Results (1-50 of 17197 matches)

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Label Class Conductor Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Equation
10000.a.160000.1 10000.a $$2^{4} \cdot 5^{4}$$ $0$ $\Z/5\Z$ $$\Q \times \Q$$ $y^2 + xy = x^6 - 2x^5 + 2x^4 - x^3 + 2x^2 - 3x + 2$
10000.b.800000.1 10000.b $$2^{4} \cdot 5^{4}$$ $0$ $\Z/10\Z$ $$\mathsf{CM}$$ $y^2 = x^5 + 1$
10005.a.50025.1 10005.a $$3 \cdot 5 \cdot 23 \cdot 29$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = x - 1$
10005.b.450225.1 10005.b $$3 \cdot 5 \cdot 23 \cdot 29$$ $2$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -2x^4 + 3x^2 + x + 2$
10016.a.641024.1 10016.a $$2^{5} \cdot 313$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\Q$$ $y^2 + xy = 8x^5 - 13x^4 - 19x^3 + 9x^2 - x$
10017.a.10017.1 10017.a $$3^{3} \cdot 7 \cdot 53$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x^2 + 1)y = -x^4 - 2x^3 - 2$
10020.a.160320.1 10020.a $$2^{2} \cdot 3 \cdot 5 \cdot 167$$ $1$ $\Z/3\Z$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^4 - 4x^3 + 7x + 4$
10023.a.30069.1 10023.a $$3 \cdot 13 \cdot 257$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + y = x^5 + 2x^4 + x^3 - 2x^2$
10025.a.10025.1 10025.a $$5^{2} \cdot 401$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + y = x^6 - x^5 - x^4 + x^2 + x$
10028.a.641792.1 10028.a $$2^{2} \cdot 23 \cdot 109$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x^2 + x)y = 2x^4 + 2x^3 + 6x^2 + 2x + 4$
10032.a.30096.1 10032.a $$2^{4} \cdot 3 \cdot 11 \cdot 19$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + x^3y = -4x^4 - 8x^3 - 8x^2 - 4x - 1$
10036.a.642304.1 10036.a $$2^{2} \cdot 13 \cdot 193$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^2 + x + 1)y = -x^5 - 4x^3 - 2x^2$
10037.a.10037.1 10037.a $$10037$$ $2$ $\mathsf{trivial}$ $$\Q$$ $y^2 + y = x^5 + x^2$
10040.a.20080.1 10040.a $$2^{3} \cdot 5 \cdot 251$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x + 1)y = 2x^5 - x^4 - 2x^3$
10040.b.321280.1 10040.b $$2^{3} \cdot 5 \cdot 251$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x + 1)y = 2x^5 - x^4 - 3x^3 + x^2 + x$
10040.c.502000.1 10040.c $$2^{3} \cdot 5 \cdot 251$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^2 + 1)y = x^5 - 3x^4 + 3x^3 - 2x$
10043.a.10043.1 10043.a $$11^{2} \cdot 83$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + y = x^5 - 2x^4 - 3x^3 + x$
10044.a.40176.1 10044.a $$2^{2} \cdot 3^{4} \cdot 31$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^2 + x + 1)y = -x^5 - 2x^2$
10048.a.10048.1 10048.a $$2^{6} \cdot 157$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x^2)y = 2x^4 - x^3 + x^2 - 4x + 2$
10048.b.160768.1 10048.b $$2^{6} \cdot 157$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x^2)y = x^4 + 3x^3 + 5x^2 + 4x + 2$
10056.a.181008.1 10056.a $$2^{3} \cdot 3 \cdot 419$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + xy = 2x^5 - 3x^4 + 4x^3 - 2x^2 + x$
10064.a.10064.1 10064.a $$2^{4} \cdot 17 \cdot 37$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x)y = -x^4 - 2x^3 + x^2 + 2x + 1$
10073.a.10073.1 10073.a $$7 \cdot 1439$$ $2$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^2 + x + 1)y = -x^5 + 2x^4 - 3x^2$
10075.a.10075.1 10075.a $$5^{2} \cdot 13 \cdot 31$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + xy = x^5 - 4x^3 - 4x^2 - x$
10075.b.654875.1 10075.b $$5^{2} \cdot 13 \cdot 31$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\Q$$ $y^2 + xy = x^5 + 2x^4 - 4x^3 - 8x^2 - 1$
10075.c.654875.1 10075.c $$5^{2} \cdot 13 \cdot 31$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\Q$$ $y^2 + xy = 5x^5 + 41x^4 + 88x^3 + 16x^2 + x$
10080.a.60480.1 10080.a $$2^{5} \cdot 3^{2} \cdot 5 \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\Q \times \Q$$ $y^2 + xy = -15x^6 + 58x^4 - 60x^2 + 7$
10080.b.60480.1 10080.b $$2^{5} \cdot 3^{2} \cdot 5 \cdot 7$$ $0$ $\Z/4\Z$ $$\Q \times \Q$$ $y^2 + xy = -15x^6 - 58x^4 - 60x^2 - 7$
10080.c.141120.1 10080.c $$2^{5} \cdot 3^{2} \cdot 5 \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = -x^6 + 35x^4 - 560x^2 + 2940$
10080.d.241920.1 10080.d $$2^{5} \cdot 3^{2} \cdot 5 \cdot 7$$ $1$ $\Z/2\Z\oplus\Z/4\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + x)y = 2x^6 - 25x^4 + 88x^2 - 105$
10081.a.10081.1 10081.a $$17 \cdot 593$$ $1$ $\Z/3\Z$ $$\Q$$ $y^2 + (x^2 + x + 1)y = x^6 + 2x^4 + x^3 + x^2$
10082.a.20164.1 10082.a $$2 \cdot 71^{2}$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^2 + x)y = -x^5 + x^3 - 2x^2 - x + 1$
10086.a.181548.1 10086.a $$2 \cdot 3 \cdot 41^{2}$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^2 + x)y = x^5 + x^4 + x^3 + 2x^2 + 2x + 1$
10086.b.413526.1 10086.b $$2 \cdot 3 \cdot 41^{2}$$ $0$ $\Z/6\Z$ $$\Q$$ $y^2 + (x^3 + x)y = -x^6 - 4x^5 - 7x^4 - 6x^3 + 3x + 3$
10095.a.30285.1 10095.a $$3 \cdot 5 \cdot 673$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^3 + x)y = -2x^4 + 4x^2 - 3x$
10097.a.10097.1 10097.a $$23 \cdot 439$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^4 + 2x^3 - 3x^2 + 2x - 1$
10098.a.272646.1 10098.a $$2 \cdot 3^{3} \cdot 11 \cdot 17$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $$\Q \times \Q$$ $y^2 + (x^3 + 1)y = -9x^6 + 16x^5 - 35x^4 + 33x^3 - 35x^2 + 16x - 9$
10102.a.323264.1 10102.a $$2 \cdot 5051$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x + 1)y = -x^5 + 3x^4 + x^3 - 3x^2$
10110.a.50550.2 10110.a $$2 \cdot 3 \cdot 5 \cdot 337$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^2 + x)y = 39x^6 - 45x^5 - 62x^4 + 22x^3 + 69x^2 + 50x - 75$
10110.a.50550.1 10110.a $$2 \cdot 3 \cdot 5 \cdot 337$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^3 + 1)y = 2x^5 + 3x^4 + 2x^3 - x - 1$
10112.a.10112.1 10112.a $$2^{7} \cdot 79$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^3 + x^2)y = 2x^4 + 2x^3 + 5x^2 + 2x + 3$
10114.a.262964.1 10114.a $$2 \cdot 13 \cdot 389$$ $0$ $\Z/6\Z$ $$\Q$$ $y^2 + (x^2 + 1)y = 2x^5 - 4x^4 - 2x^3 + 3x^2 + x + 1$
10115.a.10115.1 10115.a $$5 \cdot 7 \cdot 17^{2}$$ $1$ $\Z/2\Z$ $$\Q$$ $y^2 + (x^3 + x^2 + x)y = -x^4 + 3x^2 + x - 2$
10115.b.70805.1 10115.b $$5 \cdot 7 \cdot 17^{2}$$ $0$ $\Z/10\Z$ $$\Q$$ $y^2 + xy = 7x^5 - 12x^4 + 7x^3 - 3x^2 + x$
10115.c.70805.1 10115.c $$5 \cdot 7 \cdot 17^{2}$$ $0$ $\Z/4\Z$ $$\Q$$ $y^2 + xy = x^5 - x^4 + x$
10121.a.293509.1 10121.a $$29 \cdot 349$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + y = x^5 + 2x^4 + 4x + 3$
10125.a.10125.1 10125.a $$3^{4} \cdot 5^{3}$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -x^2 + x - 1$
10125.a.10125.2 10125.a $$3^{4} \cdot 5^{3}$$ $1$ $\Z/5\Z$ $$\Q$$ $y^2 + (x^3 + x^2 + 1)y = 9x^4 + 28x^3 - x^2 - 34x + 13$
10130.a.162080.1 10130.a $$2 \cdot 5 \cdot 1013$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x^2)y = -x^4 + 3x^2 - 5x - 10$
10137.a.10137.1 10137.a $$3 \cdot 31 \cdot 109$$ $1$ $\mathsf{trivial}$ $$\Q$$ $y^2 + (x^3 + x + 1)y = -2x^4 + 4x^2 - x - 4$
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