## Results (1-50 of 6301 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
4.1-a1 4.1-a $$\Q(\sqrt{17})$$ $$2^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(-9a+22\right){x}+106a-272$
4.1-a2 4.1-a $$\Q(\sqrt{17})$$ $$2^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-2\right){x}+4a+6$
4.1-a3 4.1-a $$\Q(\sqrt{17})$$ $$2^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(9a+13\right){x}-106a-166$
4.1-a4 4.1-a $$\Q(\sqrt{17})$$ $$2^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-3\right){x}-4a+10$
4.1-a5 4.1-a $$\Q(\sqrt{17})$$ $$2^{2}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}$
4.1-a6 4.1-a $$\Q(\sqrt{17})$$ $$2^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(981a-2517\right){x}+23628a-60528$
4.1-a7 4.1-a $$\Q(\sqrt{17})$$ $$2^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(61a-157\right){x}+348a-896$
4.1-a8 4.1-a $$\Q(\sqrt{17})$$ $$2^{2}$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(a-2\right){x}-a$
4.1-a9 4.1-a $$\Q(\sqrt{17})$$ $$2^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a-20\right){x}-28a-44$
4.1-a10 4.1-a $$\Q(\sqrt{17})$$ $$2^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-62a-95\right){x}-349a-547$
4.1-a11 4.1-a $$\Q(\sqrt{17})$$ $$2^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(11a-32\right){x}+27a-72$
4.1-a12 4.1-a $$\Q(\sqrt{17})$$ $$2^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-982a-1535\right){x}-23629a-36899$
8.3-a1 8.3-a $$\Q(\sqrt{17})$$ $$2^{3}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(4a+7\right){x}-34a-53$
8.3-a2 8.3-a $$\Q(\sqrt{17})$$ $$2^{3}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(80a+125\right){x}+1186a+1852$
8.3-a3 8.3-a $$\Q(\sqrt{17})$$ $$2^{3}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(12a-37\right){x}+46a-121$
8.3-a4 8.3-a $$\Q(\sqrt{17})$$ $$2^{3}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+3\right){x}$
8.3-a5 8.3-a $$\Q(\sqrt{17})$$ $$2^{3}$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-5a-8\right){x}+2a+3$
8.3-a6 8.3-a $$\Q(\sqrt{17})$$ $$2^{3}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-12\right){x}-29a-31$
8.4-a1 8.4-a $$\Q(\sqrt{17})$$ $$2^{3}$$ $0$ $\Z/4\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a-11\right){x}-3a+6$
8.4-a2 8.4-a $$\Q(\sqrt{17})$$ $$2^{3}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-6a+13\right){x}+33a-86$
8.4-a3 8.4-a $$\Q(\sqrt{17})$$ $$2^{3}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+2a{x}+a$
8.4-a4 8.4-a $$\Q(\sqrt{17})$$ $$2^{3}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-14a-23\right){x}-47a-74$
8.4-a5 8.4-a $$\Q(\sqrt{17})$$ $$2^{3}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-20\right){x}+15a-40$
8.4-a6 8.4-a $$\Q(\sqrt{17})$$ $$2^{3}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-80a+205\right){x}-1186a+3038$
9.1-a1 9.1-a $$\Q(\sqrt{17})$$ $$3^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(48a-123\right){x}+291a-749$
9.1-a2 9.1-a $$\Q(\sqrt{17})$$ $$3^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a-79\right){x}-131a+330$
9.1-a3 9.1-a $$\Q(\sqrt{17})$$ $$3^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(58a+92\right){x}+322a+503$
9.1-a4 9.1-a $$\Q(\sqrt{17})$$ $$3^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-22a-33\right){x}+71a+111$
9.1-a5 9.1-a $$\Q(\sqrt{17})$$ $$3^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-4\right){x}-2a+3$
9.1-a6 9.1-a $$\Q(\sqrt{17})$$ $$3^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-2\right){x}-1$
9.1-a7 9.1-a $$\Q(\sqrt{17})$$ $$3^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-49a-74\right){x}-292a-457$
9.1-a8 9.1-a $$\Q(\sqrt{17})$$ $$3^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-31a-47\right){x}+99a+152$
9.1-b1 9.1-b $$\Q(\sqrt{17})$$ $$3^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(795a-2035\right){x}+17928a-45924$
9.1-b2 9.1-b $$\Q(\sqrt{17})$$ $$3^{2}$$ $0$ $\Z/5\Z$ ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-5a+15\right){x}+2a-6$
16.1-a1 16.1-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-38a-77\right){x}-268a-444$
16.1-a2 16.1-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/6\Z$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+3\right){x}$
16.1-a3 16.1-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/6\Z$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+4{x}+a-4$
16.1-a4 16.1-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(40a-116\right){x}+229a-596$
16.4-a1 16.4-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a-3\right){x}-6a-10$
16.4-a2 16.4-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/4\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$
16.4-a3 16.4-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-9a-15\right){x}-6a-10$
16.4-a4 16.4-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+a{x}$
16.4-a5 16.4-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/8\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-124a-195\right){x}+916a+1430$
16.4-a6 16.4-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-4a{x}-5a-20$
16.5-a1 16.5-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$
16.5-a2 16.5-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(7a-2\right){x}+5a-5$
16.5-a3 16.5-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(2a+3\right){x}$
16.5-a4 16.5-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-22\right){x}-7a+26$
16.5-a5 16.5-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-4\right){x}+5a-16$
16.5-a6 16.5-a $$\Q(\sqrt{17})$$ $$2^{4}$$ $0$ $\Z/8\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(127a-317\right){x}-1109a+2848$