## Results (18 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
605.1-a1 605.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(4\phi-13\right){x}-1591\phi-1011$
605.1-a2 605.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(\phi-1\right){x}-\phi+2$
605.1-a3 605.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(\phi-6\right){x}+\phi-2$
605.1-a4 605.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(36\phi-91\right){x}+147\phi-322$
605.1-a5 605.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-34\phi-1\right){x}+83\phi+2$
605.1-a6 605.1-a $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(586\phi-1466\right){x}+10927\phi-22432$
605.1-b1 605.1-b $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\phi{x}{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-3\phi-10\right){x}+1581\phi-2595$
605.1-b2 605.1-b $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+\left(35\phi-34\right){x}-84\phi+119$
605.1-b3 605.1-b $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}-4{x}-7\phi-2$
605.1-b4 605.1-b $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+{x}$
605.1-b5 605.1-b $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+\left(-35\phi-54\right){x}-238\phi-211$
605.1-b6 605.1-b $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\phi{x}^{2}+\left(-585\phi-879\right){x}-12393\phi-12091$
605.1-c1 605.1-c $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $1$ $\Z/2\Z$ ${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(48\phi-38\right){x}-1458\phi-1109$
605.1-c2 605.1-c $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}+{x}$
605.1-c3 605.1-c $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $1$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}-4{x}+3$
605.1-c4 605.1-c $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}-52$
605.1-c5 605.1-c $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}-59{x}+190$
605.1-c6 605.1-c $$\Q(\sqrt{5})$$ $$5 \cdot 11^{2}$$ $1$ $\Z/2\Z$ ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-48\phi+9\right){x}+1410\phi-2558$