## Results (1-50 of 987 matches)

Label Class Conductor Discriminant Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Equation
249.a.6723.1 249.a $$3 \cdot 83$$ $$- 3^{4} \cdot 83$$ $0$ $\Z/28\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$
294.a.8232.1 294.a $$2 \cdot 3 \cdot 7^{2}$$ $$2^{3} \cdot 3 \cdot 7^{3}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14$
360.a.6480.1 360.a $$2^{3} \cdot 3^{2} \cdot 5$$ $$2^{4} \cdot 3^{4} \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$
394.a.3152.1 394.a $$2 \cdot 197$$ $$2^{4} \cdot 197$$ $0$ $\Z/20\Z$ $$\Q$$ $y^2 + (x + 1)y = -x^5$
427.a.2989.1 427.a $$7 \cdot 61$$ $$- 7^{2} \cdot 61$$ $0$ $\Z/14\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4$
450.a.2700.1 450.a $$2 \cdot 3^{2} \cdot 5^{2}$$ $$- 2^{2} \cdot 3^{3} \cdot 5^{2}$$ $0$ $\Z/24\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$
484.a.1936.1 484.a $$2^{2} \cdot 11^{2}$$ $$- 2^{4} \cdot 11^{2}$$ $0$ $\Z/15\Z$ $$\Q \times \Q$$ $y^2 + y = x^6 + 2x^4 + x^2$
555.a.8325.1 555.a $$3 \cdot 5 \cdot 37$$ $$3^{2} \cdot 5^{2} \cdot 37$$ $0$ $\Z/2\Z\oplus\Z/10\Z$ $$\Q$$ $y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x$
578.a.2312.1 578.a $$2 \cdot 17^{2}$$ $$2^{3} \cdot 17^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x$
604.a.9664.1 604.a $$2^{2} \cdot 151$$ $$2^{6} \cdot 151$$ $0$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21$
604.a.9664.2 604.a $$2^{2} \cdot 151$$ $$2^{6} \cdot 151$$ $0$ $\Z/27\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x$
644.a.2576.1 644.a $$2^{2} \cdot 7 \cdot 23$$ $$- 2^{4} \cdot 7 \cdot 23$$ $0$ $\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = -5x^6 + 11x^5 - 20x^4 + 20x^3 - 20x^2 + 11x - 5$
676.a.5408.1 676.a $$2^{2} \cdot 13^{2}$$ $$- 2^{5} \cdot 13^{2}$$ $0$ $\Z/21\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x^2 + x)y = x^3 + 3x^2 + 3x + 1$
688.a.2752.1 688.a $$2^{4} \cdot 43$$ $$- 2^{6} \cdot 43$$ $0$ $\Z/20\Z$ $$\Q$$ $y^2 + y = 2x^5 - 5x^4 + 4x^3 - x$
708.a.2832.1 708.a $$2^{2} \cdot 3 \cdot 59$$ $$2^{4} \cdot 3 \cdot 59$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^2 + x + 1)y = x^5$
720.a.6480.1 720.a $$2^{4} \cdot 3^{2} \cdot 5$$ $$- 2^{4} \cdot 3^{4} \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5$
726.a.1452.1 726.a $$2 \cdot 3 \cdot 11^{2}$$ $$- 2^{2} \cdot 3 \cdot 11^{2}$$ $0$ $\Z/10\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + 1)y = 2x^5 + 2x^4 + 6x^3 - 2x^2 - x$
762.a.3048.1 762.a $$2 \cdot 3 \cdot 127$$ $$- 2^{3} \cdot 3 \cdot 127$$ $0$ $\Z/12\Z$ $$\Q$$ $y^2 + (x^3 + x^2 + x)y = x^2 + x + 1$
768.a.1536.1 768.a $$2^{8} \cdot 3$$ $$2^{9} \cdot 3$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q$$ $y^2 + y = 2x^5 - x^4 - 3x^3 + x$
768.a.4608.1 768.a $$2^{8} \cdot 3$$ $$2^{9} \cdot 3^{2}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q$$ $y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2 - x - 1$
784.a.1568.1 784.a $$2^{4} \cdot 7^{2}$$ $$2^{5} \cdot 7^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -2x^4 + 3x^2 - 2$
800.a.1600.1 800.a $$2^{5} \cdot 5^{2}$$ $$2^{6} \cdot 5^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^2$
800.a.8000.1 800.a $$2^{5} \cdot 5^{2}$$ $$2^{6} \cdot 5^{3}$$ $0$ $\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x^2 + x + 1)y = -x^6 + 2x^4 + 4x^3 + 2x^2 - 1$
807.a.2421.1 807.a $$3 \cdot 269$$ $$3^{2} \cdot 269$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + (x^3 + x)y = x^5 - 2x^3 - x^2 + 2x - 1$
830.a.6640.1 830.a $$2 \cdot 5 \cdot 83$$ $$- 2^{4} \cdot 5 \cdot 83$$ $0$ $\Z/16\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = -x^5 + x^4 - 2x^2 + x + 1$
834.a.1668.1 834.a $$2 \cdot 3 \cdot 139$$ $$2^{2} \cdot 3 \cdot 139$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = -x^2 + x - 1$
847.b.9317.1 847.b $$7 \cdot 11^{2}$$ $$7 \cdot 11^{3}$$ $0$ $\Z/10\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + 1)y = x^5 + 2x^4 - 3x^3 + 2x^2 - x$
847.c.9317.1 847.c $$7 \cdot 11^{2}$$ $$7 \cdot 11^{3}$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + (x^3 + x^2)y = x^4 + x^3 - x - 2$
856.a.1712.1 856.a $$2^{3} \cdot 107$$ $$- 2^{4} \cdot 107$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q$$ $y^2 + (x^3 + x)y = -x^4 - x^3 + x$
862.a.6896.1 862.a $$2 \cdot 431$$ $$- 2^{4} \cdot 431$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q$$ $y^2 + (x^2 + x)y = 4x^5 + 6x^4 - 3x^2 - x$
864.a.1728.1 864.a $$2^{5} \cdot 3^{3}$$ $$- 2^{6} \cdot 3^{3}$$ $0$ $\Z/12\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^2$
886.a.3544.1 886.a $$2 \cdot 443$$ $$2^{3} \cdot 443$$ $0$ $\Z/15\Z$ $$\Q$$ $y^2 + (x^3 + x)y = -x^4 - x + 1$
909.a.8181.1 909.a $$3^{2} \cdot 101$$ $$3^{4} \cdot 101$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q$$ $y^2 + xy = 3x^5 - 7x^4 + x^3 + 6x^2 - 3x$
932.a.3728.1 932.a $$2^{2} \cdot 233$$ $$- 2^{4} \cdot 233$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + y = x^6 - 2x^5 + x^4 + x^2 - x$
936.a.1872.1 936.a $$2^{3} \cdot 3^{2} \cdot 13$$ $$- 2^{4} \cdot 3^{2} \cdot 13$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -x^6 - 9x^4 - 32x^2 - 39$
968.a.1936.1 968.a $$2^{3} \cdot 11^{2}$$ $$- 2^{4} \cdot 11^{2}$$ $1$ $\Z/5\Z$ $$\Q \times \Q$$ $y^2 + y = x^6 - x^4$
970.a.1940.1 970.a $$2 \cdot 5 \cdot 97$$ $$2^{2} \cdot 5 \cdot 97$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x + 1)y = x^5 + x^4 + x^3 + x^2$
980.a.7840.1 980.a $$2^{2} \cdot 5 \cdot 7^{2}$$ $$2^{5} \cdot 5 \cdot 7^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x + 1)y = -x^6 + 3x^5 - 3x^4 - x$
990.a.8910.1 990.a $$2 \cdot 3^{2} \cdot 5 \cdot 11$$ $$2 \cdot 3^{4} \cdot 5 \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = 3x^5 + 4x^4 + 7x^3 + 4x^2 + 3x$
1012.a.4048.1 1012.a $$2^{2} \cdot 11 \cdot 23$$ $$2^{4} \cdot 11 \cdot 23$$ $0$ $\Z/15\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = x^4 + x^3 + x^2 + x$
1038.a.1038.2 1038.a $$2 \cdot 3 \cdot 173$$ $$- 2 \cdot 3 \cdot 173$$ $0$ $\Z/6\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = x^4 + 2x^2 + x + 1$
1038.a.1038.1 1038.a $$2 \cdot 3 \cdot 173$$ $$2 \cdot 3 \cdot 173$$ $0$ $\Z/6\Z$ $$\Q$$ $y^2 + (x^2 + x)y = x^5 - 12x^4 + 26x^3 + 46x^2 + 21x + 3$
1042.a.1042.1 1042.a $$2 \cdot 521$$ $$2 \cdot 521$$ $0$ $\Z/9\Z$ $$\Q$$ $y^2 + (x^3 + x)y = -x^4 - x^3 - x^2 + 2x + 2$
1047.a.3141.1 1047.a $$3 \cdot 349$$ $$3^{2} \cdot 349$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^3 + x)y = x$
1051.a.1051.1 1051.a $$1051$$ $$-1051$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + y = x^5 - x^4 + x^2 - x$
1051.b.1051.1 1051.b $$1051$$ $$-1051$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + (x + 1)y = -x^5 - x^4$
1051.b.1051.2 1051.b $$1051$$ $$-1051$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\Q$$ $y^2 + xy = x^5 + 8x^4 + 16x^3 + x$
1055.a.1055.1 1055.a $$5 \cdot 211$$ $$- 5 \cdot 211$$ $0$ $\Z/6\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = -x^4 + x^2 - x - 1$
1062.a.6372.1 1062.a $$2 \cdot 3^{2} \cdot 59$$ $$2^{2} \cdot 3^{3} \cdot 59$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = x^5 - x^4 + x^2 - x$
1069.a.1069.1 1069.a $$1069$$ $$1069$$ $0$ $\Z/7\Z$ $$\Q$$ $y^2 + (x^2 + x + 1)y = x^5 + x^3$