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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
4.1-a1 4.1-a \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\mathsf{trivial}$ $1$ $7.662151750$ 1.014876791 \( -\frac{293180476215589246298781}{8} a - \frac{960141789432972248487021}{8} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 71395 a - 305260\) , \( -20071186 a + 85802856\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(71395a-305260\right){x}-20071186a+85802856$
4.1-a2 4.1-a \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\mathsf{trivial}$ $1$ $7.662151750$ 1.014876791 \( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -71396 a - 233865\) , \( 20071185 a + 65731670\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-71396a-233865\right){x}+20071185a+65731670$
4.1-a3 4.1-a \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\mathsf{trivial}$ $1$ $7.662151750$ 1.014876791 \( -\frac{699691689}{2097152} a - \frac{307208349}{2097152} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -215 a + 920\) , \( 2686 a - 11488\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-215a+920\right){x}+2686a-11488$
4.1-a4 4.1-a \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\mathsf{trivial}$ $1$ $7.662151750$ 1.014876791 \( \frac{699691689}{2097152} a - \frac{503450019}{1048576} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 214 a + 705\) , \( -2687 a - 8802\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(214a+705\right){x}-2687a-8802$
4.1-b1 4.1-b \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\Z/6\Z$ $1$ $37.29397324$ 2.469853714 \( -\frac{20297286875}{64} a + \frac{43383068421}{32} \) \( \bigl[1\) , \( -a\) , \( a\) , \( 91 a - 386\) , \( -817 a + 3486\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(91a-386\right){x}-817a+3486$
4.1-b2 4.1-b \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\Z/2\Z$ $1$ $37.29397324$ 2.469853714 \( -\frac{489}{4} a + 1841 \) \( \bigl[1\) , \( -a\) , \( a\) , \( a - 1\) , \( -7\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(a-1\right){x}-7$
4.1-b3 4.1-b \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\Z/2\Z$ $1$ $37.29397324$ 2.469853714 \( \frac{489}{4} a + \frac{6875}{4} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2 a\) , \( -a - 7\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}-2a{x}-a-7$
4.1-b4 4.1-b \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\Z/6\Z$ $1$ $37.29397324$ 2.469853714 \( \frac{20297286875}{64} a + \frac{66468849967}{64} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -92 a - 295\) , \( 816 a + 2669\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-92a-295\right){x}+816a+2669$
4.1-c1 4.1-c \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\Z/2\Z$ $1$ $3.156724381$ 0.209059179 \( -\frac{20297286875}{64} a + \frac{43383068421}{32} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -2960 a - 9690\) , \( -168414 a - 551544\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2960a-9690\right){x}-168414a-551544$
4.1-c2 4.1-c \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\Z/6\Z$ $1$ $28.41051943$ 0.209059179 \( -\frac{489}{4} a + 1841 \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( 150 a + 495\) , \( -1331 a - 4361\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(150a+495\right){x}-1331a-4361$
4.1-c3 4.1-c \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\Z/6\Z$ $1$ $28.41051943$ 0.209059179 \( \frac{489}{4} a + \frac{6875}{4} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -149 a + 645\) , \( 1181 a - 5047\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-149a+645\right){x}+1181a-5047$
4.1-c4 4.1-c \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\Z/2\Z$ $1$ $3.156724381$ 0.209059179 \( \frac{20297286875}{64} a + \frac{66468849967}{64} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( 2961 a - 12650\) , \( 171374 a - 732608\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2961a-12650\right){x}+171374a-732608$
4.1-d1 4.1-d \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.077866687$ 1.516113114 \( -\frac{293180476215589246298781}{8} a - \frac{960141789432972248487021}{8} \) \( \bigl[1\) , \( a\) , \( a\) , \( -642629 a - 2104558\) , \( -545795629 a - 1787435506\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-642629a-2104558\right){x}-545795629a-1787435506$
4.1-d2 4.1-d \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.077866687$ 1.516113114 \( \frac{293180476215589246298781}{8} a - \frac{626661132824280747392901}{4} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 642628 a - 2747187\) , \( 545795628 a - 2333231135\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(642628a-2747187\right){x}+545795628a-2333231135$
4.1-d3 4.1-d \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\Z/7\Z$ $1$ $3.815467665$ 1.516113114 \( -\frac{699691689}{2097152} a - \frac{307208349}{2097152} \) \( \bigl[1\) , \( a\) , \( a\) , \( -239 a - 778\) , \( -6021 a - 19722\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-239a-778\right){x}-6021a-19722$
4.1-d4 4.1-d \(\Q(\sqrt{57}) \) \( 2^{2} \) $0$ $\Z/7\Z$ $1$ $3.815467665$ 1.516113114 \( \frac{699691689}{2097152} a - \frac{503450019}{1048576} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 238 a - 1017\) , \( 6020 a - 25743\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(238a-1017\right){x}+6020a-25743$
4.2-a1 4.2-a \(\Q(\sqrt{57}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $-3$ $0.228592103$ $17.69503190$ 1.071531991 \( 0 \) \( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a + 5\) , \( -a - 5\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-a-5$
4.2-a2 4.2-a \(\Q(\sqrt{57}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $-3$ $0.076197367$ $17.69503190$ 1.071531991 \( 0 \) \( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( a + 5\) , \( 17422 a - 74490\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+17422a-74490$
4.3-a1 4.3-a \(\Q(\sqrt{57}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $-3$ $0.228592103$ $17.69503190$ 1.071531991 \( 0 \) \( \bigl[0\) , \( -a - 1\) , \( a\) , \( a + 5\) , \( -10\bigr] \) ${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}-10$
4.3-a2 4.3-a \(\Q(\sqrt{57}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $-3$ $0.076197367$ $17.69503190$ 1.071531991 \( 0 \) \( \bigl[0\) , \( a + 1\) , \( a\) , \( a + 5\) , \( -17423 a - 57062\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-17423a-57062$
8.3-a1 8.3-a \(\Q(\sqrt{57}) \) \( 2^{3} \) $0$ $\mathsf{trivial}$ $1$ $5.977571122$ 3.166994547 \( -7168 a - 23552 \) \( \bigl[0\) , \( -1\) , \( a\) , \( -a - 3\) , \( -a - 6\bigr] \) ${y}^2+a{y}={x}^{3}-{x}^{2}+\left(-a-3\right){x}-a-6$
8.3-b1 8.3-b \(\Q(\sqrt{57}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $0.031315266$ $41.25238393$ 0.684427934 \( -7168 a - 23552 \) \( \bigl[0\) , \( -a\) , \( a\) , \( 706 a - 3012\) , \( -94983 a + 406037\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(706a-3012\right){x}-94983a+406037$
8.4-a1 8.4-a \(\Q(\sqrt{57}) \) \( 2^{3} \) $0$ $\mathsf{trivial}$ $1$ $5.977571122$ 3.166994547 \( 7168 a - 30720 \) \( \bigl[0\) , \( -1\) , \( a + 1\) , \( a - 4\) , \( -7\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(a-4\right){x}-7$
8.4-b1 8.4-b \(\Q(\sqrt{57}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $0.031315266$ $41.25238393$ 0.684427934 \( 7168 a - 30720 \) \( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -706 a - 2306\) , \( 94982 a + 311054\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-706a-2306\right){x}+94982a+311054$
14.2-a1 14.2-a \(\Q(\sqrt{57}) \) \( 2 \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $4.972949964$ 1.317366627 \( -\frac{545882409}{5488} a - \frac{254194875}{784} \) \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -14093 a + 60285\) , \( 655027 a - 2800123\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-14093a+60285\right){x}+655027a-2800123$
14.2-a2 14.2-a \(\Q(\sqrt{57}) \) \( 2 \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $4.972949964$ 1.317366627 \( \frac{116429967}{28672} a - \frac{70335891}{4096} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -a - 5\) , \( -5\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-5\right){x}-5$
14.2-b1 14.2-b \(\Q(\sqrt{57}) \) \( 2 \cdot 7 \) $1$ $\mathsf{trivial}$ $0.060818804$ $23.51278497$ 1.515285641 \( -\frac{545882409}{5488} a - \frac{254194875}{784} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -2 a\) , \( 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}-2a{x}+3$
14.2-b2 14.2-b \(\Q(\sqrt{57}) \) \( 2 \cdot 7 \) $1$ $\mathsf{trivial}$ $0.020272934$ $23.51278497$ 1.515285641 \( \frac{116429967}{28672} a - \frac{70335891}{4096} \) \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 12784 a + 41868\) , \( 4430171 a + 14508443\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12784a+41868\right){x}+4430171a+14508443$
14.3-a1 14.3-a \(\Q(\sqrt{57}) \) \( 2 \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $4.972949964$ 1.317366627 \( -\frac{116429967}{28672} a - \frac{187960635}{14336} \) \( \bigl[a\) , \( -1\) , \( a + 1\) , \( -a - 5\) , \( -a - 5\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-a-5\right){x}-a-5$
14.3-a2 14.3-a \(\Q(\sqrt{57}) \) \( 2 \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $4.972949964$ 1.317366627 \( \frac{545882409}{5488} a - \frac{1162623267}{2744} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( 14101 a + 46176\) , \( -608844 a - 1993915\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(14101a+46176\right){x}-608844a-1993915$
14.3-b1 14.3-b \(\Q(\sqrt{57}) \) \( 2 \cdot 7 \) $1$ $\mathsf{trivial}$ $0.020272934$ $23.51278497$ 1.515285641 \( -\frac{116429967}{28672} a - \frac{187960635}{14336} \) \( \bigl[a\) , \( a\) , \( 1\) , \( -12775 a + 54636\) , \( -4375534 a + 18705071\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-12775a+54636\right){x}-4375534a+18705071$
14.3-b2 14.3-b \(\Q(\sqrt{57}) \) \( 2 \cdot 7 \) $1$ $\mathsf{trivial}$ $0.060818804$ $23.51278497$ 1.515285641 \( \frac{545882409}{5488} a - \frac{1162623267}{2744} \) \( \bigl[a\) , \( -1\) , \( 1\) , \( a - 1\) , \( 3\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(a-1\right){x}+3$
16.1-a1 16.1-a \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $-3$ $1$ $17.69503190$ 1.757823174 \( 0 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 5\) , \( 133 a - 574\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+133a-574$
16.1-a2 16.1-a \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $-3$ $1$ $17.69503190$ 1.757823174 \( 0 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 5\) , \( -133 a - 436\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-133a-436$
16.1-a3 16.1-a \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $-12$ $1$ $17.69503190$ 1.757823174 \( 54000 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 201 a - 850\) , \( 3094 a - 13232\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(201a-850\right){x}+3094a-13232$
16.1-a4 16.1-a \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $-12$ $1$ $17.69503190$ 1.757823174 \( 54000 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -199 a - 650\) , \( -3294 a - 10788\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-199a-650\right){x}-3294a-10788$
16.2-a1 16.2-a \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $22.49427591$ 1.489719814 \( -\frac{925430099}{32} a + \frac{3956137073}{32} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 320 a + 1048\) , \( 469916 a + 1538936\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(320a+1048\right){x}+469916a+1538936$
16.2-a2 16.2-a \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $22.49427591$ 1.489719814 \( \frac{7754659}{1024} a + \frac{11013279}{1024} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 888 a - 3768\) , \( -30040 a + 128464\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(888a-3768\right){x}-30040a+128464$
16.2-b1 16.2-b \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $4.340752186$ 1.437366681 \( -\frac{925430099}{32} a + \frac{3956137073}{32} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 27 a - 113\) , \( 195 a - 833\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(27a-113\right){x}+195a-833$
16.2-b2 16.2-b \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $4.340752186$ 1.437366681 \( \frac{7754659}{1024} a + \frac{11013279}{1024} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -84 a - 276\) , \( -1037 a - 3397\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-84a-276\right){x}-1037a-3397$
16.2-c1 16.2-c \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\mathsf{trivial}$ $1$ $22.13736152$ 2.932165164 \( \frac{4171}{2} a - \frac{14469}{2} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 4 a + 20\) , \( 2 a + 10\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(4a+20\right){x}+2a+10$
16.2-d1 16.2-d \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\mathsf{trivial}$ $1$ $7.567530696$ 1.002343927 \( \frac{4171}{2} a - \frac{14469}{2} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 693 a - 2958\) , \( 21766 a - 93046\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(693a-2958\right){x}+21766a-93046$
16.3-a1 16.3-a \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $22.49427591$ 1.489719814 \( -\frac{7754659}{1024} a + \frac{9383969}{512} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -882 a - 2893\) , \( 27153 a + 88921\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-882a-2893\right){x}+27153a+88921$
16.3-a2 16.3-a \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $22.49427591$ 1.489719814 \( \frac{925430099}{32} a + \frac{1515353487}{16} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -320 a + 1368\) , \( -469916 a + 2008852\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-320a+1368\right){x}-469916a+2008852$
16.3-b1 16.3-b \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $4.340752186$ 1.437366681 \( -\frac{7754659}{1024} a + \frac{9383969}{512} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 84 a - 359\) , \( 953 a - 4074\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(84a-359\right){x}+953a-4074$
16.3-b2 16.3-b \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $4.340752186$ 1.437366681 \( \frac{925430099}{32} a + \frac{1515353487}{16} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -27 a - 86\) , \( -195 a - 638\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-27a-86\right){x}-195a-638$
16.3-c1 16.3-c \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\mathsf{trivial}$ $1$ $22.13736152$ 2.932165164 \( -\frac{4171}{2} a - 5149 \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -4 a + 24\) , \( -2 a + 12\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-4a+24\right){x}-2a+12$
16.3-d1 16.3-d \(\Q(\sqrt{57}) \) \( 2^{4} \) $0$ $\mathsf{trivial}$ $1$ $7.567530696$ 1.002343927 \( -\frac{4171}{2} a - 5149 \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -693 a - 2265\) , \( -21766 a - 71280\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-693a-2265\right){x}-21766a-71280$
16.4-a1 16.4-a \(\Q(\sqrt{57}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $-19$ $3.249844398$ $2.014351525$ 1.734164921 \( -884736 \) \( \bigl[0\) , \( 0\) , \( a + 1\) , \( 41678 a - 178170\) , \( 9007428 a - 38506016\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(41678a-178170\right){x}+9007428a-38506016$
16.4-a2 16.4-a \(\Q(\sqrt{57}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $-19$ $0.171044442$ $38.27267897$ 1.734164921 \( -884736 \) \( \bigl[0\) , \( 0\) , \( a + 1\) , \( -2 a - 10\) , \( 3 a + 11\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-2a-10\right){x}+3a+11$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.