## Results (1-50 of 8419 matches)

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Label Class Conductor Discriminant Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Equation
196.a.21952.1 196.a $$2^{2} \cdot 7^{2}$$ $$- 2^{6} \cdot 7^{3}$$ $0$ $\Z/6\Z\oplus\Z/6\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^2 + x)y = x^6 + 3x^5 + 6x^4 + 7x^3 + 6x^2 + 3x + 1$
363.a.11979.1 363.a $$3 \cdot 11^{2}$$ $$- 3^{2} \cdot 11^{3}$$ $0$ $\Z/2\Z\oplus\Z/10\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + 1)y = x^5 + 2x^3 + 4x^2 + 2x$
363.a.43923.1 363.a $$3 \cdot 11^{2}$$ $$- 3 \cdot 11^{4}$$ $0$ $\Z/10\Z$ $$\Q \times \Q$$ $y^2 + x^2y = 11x^5 - 13x^4 - 7x^3 + 10x^2 + x - 2$
450.a.36450.1 450.a $$2 \cdot 3^{2} \cdot 5^{2}$$ $$2 \cdot 3^{6} \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = x^5 - 4x^4 - 9x^3 + 28x^2 - 6x - 16$
464.a.29696.1 464.a $$2^{4} \cdot 29$$ $$- 2^{10} \cdot 29$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q$$ $y^2 + (x + 1)y = 8x^5 + 3x^4 - 4x^3 - 2x^2$
464.a.29696.2 464.a $$2^{4} \cdot 29$$ $$- 2^{10} \cdot 29$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\Q$$ $y^2 + xy = 4x^5 + 33x^4 + 72x^3 + 16x^2 + x$
472.a.60416.1 472.a $$2^{3} \cdot 59$$ $$2^{10} \cdot 59$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2$
504.a.27216.1 504.a $$2^{3} \cdot 3^{2} \cdot 7$$ $$- 2^{4} \cdot 3^{5} \cdot 7$$ $0$ $\Z/4\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21$
588.a.18816.1 588.a $$2^{2} \cdot 3 \cdot 7^{2}$$ $$- 2^{7} \cdot 3 \cdot 7^{2}$$ $0$ $\Z/24\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8$
600.a.18000.1 600.a $$2^{3} \cdot 3 \cdot 5^{2}$$ $$2^{4} \cdot 3^{2} \cdot 5^{3}$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ $$\Q \times \Q$$ $y^2 + xy = 10x^5 - 18x^4 + 8x^3 + x^2 - x$
600.a.96000.1 600.a $$2^{3} \cdot 3 \cdot 5^{2}$$ $$2^{8} \cdot 3 \cdot 5^{3}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2$
600.b.30000.1 600.b $$2^{3} \cdot 3 \cdot 5^{2}$$ $$2^{4} \cdot 3 \cdot 5^{4}$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = x^4 + x^2 - 3$
630.a.34020.1 630.a $$2 \cdot 3^{2} \cdot 5 \cdot 7$$ $$2^{2} \cdot 3^{5} \cdot 5 \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = 3x^5 + 10x^4 - 23x^2 - 6x + 15$
640.a.81920.1 640.a $$2^{7} \cdot 5$$ $$- 2^{14} \cdot 5$$ $0$ $\Z/12\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + x^3y = 3x^4 + 13x^2 + 20$
640.a.81920.2 640.a $$2^{7} \cdot 5$$ $$2^{14} \cdot 5$$ $0$ $\Z/12\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + x^3y = -3x^4 + 13x^2 - 20$
644.b.14812.1 644.b $$2^{2} \cdot 7 \cdot 23$$ $$- 2^{2} \cdot 7 \cdot 23^{2}$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1$
676.b.17576.1 676.b $$2^{2} \cdot 13^{2}$$ $$- 2^{3} \cdot 13^{3}$$ $0$ $\Z/3\Z\oplus\Z/3\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$
704.a.45056.1 704.a $$2^{6} \cdot 11$$ $$- 2^{12} \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q$$ $y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2$
708.a.19116.1 708.a $$2^{2} \cdot 3 \cdot 59$$ $$- 2^{2} \cdot 3^{4} \cdot 59$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = -x^5 + 4x^2 + 4x - 1$
731.a.12427.1 731.a $$17 \cdot 43$$ $$- 17^{2} \cdot 43$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3$
741.a.28899.1 741.a $$3 \cdot 13 \cdot 19$$ $$- 3^{2} \cdot 13^{2} \cdot 19$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q$$ $y^2 + (x + 1)y = -3x^5 - x^4 + 2x^2 + x$
762.a.82296.1 762.a $$2 \cdot 3 \cdot 127$$ $$2^{3} \cdot 3^{4} \cdot 127$$ $0$ $\Z/2\Z\oplus\Z/12\Z$ $$\Q$$ $y^2 + (x^2 + x)y = x^5 - 8x^4 + 14x^3 + 2x^2 - x$
784.a.43904.1 784.a $$2^{4} \cdot 7^{2}$$ $$- 2^{7} \cdot 7^{3}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = 4x^4 + 27x^2 + 56$
784.b.12544.1 784.b $$2^{4} \cdot 7^{2}$$ $$2^{8} \cdot 7^{2}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -1$
784.b.25088.1 784.b $$2^{4} \cdot 7^{2}$$ $$- 2^{9} \cdot 7^{2}$$ $0$ $\Z/2\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + 1)y = -x^6 - 3x^5 + 7x^4 + 2x^3 - 49x^2 + 41x - 9$
784.b.76832.1 784.b $$2^{4} \cdot 7^{2}$$ $$- 2^{5} \cdot 7^{4}$$ $0$ $\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x + 1)y = -x^6 + 4x^5 - 4x^4 - 2x^3 + 10x - 9$
816.a.13872.1 816.a $$2^{4} \cdot 3 \cdot 17$$ $$- 2^{4} \cdot 3 \cdot 17^{2}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q$$ $y^2 + (x^3 + x^2)y = -2x^4 + 6x^2 - 8x + 3$
816.a.39168.1 816.a $$2^{4} \cdot 3 \cdot 17$$ $$2^{8} \cdot 3^{2} \cdot 17$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ $$\Q$$ $y^2 + (x^2 + 1)y = 3x^5 - 4x^3 - x^2 + x$
816.b.52224.1 816.b $$2^{4} \cdot 3 \cdot 17$$ $$- 2^{10} \cdot 3 \cdot 17$$ $0$ $\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -x^6 - 12x^4 - 27x^2 - 17$
826.a.11564.1 826.a $$2 \cdot 7 \cdot 59$$ $$- 2^{2} \cdot 7^{2} \cdot 59$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q$$ $y^2 + (x^2 + x)y = x^5 + x^4 + 3x^3 - 4x^2 - 4x + 3$
882.a.63504.1 882.a $$2 \cdot 3^{2} \cdot 7^{2}$$ $$2^{4} \cdot 3^{4} \cdot 7^{2}$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = x^5 + x^4 + x^3 + 3x^2 + 3x + 1$
925.a.23125.1 925.a $$5^{2} \cdot 37$$ $$5^{4} \cdot 37$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q$$ $y^2 + xy = 5x^5 + x^4 - 19x^3 + 18x^2 - 5x$
975.a.63375.1 975.a $$3 \cdot 5^{2} \cdot 13$$ $$- 3 \cdot 5^{3} \cdot 13^{2}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = -x^5 + x^3 + 2x^2 + x - 1$
1008.a.27216.1 1008.a $$2^{4} \cdot 3^{2} \cdot 7$$ $$2^{4} \cdot 3^{5} \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -4x^4 + 15x^2 - 21$
1083.a.20577.1 1083.a $$3 \cdot 19^{2}$$ $$3 \cdot 19^{3}$$ $1$ $\Z/3\Z$ $$\Q \times \Q$$ $y^2 + x^3y = x^5 - 5x^4 + 11x^3 - 13x^2 + 9x - 3$
1083.b.87723.1 1083.b $$3 \cdot 19^{2}$$ $$- 3^{5} \cdot 19^{2}$$ $0$ $\Z/15\Z$ $$\Q \times \Q$$ $y^2 + y = -x^6 - 3x^5 - 8x^4 - 11x^3 - 14x^2 - 9x - 6$
1104.a.17664.1 1104.a $$2^{4} \cdot 3 \cdot 23$$ $$2^{8} \cdot 3 \cdot 23$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 = x^5 - 2x^4 + 4x^3 - 4x^2 + 3x - 1$
1147.a.35557.1 1147.a $$31 \cdot 37$$ $$31^{2} \cdot 37$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q$$ $y^2 + xy = x^5 + 8x^4 + 18x^3 + 8x^2 + x$
1147.a.35557.2 1147.a $$31 \cdot 37$$ $$31^{2} \cdot 37$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\Q$$ $y^2 + xy = x^5 + 6x^4 - 32x^2 + x$
1148.a.47068.1 1148.a $$2^{2} \cdot 7 \cdot 41$$ $$- 2^{2} \cdot 7 \cdot 41^{2}$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^2 + x + 1)y = x^5 + 2x^4 - 5x^3 + x$
1170.a.10530.1 1170.a $$2 \cdot 3^{2} \cdot 5 \cdot 13$$ $$- 2 \cdot 3^{4} \cdot 5 \cdot 13$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = 15x^6 + 28x^5 + 62x^4 + 59x^3 + 62x^2 + 28x + 15$
1176.b.16464.1 1176.b $$2^{3} \cdot 3 \cdot 7^{2}$$ $$2^{4} \cdot 3 \cdot 7^{3}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x + 1)y = -2x^5 + x^2$
1180.a.18880.1 1180.a $$2^{2} \cdot 5 \cdot 59$$ $$- 2^{6} \cdot 5 \cdot 59$$ $0$ $\Z/18\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = -2x^4 + 4x^2 + 2x$
1192.a.19072.1 1192.a $$2^{3} \cdot 149$$ $$- 2^{7} \cdot 149$$ $0$ $\Z/22\Z$ $$\Q$$ $y^2 + (x^3 + x)y = x^3 - 2x^2 - x + 1$
1197.a.10773.1 1197.a $$3^{2} \cdot 7 \cdot 19$$ $$3^{4} \cdot 7 \cdot 19$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^3 + x^2)y = -x^3 - x^2 - x + 2$
1200.a.30000.1 1200.a $$2^{4} \cdot 3 \cdot 5^{2}$$ $$- 2^{4} \cdot 3 \cdot 5^{4}$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -2x^4 + x^2 + 3$
1216.a.19456.1 1216.a $$2^{6} \cdot 19$$ $$- 2^{10} \cdot 19$$ $0$ $\Z/2\Z$ $$\Q$$ $y^2 + x^2y = 4x^5 + 3x^4 - 11x^3 - 6x^2 + 6x - 1$
1258.a.21386.1 1258.a $$2 \cdot 17 \cdot 37$$ $$2 \cdot 17^{2} \cdot 37$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + xy = x^5 + 4x^4 - 5x^3 - 4x^2 + 5x - 1$
1280.a.12800.1 1280.a $$2^{8} \cdot 5$$ $$- 2^{9} \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q$$ $y^2 + y = 2x^5 + x^4 - x^3 - x^2$
1296.a.20736.1 1296.a $$2^{4} \cdot 3^{4}$$ $$2^{8} \cdot 3^{4}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^5 - x^4 - 3x^3 + 4x^2 - x$
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