## Results (16 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
4.1-a1 4.1-a $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(71395a-305260\right){x}-20071186a+85802856$
4.1-a2 4.1-a $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-71396a-233865\right){x}+20071185a+65731670$
4.1-a3 4.1-a $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-215a+920\right){x}+2686a-11488$
4.1-a4 4.1-a $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(214a+705\right){x}-2687a-8802$
4.1-b1 4.1-b $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(91a-386\right){x}-817a+3486$
4.1-b2 4.1-b $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(a-1\right){x}-7$
4.1-b3 4.1-b $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}-2a{x}-a-7$
4.1-b4 4.1-b $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-92a-295\right){x}+816a+2669$
4.1-c1 4.1-c $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2960a-9690\right){x}-168414a-551544$
4.1-c2 4.1-c $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(150a+495\right){x}-1331a-4361$
4.1-c3 4.1-c $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-149a+645\right){x}+1181a-5047$
4.1-c4 4.1-c $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2961a-12650\right){x}+171374a-732608$
4.1-d1 4.1-d $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-642629a-2104558\right){x}-545795629a-1787435506$
4.1-d2 4.1-d $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\mathsf{trivial}$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(642628a-2747187\right){x}+545795628a-2333231135$
4.1-d3 4.1-d $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\Z/7\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-239a-778\right){x}-6021a-19722$
4.1-d4 4.1-d $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\Z/7\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(238a-1017\right){x}+6020a-25743$