## Results (1-50 of 121 matches)

Label Class Conductor Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Equation
504.a.27216.1 504.a $$2^{3} \cdot 3^{2} \cdot 7$$ $0$ $\Z/4\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21$
523.a.523.1 523.a $$523$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x + 1)y = x^5 - x^4 - x^3$
523.a.523.2 523.a $$523$$ $0$ $\Z/2\Z$ $$\Q$$ $y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$
529.a.529.1 529.a $$23^{2}$$ $0$ $\Z/11\Z$ $$\mathsf{RM}$$ $y^2 + (x^3 + x + 1)y = -x^5$
555.a.8325.1 555.a $$3 \cdot 5 \cdot 37$$ $0$ $\Z/2\Z\oplus\Z/10\Z$ $$\Q$$ $y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x$
574.a.293888.1 574.a $$2 \cdot 7 \cdot 41$$ $0$ $\Z/2\Z\oplus\Z/10\Z$ $$\Q$$ $y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1$
576.a.576.1 576.a $$2^{6} \cdot 3^{2}$$ $0$ $\Z/10\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$
576.b.147456.1 576.b $$2^{6} \cdot 3^{2}$$ $0$ $\Z/4\Z\oplus\Z/4\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 = x^6 + 2x^4 + 2x^2 + 1$
578.a.2312.1 578.a $$2 \cdot 17^{2}$$ $0$ $\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x$
587.a.587.1 587.a $$587$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^2 - x$
588.a.18816.1 588.a $$2^{2} \cdot 3 \cdot 7^{2}$$ $0$ $\Z/24\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8$
597.a.597.1 597.a $$3 \cdot 199$$ $0$ $\Z/7\Z$ $$\Q$$ $y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x$
600.a.18000.1 600.a $$2^{3} \cdot 3 \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ $$\Q \times \Q$$ $y^2 + xy = 10x^5 - 18x^4 + 8x^3 + x^2 - x$
600.a.96000.1 600.a $$2^{3} \cdot 3 \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2$
600.b.30000.1 600.b $$2^{3} \cdot 3 \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = x^4 + x^2 - 3$
600.b.450000.1 600.b $$2^{3} \cdot 3 \cdot 5^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45$
603.a.603.1 603.a $$3^{2} \cdot 67$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x$
603.a.603.2 603.a $$3^{2} \cdot 67$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^2 + 1)y = x^5 - x^3 + x$
604.a.9664.1 604.a $$2^{2} \cdot 151$$ $0$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21$
604.a.9664.2 604.a $$2^{2} \cdot 151$$ $0$ $\Z/27\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x$
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 $$2^{2} \cdot 7 \cdot 23$$ $0$ $\Z/2\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3$
644.b.14812.1 644.b $$2^{2} \cdot 7 \cdot 23$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1$
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 $$2^{2} \cdot 13^{2}$$ $0$ $\Z/21\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x$
676.b.17576.1 676.b $$2^{2} \cdot 13^{2}$$ $0$ $\Z/3\Z\oplus\Z/3\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$
686.a.686.1 686.a $$2 \cdot 7^{3}$$ $0$ $\Z/6\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$
688.a.2752.1 688.a $$2^{4} \cdot 43$$ $0$ $\Z/20\Z$ $$\Q$$ $y^2 + y = 2x^5 - 5x^4 + 4x^3 - x$
688.a.704512.2 688.a $$2^{4} \cdot 43$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1$
688.a.704512.1 688.a $$2^{4} \cdot 43$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1$
691.a.691.1 691.a $$691$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + (x + 1)y = x^5 - x^3 - x^2$
704.a.45056.1 704.a $$2^{6} \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ $$\Q$$ $y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2$
708.a.2832.1 708.a $$2^{2} \cdot 3 \cdot 59$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^2 + x + 1)y = x^5$
708.a.19116.1 708.a $$2^{2} \cdot 3 \cdot 59$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = -x^5 + 4x^2 + 4x - 1$
708.a.181248.1 708.a $$2^{2} \cdot 3 \cdot 59$$ $0$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36$
709.a.709.1 709.a $$709$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + xy = x^5 - 2x^2 + x$
713.a.713.1 713.a $$23 \cdot 31$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^5 - x$
713.b.713.1 713.b $$23 \cdot 31$$ $0$ $\Z/9\Z$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^4$
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 $$2^{4} \cdot 3^{2} \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/12\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90$
726.a.1452.1 726.a $$2 \cdot 3 \cdot 11^{2}$$ $0$ $\Z/10\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + 1)y = 2x^5 + 2x^4 + 6x^3 - 2x^2 - x$
731.a.12427.1 731.a $$17 \cdot 43$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3$
741.a.28899.1 741.a $$3 \cdot 13 \cdot 19$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q$$ $y^2 + (x + 1)y = -3x^5 - x^4 + 2x^2 + x$
743.a.743.1 743.a $$743$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^4 + x^2$
745.a.745.1 745.a $$5 \cdot 149$$ $0$ $\Z/9\Z$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x$
762.a.3048.1 762.a $$2 \cdot 3 \cdot 127$$ $0$ $\Z/12\Z$ $$\Q$$ $y^2 + (x^3 + x^2 + x)y = x^2 + x + 1$