Results (1-50 of 854 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Weierstrass equation
20.1-a1 20.1-a $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 5$$ 0 $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2={x}^3+{x}^2-36{x}-140$
20.1-a2 20.1-a $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 5$$ 0 $\Z/6\Z$ $\mathrm{SU}(2)$ ${y}^2={x}^3+{x}^2+4{x}+4$
20.1-a3 20.1-a $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 5$$ 0 $\Z/6\Z$ $\mathrm{SU}(2)$ ${y}^2={x}^3+{x}^2-{x}$
20.1-a4 20.1-a $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 5$$ 0 $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2={x}^3+{x}^2-41{x}-116$
20.1-b1 20.1-b $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 5$$ $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3-{x}^2-5{x}+25$
20.1-b2 20.1-b $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 5$$ $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3-{x}^2+5{x}-3$
20.1-b3 20.1-b $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 5$$ $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2={x}^3+{x}^2-5{x}-5$
20.1-b4 20.1-b $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 5$$ $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2={x}^3+{x}^2-165{x}+763$
32.1-a1 32.1-a $$\Q(\sqrt{-10})$$ $$2^{5}$$ 0 $\Z/2\Z\oplus\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ ${y}^2={x}^3-{x}$
32.1-a2 32.1-a $$\Q(\sqrt{-10})$$ $$2^{5}$$ 0 $\Z/4\Z$ $-4$ $N(\mathrm{U}(1))$ ${y}^2={x}^3+4{x}$
32.1-a3 32.1-a $$\Q(\sqrt{-10})$$ $$2^{5}$$ 0 $\Z/2\Z$ $-16$ $N(\mathrm{U}(1))$ ${y}^2={x}^3-11{x}-14$
32.1-a4 32.1-a $$\Q(\sqrt{-10})$$ $$2^{5}$$ 0 $\Z/4\Z$ $-16$ $N(\mathrm{U}(1))$ ${y}^2={x}^3-11{x}+14$
32.1-b1 32.1-b $$\Q(\sqrt{-10})$$ $$2^{5}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ ${y}^2={x}^3-4{x}$
32.1-b2 32.1-b $$\Q(\sqrt{-10})$$ $$2^{5}$$ $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ ${y}^2={x}^3+{x}$
32.1-b3 32.1-b $$\Q(\sqrt{-10})$$ $$2^{5}$$ $1$ $\Z/4\Z$ $-16$ $N(\mathrm{U}(1))$ ${y}^2+a{x}{y}={x}^3+{x}^2-2{x}+3$
32.1-b4 32.1-b $$\Q(\sqrt{-10})$$ $$2^{5}$$ $1$ $\Z/2\Z$ $-16$ $N(\mathrm{U}(1))$ ${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+3{x}+2$
40.1-a1 40.1-a $$\Q(\sqrt{-10})$$ $$2^{3} \cdot 5$$ 0 $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+9{x}+5$
40.1-a2 40.1-a $$\Q(\sqrt{-10})$$ $$2^{3} \cdot 5$$ 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+4{x}+4$
40.1-a3 40.1-a $$\Q(\sqrt{-10})$$ $$2^{3} \cdot 5$$ 0 $\Z/4\Z$ $\mathrm{SU}(2)$ ${y}^2={x}^3-8{x}-8$
40.1-a4 40.1-a $$\Q(\sqrt{-10})$$ $$2^{3} \cdot 5$$ 0 $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-21{x}+69$
40.1-b1 40.1-b $$\Q(\sqrt{-10})$$ $$2^{3} \cdot 5$$ 0 $\Z/4\Z$ $\mathrm{SU}(2)$ ${y}^2={x}^3+13{x}-34$
40.1-b2 40.1-b $$\Q(\sqrt{-10})$$ $$2^{3} \cdot 5$$ 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2={x}^3-7{x}-6$
40.1-b3 40.1-b $$\Q(\sqrt{-10})$$ $$2^{3} \cdot 5$$ 0 $\Z/4\Z$ $\mathrm{SU}(2)$ ${y}^2={x}^3-2{x}+1$
40.1-b4 40.1-b $$\Q(\sqrt{-10})$$ $$2^{3} \cdot 5$$ 0 $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2={x}^3-107{x}-426$
44.1-a1 44.1-a $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 11$$ 0 $\Z/3\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-a-2\right){x}+1$
44.1-a2 44.1-a $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 11$$ 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(9a+18\right){x}+4a-131$
44.1-b1 44.1-b $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 11$$ 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ ${y}^2={x}^3+a{x}^2-{x}+a+2$
44.1-b2 44.1-b $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 11$$ 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ ${y}^2={x}^3+a{x}^2+\left(40a+79\right){x}+9a+578$
44.2-a1 44.2-a $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 11$$ 0 $\Z/3\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(a-2\right){x}+1$
44.2-a2 44.2-a $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 11$$ 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(-9a+18\right){x}-4a-131$
44.2-b1 44.2-b $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 11$$ 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ ${y}^2={x}^3-a{x}^2-{x}-a+2$
44.2-b2 44.2-b $$\Q(\sqrt{-10})$$ $$2^{2} \cdot 11$$ 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ ${y}^2={x}^3-a{x}^2+\left(-40a+79\right){x}-9a+578$
45.1-a1 45.1-a $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$
45.1-a2 45.1-a $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2$
45.1-a3 45.1-a $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$
45.1-a4 45.1-a $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$
45.1-a5 45.1-a $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$
45.1-a6 45.1-a $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$
45.1-a7 45.1-a $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$
45.1-a8 45.1-a $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$
45.1-b1 45.1-b $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ 0 $\Z/4\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3-438{x}+7038$
45.1-b2 45.1-b $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ 0 $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3+2{x}-2$
45.1-b3 45.1-b $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ 0 $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3+142{x}+222$
45.1-b4 45.1-b $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3-38{x}+78$
45.1-b5 45.1-b $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3-18{x}-18$
45.1-b6 45.1-b $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3-538{x}+5278$
45.1-b7 45.1-b $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ 0 $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3-318{x}-1938$
45.1-b8 45.1-b $$\Q(\sqrt{-10})$$ $$3^{2} \cdot 5$$ 0 $\Z/2\Z$ $\mathrm{SU}(2)$ ${y}^2+a{x}{y}={x}^3-8638{x}+316318$
49.1-a1 49.1-a $$\Q(\sqrt{-10})$$ $$7^{2}$$ 0 $\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ ${y}^2={x}^3+\left(-a+1\right){x}^2+\left(-4a+2\right){x}-2a-24$
49.1-a2 49.1-a $$\Q(\sqrt{-10})$$ $$7^{2}$$ 0 $\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(a+7\right){x}-a+2$
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*The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.