Results (1-50 of 1807 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
43.1-a1 43.1-a $$\Q(\sqrt{-43})$$ $$43$$ $1$ $\mathsf{trivial}$ ${y}^2+{y}={x}^3+{x}^2$
121.2-a1 121.2-a $$\Q(\sqrt{-43})$$ $$11^{2}$$ $1$ $\mathsf{trivial}$ ${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$
121.2-a2 121.2-a $$\Q(\sqrt{-43})$$ $$11^{2}$$ $1$ $\Z/5\Z$ ${y}^2+{y}={x}^3-{x}^2-10{x}-20$
121.2-a3 121.2-a $$\Q(\sqrt{-43})$$ $$11^{2}$$ $1$ $\Z/5\Z$ ${y}^2+{y}={x}^3-{x}^2$
124.1-a1 124.1-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 31$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-16a+104\right){x}-84a-258$
124.1-a2 124.1-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 31$$ $1$ $\Z/3\Z$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a-1\right){x}$
124.1-a3 124.1-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 31$$ $1$ $\Z/3\Z$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(4a+4\right){x}-4a-50$
124.2-a1 124.2-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 31$$ $1$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(15a+89\right){x}+84a-342$
124.2-a2 124.2-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 31$$ $1$ $\Z/3\Z$ ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-5a+9\right){x}+4a-54$
124.2-a3 124.2-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 31$$ $1$ $\Z/3\Z$ ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2-{x}$
193.1-a1 193.1-a $$\Q(\sqrt{-43})$$ $$193$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){y}={x}^3-a{x}^2-2{x}-a+1$
193.2-a1 193.2-a $$\Q(\sqrt{-43})$$ $$193$$ $1$ $\mathsf{trivial}$ ${y}^2+a{y}={x}^3+\left(a-1\right){x}^2-2{x}+1$
196.1-a1 196.1-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 7^{2}$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3-171{x}-874$
196.1-a2 196.1-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 7^{2}$$ $1$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^3-{x}$
196.1-a3 196.1-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 7^{2}$$ $1$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^3+4{x}-6$
196.1-a4 196.1-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 7^{2}$$ $1$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^3-36{x}-70$
196.1-a5 196.1-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 7^{2}$$ $1$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^3-11{x}+12$
196.1-a6 196.1-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 7^{2}$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$
225.1-a1 225.1-a $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$
225.1-a2 225.1-a $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2$
225.1-a3 225.1-a $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/8\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$
225.1-a4 225.1-a $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$
225.1-a5 225.1-a $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$
225.1-a6 225.1-a $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$
225.1-a7 225.1-a $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$
225.1-a8 225.1-a $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 5^{2}$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$
256.1-a1 256.1-a $$\Q(\sqrt{-43})$$ $$2^{8}$$ $1$ $\mathsf{trivial}$ ${y}^2={x}^3+\left(-a-1\right){x}^2+\left(a-2\right){x}+1$
256.1-b1 256.1-b $$\Q(\sqrt{-43})$$ $$2^{8}$$ $1$ $\mathsf{trivial}$ ${y}^2={x}^3+\left(a+1\right){x}^2+\left(a-2\right){x}-1$
289.2-a1 289.2-a $$\Q(\sqrt{-43})$$ $$17^{2}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$
289.2-a2 289.2-a $$\Q(\sqrt{-43})$$ $$17^{2}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$
289.2-a3 289.2-a $$\Q(\sqrt{-43})$$ $$17^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$
289.2-a4 289.2-a $$\Q(\sqrt{-43})$$ $$17^{2}$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$
289.2-b1 289.2-b $$\Q(\sqrt{-43})$$ $$17^{2}$$ $0$ $\Z/3\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-3a-6\right){x}+8$
289.2-b2 289.2-b $$\Q(\sqrt{-43})$$ $$17^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-8a+94\right){x}+175a-41$
289.2-c1 289.2-c $$\Q(\sqrt{-43})$$ $$17^{2}$$ $0$ $\Z/3\Z$ ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-2a+2\right){x}-a+5$
289.2-c2 289.2-c $$\Q(\sqrt{-43})$$ $$17^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(3a+97\right){x}-76a+76$
361.1-a1 361.1-a $$\Q(\sqrt{-43})$$ $$19^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+{y}={x}^3+{x}^2-769{x}-8470$
361.1-a2 361.1-a $$\Q(\sqrt{-43})$$ $$19^{2}$$ $0$ $\Z/3\Z$ ${y}^2+{y}={x}^3+{x}^2-9{x}-15$
361.1-a3 361.1-a $$\Q(\sqrt{-43})$$ $$19^{2}$$ $0$ $\Z/3\Z$ ${y}^2+{y}={x}^3+{x}^2+{x}$
387.1-a1 387.1-a $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 43$$ $2$ $\mathsf{trivial}$ ${y}^2+{y}={x}^3-{x}^2-19{x}+39$
387.1-b1 387.1-b $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 43$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3+105{x}-191$
387.1-b2 387.1-b $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 43$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^3-30{x}-29$
387.1-b3 387.1-b $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 43$$ $0$ $\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3-245{x}+1433$
387.1-b4 387.1-b $$\Q(\sqrt{-43})$$ $$3^{2} \cdot 43$$ $0$ $\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^3-25{x}-49$
396.1-a1 396.1-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 3^{2} \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-3a+7\right){x}+3$
396.1-a2 396.1-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 3^{2} \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-3a+17\right){x}+6a-11$
396.2-a1 396.2-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 3^{2} \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(a+6\right){x}-a+4$
396.2-a2 396.2-a $$\Q(\sqrt{-43})$$ $$2^{2} \cdot 3^{2} \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(a+16\right){x}-7a-4$
400.1-a1 400.1-a $$\Q(\sqrt{-43})$$ $$2^{4} \cdot 5^{2}$$ $0$ $\Z/2\Z$ ${y}^2={x}^3+{x}^2-36{x}-140$
400.1-a2 400.1-a $$\Q(\sqrt{-43})$$ $$2^{4} \cdot 5^{2}$$ $0$ $\Z/6\Z$ ${y}^2={x}^3+{x}^2+4{x}+4$