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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
2268.1-a1 2268.1-a \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.748158239$ 1.525917611 \( -\frac{11527859979}{28} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 423 a - 1272\) , \( -7749 a + 21202\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(423a-1272\right){x}-7749a+21202$
2268.1-a2 2268.1-a \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.748158239$ 1.525917611 \( -\frac{5000211}{21952} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -34 a - 64\) , \( -474 a - 836\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-34a-64\right){x}-474a-836$
2268.1-a3 2268.1-a \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.748158239$ 1.525917611 \( \frac{381790581}{1835008} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -32 a + 94\) , \( 413 a - 1136\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-32a+94\right){x}+413a-1136$
2268.1-b1 2268.1-b \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $0.708865907$ 4.640616684 \( \frac{38983348653}{26353376} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2205 a + 3969\) , \( 37704 a + 67553\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(2205a+3969\right){x}+37704a+67553$
2268.1-c1 2268.1-c \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.440479499$ 0.628676794 \( -\frac{15733239981}{67228} a - \frac{7026130191}{16807} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -18 a + 18\) , \( -40 a - 4\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-18a+18\right){x}-40a-4$
2268.1-c2 2268.1-c \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.440479499$ 0.628676794 \( \frac{81233717967}{14} a - \frac{453493383129}{28} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 121 a - 344\) , \( 1089 a - 3028\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(121a-344\right){x}+1089a-3028$
2268.1-c3 2268.1-c \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.440479499$ 0.628676794 \( \frac{830169}{1568} a - \frac{4252203}{3136} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 23 a + 38\) , \( -292 a - 526\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(23a+38\right){x}-292a-526$
2268.1-d1 2268.1-d \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\Z/3\Z$ $0.624993581$ $3.675737829$ 6.015776378 \( -\frac{15733239981}{67228} a - \frac{7026130191}{16807} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -159 a + 426\) , \( -1113 a + 3122\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-159a+426\right){x}-1113a+3122$
2268.1-d2 2268.1-d \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\mathsf{trivial}$ $5.624942235$ $1.225245943$ 6.015776378 \( \frac{81233717967}{14} a - \frac{453493383129}{28} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 6 a - 24\) , \( 24 a - 96\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-24\right){x}+24a-96$
2268.1-d3 2268.1-d \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\Z/3\Z$ $1.874980745$ $3.675737829$ 6.015776378 \( \frac{830169}{1568} a - \frac{4252203}{3136} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 21 a - 54\) , \( 99 a - 274\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(21a-54\right){x}+99a-274$
2268.1-e1 2268.1-e \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $2$ $\Z/3\Z$ $0.690755389$ $19.11797416$ 5.123113506 \( -\frac{11527859979}{28} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -141\) , \( 681\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-141{x}+681$
2268.1-e2 2268.1-e \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $2$ $\Z/3\Z$ $0.076750598$ $6.372658054$ 5.123113506 \( -\frac{5000211}{21952} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 52 a - 147\) , \( -882 a + 2462\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(52a-147\right){x}-882a+2462$
2268.1-e3 2268.1-e \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $2$ $\mathsf{trivial}$ $0.076750598$ $0.708073117$ 5.123113506 \( \frac{381790581}{1835008} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 472 a + 850\) , \( -22302 a - 39958\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(472a+850\right){x}-22302a-39958$
2268.1-f1 2268.1-f \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\Z/3\Z$ $1$ $14.96053621$ 3.264656649 \( -\frac{5015840679}{7} a - \frac{17969612427}{14} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -62 a + 171\) , \( 192 a - 536\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-62a+171\right){x}+192a-536$
2268.1-f2 2268.1-f \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\Z/3\Z$ $1$ $4.986845405$ 3.264656649 \( \frac{2694303}{196} a - \frac{15380361}{392} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 6 a - 18\) , \( 12 a - 32\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(6a-18\right){x}+12a-32$
2268.1-f3 2268.1-f \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $0.554093933$ 3.264656649 \( \frac{823614934625697}{14} a - \frac{1149473179006566}{7} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 516 a - 1428\) , \( 9450 a - 26402\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(516a-1428\right){x}+9450a-26402$
2268.1-g1 2268.1-g \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\mathsf{trivial}$ $0.611331681$ $1.107074795$ 4.135254572 \( \frac{38983348653}{26353376} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -143 a + 448\) , \( -597 a + 1730\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-143a+448\right){x}-597a+1730$
2268.1-h1 2268.1-h \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\Z/3\Z$ $1.618609852$ $10.53442194$ 4.961145663 \( -\frac{545407363875}{14} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -1062\) , \( 13590\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-1062{x}+13590$
2268.1-h2 2268.1-h \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\Z/3\Z$ $0.539536617$ $10.53442194$ 4.961145663 \( -\frac{7414875}{2744} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -12\) , \( 24\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-12{x}+24$
2268.1-h3 2268.1-h \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\mathsf{trivial}$ $0.179845539$ $3.511473982$ 4.961145663 \( \frac{4492125}{3584} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -53 a + 147\) , \( 126 a - 352\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-53a+147\right){x}+126a-352$
2268.1-i1 2268.1-i \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $5.404963627$ 2.358919519 \( -\frac{81233717967}{14} a - \frac{291025947195}{28} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 16 a - 73\) , \( 377 a - 1009\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(16a-73\right){x}+377a-1009$
2268.1-i2 2268.1-i \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $5.404963627$ 2.358919519 \( -\frac{830169}{1568} a - \frac{2591865}{3136} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -14 a - 20\) , \( 48 a + 98\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-14a-20\right){x}+48a+98$
2268.1-i3 2268.1-i \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $5.404963627$ 2.358919519 \( \frac{15733239981}{67228} a - \frac{43837760745}{67228} \) \( \bigl[a\) , \( -1\) , \( 1\) , \( 177 a - 493\) , \( -1953 a + 5451\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(177a-493\right){x}-1953a+5451$
2268.1-j1 2268.1-j \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\mathsf{trivial}$ $0.064494142$ $11.34849732$ 3.833188948 \( -\frac{3}{28} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( 4\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+4$
2268.1-k1 2268.1-k \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $2.350635247$ 1.025901328 \( -\frac{545407363875}{14} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -354 a - 708\) , \( -6040 a - 10570\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-354a-708\right){x}-6040a-10570$
2268.1-k2 2268.1-k \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $2.350635247$ 1.025901328 \( -\frac{7414875}{2744} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 36 a - 111\) , \( -252 a + 682\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(36a-111\right){x}-252a+682$
2268.1-k3 2268.1-k \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $2.350635247$ 1.025901328 \( \frac{4492125}{3584} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 29 a + 62\) , \( 93 a + 172\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(29a+62\right){x}+93a+172$
2268.1-l1 2268.1-l \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\mathsf{trivial}$ $0.205677769$ $11.17579682$ 4.012787769 \( -\frac{3}{28} \) \( \bigl[a\) , \( a\) , \( 1\) , \( a + 3\) , \( -a - 2\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a+3\right){x}-a-2$
2268.1-m1 2268.1-m \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.238368991$ 0.270234268 \( -\frac{5015840679}{7} a - \frac{17969612427}{14} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -52 a - 82\) , \( -282 a - 500\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-52a-82\right){x}-282a-500$
2268.1-m2 2268.1-m \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.238368991$ 0.270234268 \( \frac{2694303}{196} a - \frac{15380361}{392} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 90 a - 255\) , \( 726 a - 2030\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(90a-255\right){x}+726a-2030$
2268.1-m3 2268.1-m \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.238368991$ 0.270234268 \( \frac{823614934625697}{14} a - \frac{1149473179006566}{7} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 41 a - 89\) , \( 181 a - 428\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(41a-89\right){x}+181a-428$
2268.1-n1 2268.1-n \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\Z/3\Z$ $1$ $7.562107224$ 1.650187084 \( -\frac{823614934625697}{14} a - \frac{1475331423387435}{14} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -84 a + 132\) , \( -498 a + 1784\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-84a+132\right){x}-498a+1784$
2268.1-n2 2268.1-n \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\Z/3\Z$ $1$ $7.562107224$ 1.650187084 \( -\frac{2694303}{196} a - \frac{9991755}{392} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 6 a - 18\) , \( 36 a - 100\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-18\right){x}+36a-100$
2268.1-n3 2268.1-n \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $2.520702408$ 1.650187084 \( \frac{5015840679}{7} a - \frac{28001293785}{14} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 6 a - 5\) , \( 6 a - 9\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(6a-5\right){x}+6a-9$
2268.1-o1 2268.1-o \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\mathsf{trivial}$ $5.624942235$ $1.225245943$ 6.015776378 \( -\frac{81233717967}{14} a - \frac{291025947195}{28} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -6 a - 18\) , \( -24 a - 72\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-6a-18\right){x}-24a-72$
2268.1-o2 2268.1-o \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\Z/3\Z$ $1.874980745$ $3.675737829$ 6.015776378 \( -\frac{830169}{1568} a - \frac{2591865}{3136} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -21 a - 33\) , \( -99 a - 175\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-21a-33\right){x}-99a-175$
2268.1-o3 2268.1-o \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\Z/3\Z$ $0.624993581$ $3.675737829$ 6.015776378 \( \frac{15733239981}{67228} a - \frac{43837760745}{67228} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 159 a + 267\) , \( 1113 a + 2009\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(159a+267\right){x}+1113a+2009$
2268.1-p1 2268.1-p \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.238368991$ 0.270234268 \( -\frac{823614934625697}{14} a - \frac{1475331423387435}{14} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -36 a - 45\) , \( -269 a - 443\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-36a-45\right){x}-269a-443$
2268.1-p2 2268.1-p \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.238368991$ 0.270234268 \( -\frac{2694303}{196} a - \frac{9991755}{392} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -92 a - 163\) , \( -727 a - 1303\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-92a-163\right){x}-727a-1303$
2268.1-p3 2268.1-p \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.238368991$ 0.270234268 \( \frac{5015840679}{7} a - \frac{28001293785}{14} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 50 a - 133\) , \( 281 a - 781\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(50a-133\right){x}+281a-781$
2268.1-q1 2268.1-q \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $0.554093933$ 3.264656649 \( -\frac{823614934625697}{14} a - \frac{1475331423387435}{14} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -516 a - 912\) , \( -9450 a - 16952\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-516a-912\right){x}-9450a-16952$
2268.1-q2 2268.1-q \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\Z/3\Z$ $1$ $4.986845405$ 3.264656649 \( -\frac{2694303}{196} a - \frac{9991755}{392} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -6 a - 12\) , \( -12 a - 20\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-6a-12\right){x}-12a-20$
2268.1-q3 2268.1-q \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\Z/3\Z$ $1$ $14.96053621$ 3.264656649 \( \frac{5015840679}{7} a - \frac{28001293785}{14} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 61 a + 109\) , \( -192 a - 344\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(61a+109\right){x}-192a-344$
2268.1-r1 2268.1-r \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.440479499$ 0.628676794 \( -\frac{81233717967}{14} a - \frac{291025947195}{28} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -122 a - 222\) , \( -1090 a - 1938\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-122a-222\right){x}-1090a-1938$
2268.1-r2 2268.1-r \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.440479499$ 0.628676794 \( -\frac{830169}{1568} a - \frac{2591865}{3136} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -25 a + 62\) , \( 291 a - 818\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-25a+62\right){x}+291a-818$
2268.1-r3 2268.1-r \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $1.440479499$ 0.628676794 \( \frac{15733239981}{67228} a - \frac{43837760745}{67228} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 18 a\) , \( 40 a - 44\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+18a{x}+40a-44$
2268.1-s1 2268.1-s \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $1$ $\mathsf{trivial}$ $0.868994067$ $3.668574818$ 5.565376271 \( -\frac{3}{28} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 0\) , \( -96 a - 172\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-96a-172$
2268.1-t1 2268.1-t \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $10.15073318$ 2.215071580 \( -\frac{823614934625697}{14} a - \frac{1475331423387435}{14} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -99 a + 270\) , \( 935 a - 2599\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-99a+270\right){x}+935a-2599$
2268.1-t2 2268.1-t \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $10.15073318$ 2.215071580 \( -\frac{2694303}{196} a - \frac{9991755}{392} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -21\) , \( -12 a + 40\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-21{x}-12a+40$
2268.1-t3 2268.1-t \(\Q(\sqrt{21}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $10.15073318$ 2.215071580 \( \frac{5015840679}{7} a - \frac{28001293785}{14} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 38 a + 62\) , \( 132 a + 238\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(38a+62\right){x}+132a+238$
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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.