## Results (1-50 of 3120 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 $$\Q(\sqrt{57})$$ $$2^{2}$$ $0$ $\Z/7\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(238a-1017\right){x}+6020a-25743$
4.2-a1 4.2-a $$\Q(\sqrt{57})$$ $$2^{2}$$ $1$ $\mathsf{trivial}$ $-3$ ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-a-5$
4.2-a2 4.2-a $$\Q(\sqrt{57})$$ $$2^{2}$$ $1$ $\mathsf{trivial}$ $-3$ ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+17422a-74490$
4.3-a1 4.3-a $$\Q(\sqrt{57})$$ $$2^{2}$$ $1$ $\mathsf{trivial}$ $-3$ ${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}-10$
4.3-a2 4.3-a $$\Q(\sqrt{57})$$ $$2^{2}$$ $1$ $\mathsf{trivial}$ $-3$ ${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-17423a-57062$
8.3-a1 8.3-a $$\Q(\sqrt{57})$$ $$2^{3}$$ $0$ $\mathsf{trivial}$ ${y}^2+a{y}={x}^{3}-{x}^{2}+\left(-a-3\right){x}-a-6$
8.3-b1 8.3-b $$\Q(\sqrt{57})$$ $$2^{3}$$ $1$ $\mathsf{trivial}$ ${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(706a-3012\right){x}-94983a+406037$
8.4-a1 8.4-a $$\Q(\sqrt{57})$$ $$2^{3}$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(a-4\right){x}-7$
8.4-b1 8.4-b $$\Q(\sqrt{57})$$ $$2^{3}$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-706a-2306\right){x}+94982a+311054$
14.2-a1 14.2-a $$\Q(\sqrt{57})$$ $$2 \cdot 7$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-14093a+60285\right){x}+655027a-2800123$
14.2-a2 14.2-a $$\Q(\sqrt{57})$$ $$2 \cdot 7$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-5\right){x}-5$
14.2-b1 14.2-b $$\Q(\sqrt{57})$$ $$2 \cdot 7$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}-2a{x}+3$
14.2-b2 14.2-b $$\Q(\sqrt{57})$$ $$2 \cdot 7$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12784a+41868\right){x}+4430171a+14508443$
14.3-a1 14.3-a $$\Q(\sqrt{57})$$ $$2 \cdot 7$$ $0$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-a-5\right){x}-a-5$
14.3-a2 14.3-a $$\Q(\sqrt{57})$$ $$2 \cdot 7$$ $0$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(14101a+46176\right){x}-608844a-1993915$
14.3-b1 14.3-b $$\Q(\sqrt{57})$$ $$2 \cdot 7$$ $1$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-12775a+54636\right){x}-4375534a+18705071$
14.3-b2 14.3-b $$\Q(\sqrt{57})$$ $$2 \cdot 7$$ $1$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(a-1\right){x}+3$
16.1-a1 16.1-a $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\Z/2\Z$ $-3$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+133a-574$
16.1-a2 16.1-a $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\Z/2\Z$ $-3$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-133a-436$
16.1-a3 16.1-a $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\Z/2\Z$ $-12$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(201a-850\right){x}+3094a-13232$
16.1-a4 16.1-a $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\Z/2\Z$ $-12$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-199a-650\right){x}-3294a-10788$
16.2-a1 16.2-a $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(320a+1048\right){x}+469916a+1538936$
16.2-a2 16.2-a $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(888a-3768\right){x}-30040a+128464$
16.2-b1 16.2-b $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(27a-113\right){x}+195a-833$
16.2-b2 16.2-b $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-84a-276\right){x}-1037a-3397$
16.2-c1 16.2-c $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(4a+20\right){x}+2a+10$
16.2-d1 16.2-d $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(693a-2958\right){x}+21766a-93046$
16.3-a1 16.3-a $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-882a-2893\right){x}+27153a+88921$
16.3-a2 16.3-a $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-320a+1368\right){x}-469916a+2008852$
16.3-b1 16.3-b $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(84a-359\right){x}+953a-4074$
16.3-b2 16.3-b $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(-27a-86\right){x}-195a-638$
16.3-c1 16.3-c $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\mathsf{trivial}$ ${y}^2+a{x}{y}={x}^{3}+\left(-4a+24\right){x}-2a+12$
16.3-d1 16.3-d $$\Q(\sqrt{57})$$ $$2^{4}$$ $0$ $\mathsf{trivial}$ ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-693a-2265\right){x}-21766a-71280$
16.4-a1 16.4-a $$\Q(\sqrt{57})$$ $$2^{4}$$ $1$ $\mathsf{trivial}$ $-19$ ${y}^2+\left(a+1\right){y}={x}^{3}+\left(41678a-178170\right){x}+9007428a-38506016$
16.4-a2 16.4-a $$\Q(\sqrt{57})$$ $$2^{4}$$ $1$ $\mathsf{trivial}$ $-19$ ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-2a-10\right){x}+3a+11$