## Results (40 matches)

Label Class Conductor Discriminant Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Equation
256.a.512.1 256.a $$2^{8}$$ $$- 2^{9}$$ $0$ $\Z/2\Z\oplus\Z/10\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$
324.a.648.1 324.a $$2^{2} \cdot 3^{4}$$ $$- 2^{3} \cdot 3^{4}$$ $0$ $\Z/21\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$
388.a.776.1 388.a $$2^{2} \cdot 97$$ $$2^{3} \cdot 97$$ $0$ $\Z/21\Z$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x$
472.a.944.1 472.a $$2^{3} \cdot 59$$ $$- 2^{4} \cdot 59$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ $$\Q$$ $y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x$
476.a.952.1 476.a $$2^{2} \cdot 7 \cdot 17$$ $$- 2^{3} \cdot 7 \cdot 17$$ $0$ $\Z/3\Z\oplus\Z/6\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54$
523.a.523.1 523.a $$523$$ $$-523$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x + 1)y = x^5 - x^4 - x^3$
523.a.523.2 523.a $$523$$ $$-523$$ $0$ $\Z/2\Z$ $$\Q$$ $y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$
529.a.529.1 529.a $$23^{2}$$ $$23^{2}$$ $0$ $\Z/11\Z$ $$\mathsf{RM}$$ $y^2 + (x^3 + x + 1)y = -x^5$
576.a.576.1 576.a $$2^{6} \cdot 3^{2}$$ $$- 2^{6} \cdot 3^{2}$$ $0$ $\Z/10\Z$ $$\mathrm{M}_2(\Q)$$ $y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$
587.a.587.1 587.a $$587$$ $$587$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^2 - x$
597.a.597.1 597.a $$3 \cdot 199$$ $$3 \cdot 199$$ $0$ $\Z/7\Z$ $$\Q$$ $y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x$
603.a.603.1 603.a $$3^{2} \cdot 67$$ $$- 3^{2} \cdot 67$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x$
603.a.603.2 603.a $$3^{2} \cdot 67$$ $$- 3^{2} \cdot 67$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^2 + 1)y = x^5 - x^3 + x$
686.a.686.1 686.a $$2 \cdot 7^{3}$$ $$2 \cdot 7^{3}$$ $0$ $\Z/6\Z$ $$\mathsf{CM} \times \Q$$ $y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$
691.a.691.1 691.a $$691$$ $$-691$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + (x + 1)y = x^5 - x^3 - x^2$
709.a.709.1 709.a $$709$$ $$709$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + xy = x^5 - 2x^2 + x$
713.a.713.1 713.a $$23 \cdot 31$$ $$23 \cdot 31$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^5 - x$
713.b.713.1 713.b $$23 \cdot 31$$ $$23 \cdot 31$$ $0$ $\Z/9\Z$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^4$
743.a.743.1 743.a $$743$$ $$-743$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^4 + x^2$
745.a.745.1 745.a $$5 \cdot 149$$ $$- 5 \cdot 149$$ $0$ $\Z/9\Z$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x$
763.a.763.1 763.a $$7 \cdot 109$$ $$- 7 \cdot 109$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + (x^3 + x)y = -2x^4 + 2x^2 - x$
797.a.797.1 797.a $$797$$ $$797$$ $0$ $\Z/7\Z$ $$\Q$$ $y^2 + y = x^5 - x^4 + x^3$
832.a.832.1 832.a $$2^{6} \cdot 13$$ $$- 2^{6} \cdot 13$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + (x^3 + x)y = x^5 - x^3 + x^2 + 2x - 1$
841.a.841.1 841.a $$29^{2}$$ $$- 29^{2}$$ $0$ $\Z/7\Z$ $$\mathsf{RM}$$ $y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 3x^2 + x + 2$
847.a.847.1 847.a $$7 \cdot 11^{2}$$ $$- 7 \cdot 11^{2}$$ $1$ $\Z/5\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2$
847.d.847.1 847.d $$7 \cdot 11^{2}$$ $$- 7 \cdot 11^{2}$$ $0$ $\Z/3\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x^2 + x + 1)y = -12x^6 - 15x^5 + 9x^4 + 31x^3 + 9x^2 - 15x - 12$
862.a.862.1 862.a $$2 \cdot 431$$ $$- 2 \cdot 431$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = x^5 - 2x^4 - 7x^3 + 7x^2 + 2x + 5$
862.b.862.1 862.b $$2 \cdot 431$$ $$2 \cdot 431$$ $0$ $\Z/9\Z$ $$\Q$$ $y^2 + (x^3 + x)y = -2x^4 + 3x^2 - x - 1$
893.a.893.1 893.a $$19 \cdot 47$$ $$19 \cdot 47$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^4 - x^2$
909.a.909.1 909.a $$3^{2} \cdot 101$$ $$3^{2} \cdot 101$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + (x^3 + x)y = -x^4 + x^2 - x$
925.a.925.1 925.a $$5^{2} \cdot 37$$ $$5^{2} \cdot 37$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + (x + 1)y = -x^5 + 2x^4 - x^3 - x^2$
930.a.930.1 930.a $$2 \cdot 3 \cdot 5 \cdot 31$$ $$2 \cdot 3 \cdot 5 \cdot 31$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15$
953.a.953.1 953.a $$953$$ $$-953$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = x^3 + x^2$
961.a.961.1 961.a $$31^{2}$$ $$- 31^{2}$$ $0$ $\mathsf{trivial}$ $$\mathsf{RM}$$ $y^2 + (x^3 + x + 1)y = -x^6 - x^5 - 7x^4 + 74x^3 - 145x^2 + 99x - 33$
961.a.961.2 961.a $$31^{2}$$ $$- 31^{2}$$ $0$ $\Z/5\Z$ $$\mathsf{RM}$$ $y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 8x^4 + 12x^3 - 18x^2 + 12x - 7$
961.a.961.3 961.a $$31^{2}$$ $$31^{2}$$ $0$ $\Z/5\Z$ $$\mathsf{RM}$$ $y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3 - x - 1$
971.a.971.1 971.a $$971$$ $$-971$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + y = x^5 - 2x^3 + x$
997.a.997.1 997.a $$997$$ $$997$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q$$ $y^2 + xy = x^5 - 8x^4 + 16x^3 - x$
997.a.997.2 997.a $$997$$ $$997$$ $0$ $\Z/8\Z$ $$\Q$$ $y^2 + (x + 1)y = x^5 + x^4$
997.b.997.1 997.b $$997$$ $$997$$ $1$ $\Z/3\Z$ $$\Q$$ $y^2 + y = x^5 - 2x^4 + 2x^3 - x^2$