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Label Base field Conductor norm Conductor label Isogeny class Weierstrass coefficients
4.1-a1 \(\Q(\sqrt{217}) \) 4 4.1 4.1-a \( \bigl[1\) , \( 1\) , \( 0\) , \( -4575 a + 35985\) , \( -2480637 a + 19511351\bigr] \)
4.1-a2 \(\Q(\sqrt{217}) \) 4 4.1 4.1-a \( \bigl[1\) , \( 1\) , \( 0\) , \( 4575 a + 31410\) , \( 2480637 a + 17030714\bigr] \)
4.1-a3 \(\Q(\sqrt{217}) \) 4 4.1 4.1-a \( \bigl[1\) , \( 1\) , \( 0\) , \( -89895 a - 617170\) , \( 37511019 a + 257530398\bigr] \)
4.1-a4 \(\Q(\sqrt{217}) \) 4 4.1 4.1-a \( \bigl[1\) , \( 1\) , \( 0\) , \( 89895 a - 707065\) , \( -37511019 a + 295041417\bigr] \)
4.1-b1 \(\Q(\sqrt{217}) \) 4 4.1 4.1-b \( \bigl[1\) , \( 0\) , \( 0\) , \( -5894 a - 40465\) , \( 851278 a + 5844415\bigr] \)
4.1-b2 \(\Q(\sqrt{217}) \) 4 4.1 4.1-b \( \bigl[1\) , \( 0\) , \( 0\) , \( 5894 a - 46359\) , \( -851278 a + 6695693\bigr] \)
4.1-c1 \(\Q(\sqrt{217}) \) 4 4.1 4.1-c \( \bigl[1\) , \( 1\) , \( 1\) , \( -7682232 a + 60424288\) , \( -18970234890 a + 149209622415\bigr] \)
4.1-c2 \(\Q(\sqrt{217}) \) 4 4.1 4.1-c \( \bigl[1\) , \( 1\) , \( 1\) , \( 7682232 a + 52742056\) , \( 18970234890 a + 130239387525\bigr] \)
4.1-d1 \(\Q(\sqrt{217}) \) 4 4.1 4.1-d \( \bigl[1\) , \( 0\) , \( 1\) , \( -76876685 a - 527793801\) , \( -996242529392 a - 6839663167426\bigr] \)
4.1-d2 \(\Q(\sqrt{217}) \) 4 4.1 4.1-d \( \bigl[1\) , \( 0\) , \( 1\) , \( 76876685 a - 604670486\) , \( 996242529392 a - 7835905696818\bigr] \)
4.1-d3 \(\Q(\sqrt{217}) \) 4 4.1 4.1-d \( \bigl[1\) , \( 0\) , \( 1\) , \( 1230190055 a - 9676010586\) , \( 63741468271084 a - 501355964650234\bigr] \)
4.1-d4 \(\Q(\sqrt{217}) \) 4 4.1 4.1-d \( \bigl[1\) , \( 0\) , \( 1\) , \( -1230190055 a - 8445820531\) , \( -63741468271084 a - 437614496379150\bigr] \)
6.1-a1 \(\Q(\sqrt{217}) \) 6 6.1 6.1-a \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -a + 18\) , \( -5 a + 9\bigr] \)
6.1-b1 \(\Q(\sqrt{217}) \) 6 6.1 6.1-b \( \bigl[1\) , \( a\) , \( a\) , \( -83592993998 a - 573904350815\) , \( 35287915421569989 a + 242267769386884299\bigr] \)
6.2-a1 \(\Q(\sqrt{217}) \) 6 6.2 6.2-a \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 1454820719431 a + 9988013356524\) , \( 857134272549098597 a + 5884621003953910568\bigr] \)
6.2-b1 \(\Q(\sqrt{217}) \) 6 6.2 6.2-b \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 7 a + 83\) , \( 20 a + 171\bigr] \)
6.3-a1 \(\Q(\sqrt{217}) \) 6 6.3 6.3-a \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -1454820719433 a + 11442834075956\) , \( -857134272549098598 a + 6741755276503009165\bigr] \)
6.3-b1 \(\Q(\sqrt{217}) \) 6 6.3 6.3-b \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -7 a + 36\) , \( -14 a + 101\bigr] \)
6.4-a1 \(\Q(\sqrt{217}) \) 6 6.4 6.4-a \( \bigl[1\) , \( a\) , \( a\) , \( 18\) , \( 4 a + 5\bigr] \)
6.4-b1 \(\Q(\sqrt{217}) \) 6 6.4 6.4-b \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 83592993997 a - 657497344813\) , \( -35287915421569990 a + 277555684808454288\bigr] \)
7.1-a1 \(\Q(\sqrt{217}) \) 7 7.1 7.1-a \( \bigl[1\) , \( -1\) , \( 1\) , \( 945951 a - 7440340\) , \( -23919915394 a + 188141136092\bigr] \)
7.1-a2 \(\Q(\sqrt{217}) \) 7 7.1 7.1-a \( \bigl[1\) , \( -1\) , \( 1\) , \( 173213478909 a - 1362403677925\) , \( -106496592842533228 a + 837644683825909912\bigr] \)
7.1-a3 \(\Q(\sqrt{217}) \) 7 7.1 7.1-a \( \bigl[1\) , \( -1\) , \( 1\) , \( 3555471 a - 27965415\) , \( -9820546524 a + 77243115188\bigr] \)
7.1-a4 \(\Q(\sqrt{217}) \) 7 7.1 7.1-a \( \bigl[1\) , \( -1\) , \( 1\) , \( 129 a - 1015\) , \( 656 a - 5160\bigr] \)
7.1-b1 \(\Q(\sqrt{217}) \) 7 7.1 7.1-b \( \bigl[1\) , \( -1\) , \( 1\) , \( -945951 a - 6494389\) , \( 23919915394 a + 164221220698\bigr] \)
7.1-b2 \(\Q(\sqrt{217}) \) 7 7.1 7.1-b \( \bigl[1\) , \( -1\) , \( 1\) , \( -129 a - 886\) , \( -656 a - 4504\bigr] \)
7.1-b3 \(\Q(\sqrt{217}) \) 7 7.1 7.1-b \( \bigl[1\) , \( -1\) , \( 1\) , \( -3555471 a - 24409944\) , \( 9820546524 a + 67422568664\bigr] \)
7.1-b4 \(\Q(\sqrt{217}) \) 7 7.1 7.1-b \( \bigl[1\) , \( -1\) , \( 1\) , \( -173213478909 a - 1189190199016\) , \( 106496592842533228 a + 731148090983376684\bigr] \)
8.1-a1 \(\Q(\sqrt{217}) \) 8 8.1 8.1-a \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -113 a - 696\) , \( 1555 a + 10865\bigr] \)
8.1-a2 \(\Q(\sqrt{217}) \) 8 8.1 8.1-a \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 2 a + 94\) , \( -a + 185\bigr] \)
8.1-b1 \(\Q(\sqrt{217}) \) 8 8.1 8.1-b \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 1869574935893 a - 14705066746888\) , \( 3779122287683704783 a - 29724534929365231599\bigr] \)
8.1-b2 \(\Q(\sqrt{217}) \) 8 8.1 8.1-b \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -24740869992 a + 194598321582\) , \( 22630333034170967 a - 177997977712882799\bigr] \)
8.2-a1 \(\Q(\sqrt{217}) \) 8 8.2 8.2-a \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 114 a - 755\) , \( -1442 a + 11665\bigr] \)
8.2-a2 \(\Q(\sqrt{217}) \) 8 8.2 8.2-a \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -a + 150\) , \( -a + 334\bigr] \)
8.2-b1 \(\Q(\sqrt{217}) \) 8 8.2 8.2-b \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -1869574935895 a - 12835491810995\) , \( -3779122287683704784 a - 25945412641681526816\bigr] \)
8.2-b2 \(\Q(\sqrt{217}) \) 8 8.2 8.2-b \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 24740869990 a + 169857451590\) , \( -22630333034170968 a - 155367644678711832\bigr] \)
8.3-a1 \(\Q(\sqrt{217}) \) 8 8.3 8.3-a \( \bigl[0\) , \( -a + 1\) , \( a\) , \( 5238176497 a + 35962490874\) , \( -66537844035834579 a - 456812902144981867\bigr] \)
8.3-b1 \(\Q(\sqrt{217}) \) 8 8.3 8.3-b \( \bigl[0\) , \( a - 1\) , \( a\) , \( 17 a - 118\) , \( 63 a - 499\bigr] \)
8.4-a1 \(\Q(\sqrt{217}) \) 8 8.4 8.4-a \( \bigl[0\) , \( a\) , \( a + 1\) , \( -5238176497 a + 41200667371\) , \( 66537844035834578 a - 523350746180816446\bigr] \)
8.4-b1 \(\Q(\sqrt{217}) \) 8 8.4 8.4-b \( \bigl[0\) , \( -a\) , \( a + 1\) , \( -17 a - 101\) , \( -64 a - 436\bigr] \)
12.1-a1 \(\Q(\sqrt{217}) \) 12 12.1 12.1-a \( \bigl[1\) , \( a + 1\) , \( a\) , \( 2401258290 a - 18887000841\) , \( -1781930806827389 a + 14015705361500025\bigr] \)
12.1-b1 \(\Q(\sqrt{217}) \) 12 12.1 12.1-b \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -269 a - 1827\) , \( 7022 a + 48214\bigr] \)
12.1-c1 \(\Q(\sqrt{217}) \) 12 12.1 12.1-c \( \bigl[1\) , \( a + 1\) , \( a\) , \( 5 a - 12\) , \( 8 a - 36\bigr] \)
12.1-c2 \(\Q(\sqrt{217}) \) 12 12.1 12.1-c \( \bigl[1\) , \( a + 1\) , \( a\) , \( 65 a - 512\) , \( 668 a - 5280\bigr] \)
12.1-d1 \(\Q(\sqrt{217}) \) 12 12.1 12.1-d \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -97 a - 663\) , \( -1164 a - 8000\bigr] \)
12.1-d2 \(\Q(\sqrt{217}) \) 12 12.1 12.1-d \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -10256644 a + 80673218\) , \( -2022736447430 a + 15909752478878\bigr] \)
12.1-e1 \(\Q(\sqrt{217}) \) 12 12.1 12.1-e \( \bigl[1\) , \( 1\) , \( a\) , \( 15849071845 a - 124660239549\) , \( -122912772997547574 a + 966765491060639043\bigr] \)
12.1-e2 \(\Q(\sqrt{217}) \) 12 12.1 12.1-e \( \bigl[1\) , \( 1\) , \( a\) , \( -1275546 a - 8757206\) , \( 2127641751 a + 14607239178\bigr] \)
12.1-f1 \(\Q(\sqrt{217}) \) 12 12.1 12.1-f \( \bigl[1\) , \( a\) , \( a\) , \( 315558654 a - 2482013931\) , \( -10476032628218 a + 82398814876539\bigr] \)
12.1-g1 \(\Q(\sqrt{217}) \) 12 12.1 12.1-g \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -345489 a - 2371916\) , \( -269827466 a - 1852489645\bigr] \)

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