## Results (1-50 of 9713 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
31.1-a1 31.1-a $$\Q(\sqrt{5})$$ $$31$$ $0$ $\Z/8\Z$ ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\phi{x}$
31.1-a2 31.1-a $$\Q(\sqrt{5})$$ $$31$$ $0$ $\Z/2\Z$ ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(133\phi-141\right){x}+737\phi-764$
31.1-a3 31.1-a $$\Q(\sqrt{5})$$ $$31$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(-12\phi-21\right){x}+42\phi+10$
31.1-a4 31.1-a $$\Q(\sqrt{5})$$ $$31$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(31\phi-75\right){x}+141\phi-303$
31.1-a5 31.1-a $$\Q(\sqrt{5})$$ $$31$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(\phi-5\right){x}+3\phi-5$
31.1-a6 31.1-a $$\Q(\sqrt{5})$$ $$31$$ $0$ $\Z/4\Z$ ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-18\phi+15\right){x}+171\phi-265$
31.2-a1 31.2-a $$\Q(\sqrt{5})$$ $$31$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-30\phi-45\right){x}-111\phi-117$
31.2-a2 31.2-a $$\Q(\sqrt{5})$$ $$31$$ $0$ $\Z/4\Z$ ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(16\phi-2\right){x}-172\phi-94$
31.2-a3 31.2-a $$\Q(\sqrt{5})$$ $$31$$ $0$ $\Z/8\Z$ ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}$
31.2-a4 31.2-a $$\Q(\sqrt{5})$$ $$31$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}-5{x}-3\phi+3$
31.2-a5 31.2-a $$\Q(\sqrt{5})$$ $$31$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(10\phi-32\right){x}-43\phi+53$
31.2-a6 31.2-a $$\Q(\sqrt{5})$$ $$31$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-135\phi-7\right){x}-738\phi-26$
36.1-a1 36.1-a $$\Q(\sqrt{5})$$ $$2^{2} \cdot 3^{2}$$ $0$ $\Z/10\Z$ ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}$
36.1-a2 36.1-a $$\Q(\sqrt{5})$$ $$2^{2} \cdot 3^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-5\phi-5\right){x}-51\phi-37$
36.1-a3 36.1-a $$\Q(\sqrt{5})$$ $$2^{2} \cdot 3^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(165\phi-331\right){x}+1352\phi-2408$
36.1-a4 36.1-a $$\Q(\sqrt{5})$$ $$2^{2} \cdot 3^{2}$$ $0$ $\Z/10\Z$ ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(10\phi-21\right){x}-31\phi+51$
41.1-a1 41.1-a $$\Q(\sqrt{5})$$ $$41$$ $0$ $\Z/7\Z$ ${y}^2+\phi{y}={x}^{3}-\phi{x}^{2}$
41.1-a2 41.1-a $$\Q(\sqrt{5})$$ $$41$$ $0$ $\mathsf{trivial}$ ${y}^2+\phi{y}={x}^{3}-\phi{x}^{2}+\left(10\phi-40\right){x}+31\phi-113$
41.2-a1 41.2-a $$\Q(\sqrt{5})$$ $$41$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-10\phi-30\right){x}-32\phi-82$
41.2-a2 41.2-a $$\Q(\sqrt{5})$$ $$41$$ $0$ $\Z/7\Z$ ${y}^2+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}-\phi$
45.1-a1 45.1-a $$\Q(\sqrt{5})$$ $$3^{2} \cdot 5$$ $0$ $\Z/2\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(-4364\phi-7739\right){x}-255406\phi-296465$
45.1-a2 45.1-a $$\Q(\sqrt{5})$$ $$3^{2} \cdot 5$$ $0$ $\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$
45.1-a3 45.1-a $$\Q(\sqrt{5})$$ $$3^{2} \cdot 5$$ $0$ $\Z/8\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
45.1-a4 45.1-a $$\Q(\sqrt{5})$$ $$3^{2} \cdot 5$$ $0$ $\Z/8\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
45.1-a5 45.1-a $$\Q(\sqrt{5})$$ $$3^{2} \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$
45.1-a6 45.1-a $$\Q(\sqrt{5})$$ $$3^{2} \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/8\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
45.1-a7 45.1-a $$\Q(\sqrt{5})$$ $$3^{2} \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$
45.1-a8 45.1-a $$\Q(\sqrt{5})$$ $$3^{2} \cdot 5$$ $0$ $\Z/8\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
45.1-a9 45.1-a $$\Q(\sqrt{5})$$ $$3^{2} \cdot 5$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
45.1-a10 45.1-a $$\Q(\sqrt{5})$$ $$3^{2} \cdot 5$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(4364\phi-12105\right){x}+243301\phi-535402$
49.1-a1 49.1-a $$\Q(\sqrt{5})$$ $$7^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-30\phi-29\right){x}-102\phi-84$
49.1-a2 49.1-a $$\Q(\sqrt{5})$$ $$7^{2}$$ $0$ $\Z/5\Z$ ${y}^2+{y}={x}^{3}+\phi{x}^{2}+{x}$
55.1-a1 55.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(9\phi-25\right){x}-6\phi+44$
55.1-a2 55.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+54\phi{x}-374\phi-198$
55.1-a3 55.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/6\Z$ ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}-\phi$
55.1-a4 55.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-21\phi-25\right){x}-54\phi-58$
55.1-a5 55.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-16\phi-210\right){x}+1110\phi-534$
55.1-a6 55.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(4\phi-11\right){x}-9\phi+13$
55.1-a7 55.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-6\phi-1\right){x}+\phi-17$
55.1-a8 55.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/6\Z$ ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-6\phi-26\right){x}+28\phi+8$
55.2-a1 55.2-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/6\Z$ ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}-\phi{x}$
55.2-a2 55.2-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(4\phi-5\right){x}-2\phi-15$
55.2-a3 55.2-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/6\Z$ ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(4\phi-30\right){x}-29\phi+37$
55.2-a4 55.2-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(-54\phi+54\right){x}+374\phi-572$
55.2-a5 55.2-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(21\phi-46\right){x}+54\phi-112$
55.2-a6 55.2-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-6\phi-5\right){x}+8\phi+5$
55.2-a7 55.2-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(16\phi-226\right){x}-1110\phi+576$
55.2-a8 55.2-a $$\Q(\sqrt{5})$$ $$5 \cdot 11$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(-9\phi-16\right){x}+6\phi+38$
64.1-a1 64.1-a $$\Q(\sqrt{5})$$ $$2^{6}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(14\phi-25\right){x}+\phi-59$
64.1-a2 64.1-a $$\Q(\sqrt{5})$$ $$2^{6}$$ $0$ $\Z/8\Z$ ${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+4\phi{x}+4$