 880.a $$2^{4} \cdot 5 \cdot 11$$ $$- 2^{12} \cdot 5 \cdot 11$$ $0$ $\Z/2\Z$ $$\Q \times \Q$$ $y^2 = x^5 + 13x^4 + 55x^3 + 76x^2 - 44$
882.a.302526.1 882.a $$2 \cdot 3^{2} \cdot 7^{2}$$ $$- 2 \cdot 3^{2} \cdot 7^{5}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = x^5 - 2x^4 - 5x^3 + 11x^2 - 12x + 5$
960.a.245760.1 960.a $$2^{6} \cdot 3 \cdot 5$$ $$2^{14} \cdot 3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 = 2x^5 + x^4 + 4x^3 + x^2 + 2x$
960.a.368640.1 960.a $$2^{6} \cdot 3 \cdot 5$$ $$2^{13} \cdot 3^{2} \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 = x^5 + 13x^4 + 44x^3 + 13x^2 + x$
960.a.983040.1 960.a $$2^{6} \cdot 3 \cdot 5$$ $$- 2^{16} \cdot 3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 = x^5 - 2x^4 - x^3 - 2x^2 + x$
961.a.923521.1 961.a $$31^{2}$$ $$31^{4}$$ $0$ $\Z/5\Z$ $$\mathsf{RM}$$ $y^2 + (x^3 + x^2 + 1)y = -5x^4 + 4x^3 + 3x^2 - 2x - 3$
966.a.834624.1 966.a $$2 \cdot 3 \cdot 7 \cdot 23$$ $$2^{6} \cdot 3^{4} \cdot 7 \cdot 23$$ $0$ $\Z/2\Z\oplus\Z/12\Z$ $$\Q$$ $y^2 + (x^2 + x)y = x^5 - x^4 + x^3 + x^2 - x + 1$
968.a.234256.1 968.a $$2^{3} \cdot 11^{2}$$ $$- 2^{4} \cdot 11^{4}$$ $1$ $\Z/5\Z$ $$\Q \times \Q$$ $y^2 + x^3y = 6x^4 + 47x^2 + 121$
976.a.999424.1 976.a $$2^{4} \cdot 61$$ $$2^{14} \cdot 61$$ $0$ $\Z/29\Z$ $$\Q$$ $y^2 + (x + 1)y = x^6 - 2x^5 + 2x^3 - x^2$
980.a.878080.1 980.a $$2^{2} \cdot 5 \cdot 7^{2}$$ $$- 2^{9} \cdot 5 \cdot 7^{3}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = -x^6 + x^5 - 4x^4 + 2x^3 - 4x^2 + x - 1$
990.a.240570.1 990.a $$2 \cdot 3^{2} \cdot 5 \cdot 11$$ $$2 \cdot 3^{7} \cdot 5 \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = 3x^5 + 28x^4 + 72x^3 + 28x^2 + 3x$
1050.a.131250.1 1050.a $$2 \cdot 3 \cdot 5^{2} \cdot 7$$ $$- 2 \cdot 3 \cdot 5^{5} \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = 3x^6 + 8x^5 + 15x^4 + 17x^3 + 15x^2 + 8x + 3$
1083.b.390963.1 1083.b $$3 \cdot 19^{2}$$ $$- 3 \cdot 19^{4}$$ $0$ $\mathsf{trivial}$ $$\Q \times \Q$$ $y^2 + y = -x^6 + 3x^5 - 50x^4 + 95x^3 - 14x^2 - 33x - 6$
1104.b.141312.1 1104.b $$2^{4} \cdot 3 \cdot 23$$ $$- 2^{11} \cdot 3 \cdot 23$$ $0$ $\Z/2\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -x^6 - 3x^4 + 29x^2 - 46$
1116.a.214272.1 1116.a $$2^{2} \cdot 3^{2} \cdot 31$$ $$- 2^{8} \cdot 3^{3} \cdot 31$$ $0$ $\Z/39\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = x^4 + 2x^3 + x^2 - x$
1125.a.151875.1 1125.a $$3^{2} \cdot 5^{3}$$ $$- 3^{5} \cdot 5^{4}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\Q \times \Q$$ $y^2 + xy = 15x^5 + 50x^4 + 55x^3 + 22x^2 + 3x$
1136.a.290816.1 1136.a $$2^{4} \cdot 71$$ $$2^{12} \cdot 71$$ $0$ $\Z/14\Z$ $$\Q$$ $y^2 + (x^3 + x^2)y = -5x^4 - 9x^3 + 25x^2 + 40x - 24$
1145.a.143125.1 1145.a $$5 \cdot 229$$ $$- 5^{4} \cdot 229$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^3 + x^2 + x)y = 2x^4 + 4x^3 + 9x^2 + 10x + 9$
1152.a.147456.1 1152.a $$2^{7} \cdot 3^{2}$$ $$2^{14} \cdot 3^{2}$$ $0$ $\Z/8\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^6 - 2x^4 + 2x^2 - 1$
1164.b.670464.1 1164.b $$2^{2} \cdot 3 \cdot 97$$ $$2^{8} \cdot 3^{3} \cdot 97$$ $0$ $\Z/21\Z$ $$\Q$$ $y^2 + (x^2 + x + 1)y = 2x^5 - 2x^4 + x^3 - x^2$
1184.a.606208.2 1184.a $$2^{5} \cdot 37$$ $$- 2^{14} \cdot 37$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 = x^6 - 2x^5 + 5x^4 - 4x^3 + 6x^2 - 2x + 2$
1184.a.606208.1 1184.a $$2^{5} \cdot 37$$ $$2^{14} \cdot 37$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q$$ $y^2 = 2x^5 + x^4 - 8x^3 - 8x^2 - 2x$
1197.a.410571.1 1197.a $$3^{2} \cdot 7 \cdot 19$$ $$- 3^{2} \cdot 7^{4} \cdot 19$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^2 + 1)y = x^5 + 12x^4 - 7x^3 - 3x^2 + x$
1200.a.450000.1 1200.a $$2^{4} \cdot 3 \cdot 5^{2}$$ $$- 2^{4} \cdot 3^{2} \cdot 5^{5}$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = 4x^4 + 25x^2 + 45$
1269.b.102789.1 1269.b $$3^{3} \cdot 47$$ $$- 3^{7} \cdot 47$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^3 + x)y = -2x^6 - x^5 - 21x^4 - 8x^3 - 80x^2 - 16x - 103$
1269.b.102789.2 1269.b $$3^{3} \cdot 47$$ $$3^{7} \cdot 47$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + xy = x^5 - x^4 + x^2 + x$
1270.a.325120.1 1270.a $$2 \cdot 5 \cdot 127$$ $$2^{9} \cdot 5 \cdot 127$$ $0$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^2 + x)y = x^5 + 17x^4 + 76x^3 + 14x^2 - 32x + 3$
1272.a.122112.1 1272.a $$2^{3} \cdot 3 \cdot 53$$ $$- 2^{8} \cdot 3^{2} \cdot 53$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q$$ $y^2 + (x^2 + 1)y = 3x^5 + 4x^4 + 2x^3 - x^2 - x$
1300.a.130000.1 1300.a $$2^{2} \cdot 5^{2} \cdot 13$$ $$- 2^{4} \cdot 5^{4} \cdot 13$$ $1$ $\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = 2x^4 + 9x^2 + 13$
1311.a.814131.1 1311.a $$3 \cdot 19 \cdot 23$$ $$- 3^{4} \cdot 19 \cdot 23^{2}$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q$$ $y^2 + xy = x^5 + 5x^4 + 5x^3 + 4x^2 + x$
1312.c.671744.1 1312.c $$2^{5} \cdot 41$$ $$- 2^{14} \cdot 41$$ $0$ $\Z/22\Z$ $$\Q$$ $y^2 + (x + 1)y = x^6 + 4x^5 + 7x^4 + 5x^3 + 2x^2$