## Results (20 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
4900.1-a1 4900.1-a $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(12\phi+12\right){x}+55\phi+41$
4900.1-a2 4900.1-a $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-88\phi-88\right){x}+375\phi+281$
4900.1-a3 4900.1-a $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-438\phi-438\right){x}-6345\phi-4759$
4900.1-a4 4900.1-a $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(1338\phi-2677\right){x}-33714\phi+59332$
4900.1-b1 4900.1-b $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-227\phi-227\right){x}+3019\phi+2321$
4900.1-b2 4900.1-b $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-23\phi+45\right){x}+76\phi-128$
4900.1-c1 4900.1-c $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-180{x}+1047$
4900.1-d1 4900.1-d $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}-{x}^{2}+\left(852\phi-1705\right){x}-17475\phi+30581$
4900.1-d2 4900.1-d $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-3\phi-3\right){x}-5\phi-4$
4900.1-d3 4900.1-d $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-23\phi+45\right){x}-115\phi+201$
4900.1-d4 4900.1-d $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-178\phi-178\right){x}+1395\phi+1046$
4900.1-d5 4900.1-d $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-53\phi-53\right){x}-245\phi-184$
4900.1-d6 4900.1-d $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-13653\phi-13653\right){x}+1102915\phi+827186$
4900.1-e1 4900.1-e $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(33\phi-5\right){x}+76\phi-30$
4900.1-f1 4900.1-f $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-35\phi+30\right){x}-77\phi+47$
4900.1-g1 4900.1-g $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(7\phi-8\right){x}-16\phi+25$
4900.1-h1 4900.1-h $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}-\phi{x}^{2}+\left(-8\phi-1\right){x}+15\phi+9$
4900.1-i1 4900.1-i $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(36\phi-72\right){x}+160\phi-272$
4900.1-j1 4900.1-j $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}={x}^{3}+{x}^{2}-45{x}-185$
4900.1-j2 4900.1-j $$\Q(\sqrt{5})$$ $$2^{2} \cdot 5^{2} \cdot 7^{2}$$ $1$ $\Z/3\Z$ ${y}^2+{x}{y}={x}^{3}+{x}^{2}+5{x}+5$