Results (1-50 of 10052 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
15.1-a1 15.1-a $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/4\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-a{x}-4a-7$
15.1-a2 15.1-a $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(174a+260\right){x}+145a+374$
15.1-a3 15.1-a $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-41a-75\right){x}+73a+131$
15.1-a4 15.1-a $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(27a-62\right){x}-106a+305$
15.1-a5 15.1-a $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(382a-1057\right){x}-6554a+18298$
15.1-a6 15.1-a $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(67a-177\right){x}+271a-757$
15.1-b1 15.1-b $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/4\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+{x}$
15.1-b2 15.1-b $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(275a-734\right){x}+3747a-10492$
15.1-b3 15.1-b $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(15a-49\right){x}+66a-181$
15.1-b4 15.1-b $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-4{x}+3a-1$
15.1-b5 15.1-b $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-84\right){x}-3a-310$
15.1-b6 15.1-b $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/8\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a-39\right){x}+72a+135$
15.2-a1 15.2-a $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-379a-681\right){x}+5873a+10526$
15.2-a2 15.2-a $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/4\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+3a-10$
15.2-a3 15.2-a $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-64a-116\right){x}-387a-694$
15.2-a4 15.2-a $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-24a-41\right){x}+65a+116$
15.2-a5 15.2-a $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(40a-115\right){x}-74a+205$
15.2-a6 15.2-a $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-175a+435\right){x}-146a+520$
15.2-b1 15.2-b $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(5a-90\right){x}+8a-403$
15.2-b2 15.2-b $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}$
15.2-b3 15.2-b $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/8\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(15a-55\right){x}-57a+152$
15.2-b4 15.2-b $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-5{x}-3a-3$
15.2-b5 15.2-b $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-15a-35\right){x}-81a-150$
15.2-b6 15.2-b $$\Q(\sqrt{21})$$ $$3 \cdot 5$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-275a-460\right){x}-4022a-7205$
16.1-a1 16.1-a $$\Q(\sqrt{21})$$ $$2^{4}$$ $0$ $\Z/2\Z$ $-3$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-2$
16.1-a2 16.1-a $$\Q(\sqrt{21})$$ $$2^{4}$$ $0$ $\Z/2\Z$ $-3$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}$
16.1-a3 16.1-a $$\Q(\sqrt{21})$$ $$2^{4}$$ $0$ $\Z/2\Z$ $-12$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-13\right){x}+11a-31$
16.1-a4 16.1-a $$\Q(\sqrt{21})$$ $$2^{4}$$ $0$ $\Z/2\Z$ $-12$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-8\right){x}-16a-28$
17.1-a1 17.1-a $$\Q(\sqrt{21})$$ $$17$$ $0$ $\Z/3\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-7{x}-2a+2$
17.1-a2 17.1-a $$\Q(\sqrt{21})$$ $$17$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-15a+33\right){x}+10a-33$
17.1-b1 17.1-b $$\Q(\sqrt{21})$$ $$17$$ $1$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-a+1\right){x}$
17.1-b2 17.1-b $$\Q(\sqrt{21})$$ $$17$$ $1$ $\Z/3\Z$ ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-11a-14\right){x}+26a+50$
17.2-a1 17.2-a $$\Q(\sqrt{21})$$ $$17$$ $0$ $\Z/3\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-2a-5\right){x}+a+1$
17.2-a2 17.2-a $$\Q(\sqrt{21})$$ $$17$$ $0$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(13a+20\right){x}-11a-22$
17.2-b1 17.2-b $$\Q(\sqrt{21})$$ $$17$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}$
17.2-b2 17.2-b $$\Q(\sqrt{21})$$ $$17$$ $1$ $\Z/3\Z$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(10a-25\right){x}-26a+76$
21.1-a1 21.1-a $$\Q(\sqrt{21})$$ $$3 \cdot 7$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(170a-477\right){x}-5038a+14062$
21.1-a2 21.1-a $$\Q(\sqrt{21})$$ $$3 \cdot 7$$ $0$ $\Z/4\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-5a+13\right){x}-5a+13$
21.1-a3 21.1-a $$\Q(\sqrt{21})$$ $$3 \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(20a-57\right){x}-4a+10$
21.1-a4 21.1-a $$\Q(\sqrt{21})$$ $$3 \cdot 7$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(195a-547\right){x}+2355a-6577$
21.1-a5 21.1-a $$\Q(\sqrt{21})$$ $$3 \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(245a-687\right){x}-3019a+8425$
21.1-a6 21.1-a $$\Q(\sqrt{21})$$ $$3 \cdot 7$$ $0$ $\Z/4\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(3920a-10977\right){x}-200440a+559528$
21.1-b1 21.1-b $$\Q(\sqrt{21})$$ $$3 \cdot 7$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}={x}^{3}-34{x}-217$
21.1-b2 21.1-b $$\Q(\sqrt{21})$$ $$3 \cdot 7$$ $1$ $\Z/8\Z$ ${y}^2+{x}{y}={x}^{3}+{x}$
21.1-b3 21.1-b $$\Q(\sqrt{21})$$ $$3 \cdot 7$$ $1$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}={x}^{3}-4{x}-1$
21.1-b4 21.1-b $$\Q(\sqrt{21})$$ $$3 \cdot 7$$ $1$ $\Z/8\Z$ ${y}^2+{x}{y}={x}^{3}-39{x}+90$
21.1-b5 21.1-b $$\Q(\sqrt{21})$$ $$3 \cdot 7$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}={x}^{3}-49{x}-136$
21.1-b6 21.1-b $$\Q(\sqrt{21})$$ $$3 \cdot 7$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}={x}^{3}-784{x}-8515$
25.1-a1 25.1-a $$\Q(\sqrt{21})$$ $$5^{2}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-26a-43\right){x}+84a+148$
25.1-a2 25.1-a $$\Q(\sqrt{21})$$ $$5^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(29a-66\right){x}-125a+369$