## Results (1-50 of 849 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
67.1-a1 67.1-a $$\Q(\sqrt{-67})$$ $$67$$ $0$ $\mathsf{trivial}$ ${y}^2+{y}={x}^3+{x}^2-12{x}-21$
121.1-a1 121.1-a $$\Q(\sqrt{-67})$$ $$11^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$
121.1-a2 121.1-a $$\Q(\sqrt{-67})$$ $$11^{2}$$ $0$ $\Z/5\Z$ ${y}^2+{y}={x}^3-{x}^2-10{x}-20$
121.1-a3 121.1-a $$\Q(\sqrt{-67})$$ $$11^{2}$$ $0$ $\Z/5\Z$ ${y}^2+{y}={x}^3-{x}^2$
153.1-a1 153.1-a $$\Q(\sqrt{-67})$$ $$3^{2} \cdot 17$$ $1$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-3a-1\right){x}-5a+16$
153.2-a1 153.2-a $$\Q(\sqrt{-67})$$ $$3^{2} \cdot 17$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-5a-14\right){x}+20$
196.1-a1 196.1-a $$\Q(\sqrt{-67})$$ $$2^{2} \cdot 7^{2}$$ $0 \le r \le 1$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3-171{x}-874$
196.1-a2 196.1-a $$\Q(\sqrt{-67})$$ $$2^{2} \cdot 7^{2}$$ $0 \le r \le 1$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^3-{x}$
196.1-a3 196.1-a $$\Q(\sqrt{-67})$$ $$2^{2} \cdot 7^{2}$$ $0 \le r \le 1$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^3+4{x}-6$
196.1-a4 196.1-a $$\Q(\sqrt{-67})$$ $$2^{2} \cdot 7^{2}$$ $0 \le r \le 1$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^3-36{x}-70$
196.1-a5 196.1-a $$\Q(\sqrt{-67})$$ $$2^{2} \cdot 7^{2}$$ $0 \le r \le 1$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^3-11{x}+12$
196.1-a6 196.1-a $$\Q(\sqrt{-67})$$ $$2^{2} \cdot 7^{2}$$ $0 \le r \le 1$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$
225.1-a1 225.1-a $$\Q(\sqrt{-67})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$
225.1-a2 225.1-a $$\Q(\sqrt{-67})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2$
225.1-a3 225.1-a $$\Q(\sqrt{-67})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/8\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$
225.1-a4 225.1-a $$\Q(\sqrt{-67})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$
225.1-a5 225.1-a $$\Q(\sqrt{-67})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$
225.1-a6 225.1-a $$\Q(\sqrt{-67})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$
225.1-a7 225.1-a $$\Q(\sqrt{-67})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$
225.1-a8 225.1-a $$\Q(\sqrt{-67})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$
261.1-a1 261.1-a $$\Q(\sqrt{-67})$$ $$3^{2} \cdot 29$$ $0$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-4a+6\right){x}+12$
261.2-a1 261.2-a $$\Q(\sqrt{-67})$$ $$3^{2} \cdot 29$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-4a-6\right){x}-3a+17$
284.1-a1 284.1-a $$\Q(\sqrt{-67})$$ $$2^{2} \cdot 71$$ $0$ $\mathsf{trivial}$ ${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(18a+36\right){x}+8a-552$
284.1-a2 284.1-a $$\Q(\sqrt{-67})$$ $$2^{2} \cdot 71$$ $0$ $\Z/3\Z$ ${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-2a-4\right){x}+4$
284.2-a1 284.2-a $$\Q(\sqrt{-67})$$ $$2^{2} \cdot 71$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-26a+61\right){x}+53a-244$
284.2-a2 284.2-a $$\Q(\sqrt{-67})$$ $$2^{2} \cdot 71$$ $0$ $\Z/3\Z$ ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-6a+1\right){x}+a+24$
289.2-a1 289.2-a $$\Q(\sqrt{-67})$$ $$17^{2}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$
289.2-a2 289.2-a $$\Q(\sqrt{-67})$$ $$17^{2}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$
289.2-a3 289.2-a $$\Q(\sqrt{-67})$$ $$17^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$
289.2-a4 289.2-a $$\Q(\sqrt{-67})$$ $$17^{2}$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$
289.2-b1 289.2-b $$\Q(\sqrt{-67})$$ $$17^{2}$$ $0 \le r \le 1$ $\Z/4\Z$ ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(-a+17\right){x}$
289.2-b2 289.2-b $$\Q(\sqrt{-67})$$ $$17^{2}$$ $0 \le r \le 1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(-a+12\right){x}-a+14$
289.2-b3 289.2-b $$\Q(\sqrt{-67})$$ $$17^{2}$$ $0 \le r \le 1$ $\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(-6a+17\right){x}-a+31$
289.2-b4 289.2-b $$\Q(\sqrt{-67})$$ $$17^{2}$$ $0 \le r \le 1$ $\Z/4\Z$ ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(4a-73\right){x}-45a+473$
289.2-c1 289.2-c $$\Q(\sqrt{-67})$$ $$17^{2}$$ $1$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-a+16\right){x}-a$
289.2-c2 289.2-c $$\Q(\sqrt{-67})$$ $$17^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-a+11\right){x}+13$
289.2-c3 289.2-c $$\Q(\sqrt{-67})$$ $$17^{2}$$ $1$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(4a+11\right){x}+30$
289.2-c4 289.2-c $$\Q(\sqrt{-67})$$ $$17^{2}$$ $1$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-6a-69\right){x}+44a+428$
323.1-a1 323.1-a $$\Q(\sqrt{-67})$$ $$17 \cdot 19$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-16a+79\right){x}+27a+217$
323.1-a2 323.1-a $$\Q(\sqrt{-67})$$ $$17 \cdot 19$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-11a+84\right){x}-5a+394$
323.1-a3 323.1-a $$\Q(\sqrt{-67})$$ $$17 \cdot 19$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-a-1\right){x}$
323.1-a4 323.1-a $$\Q(\sqrt{-67})$$ $$17 \cdot 19$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-261a+1354\right){x}+2647a+18968$
323.4-a1 323.4-a $$\Q(\sqrt{-67})$$ $$17 \cdot 19$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(17a+63\right){x}-12a+308$
323.4-a2 323.4-a $$\Q(\sqrt{-67})$$ $$17 \cdot 19$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(12a+73\right){x}+15a+463$
323.4-a3 323.4-a $$\Q(\sqrt{-67})$$ $$17 \cdot 19$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(2a-2\right){x}-1$
323.4-a4 323.4-a $$\Q(\sqrt{-67})$$ $$17 \cdot 19$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(262a+1093\right){x}-2387a+22709$
361.2-a1 361.2-a $$\Q(\sqrt{-67})$$ $$19^{2}$$ $1$ $\mathsf{trivial}$ ${y}^2+{y}={x}^3+{x}^2-769{x}-8470$
361.2-a2 361.2-a $$\Q(\sqrt{-67})$$ $$19^{2}$$ $1$ $\Z/3\Z$ ${y}^2+{y}={x}^3+{x}^2-9{x}-15$
361.2-a3 361.2-a $$\Q(\sqrt{-67})$$ $$19^{2}$$ $1$ $\Z/3\Z$ ${y}^2+{y}={x}^3+{x}^2+{x}$
400.1-a1 400.1-a $$\Q(\sqrt{-67})$$ $$2^{4} \cdot 5^{2}$$ $0$ $\Z/2\Z$ ${y}^2={x}^3+{x}^2-36{x}-140$