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Label Base field Conductor norm Conductor label Isogeny class Weierstrass coefficients
1.1-a1 \(\Q(\sqrt{209}) \) 1 1.1 1.1-a \( \bigl[0\) , \( 0\) , \( 1\) , \( 12880 a - 99542\) , \( -2141323 a + 16549035\bigr] \)
1.1-a2 \(\Q(\sqrt{209}) \) 1 1.1 1.1-a \( \bigl[0\) , \( 0\) , \( 1\) , \( -12880 a - 86662\) , \( 2141323 a + 14407712\bigr] \)
2.1-a1 \(\Q(\sqrt{209}) \) 2 2.1 2.1-a \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 333486 a - 2577189\) , \( -412096662 a + 3184854795\bigr] \)
2.1-b1 \(\Q(\sqrt{209}) \) 2 2.1 2.1-b \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -166349 a - 1119240\) , \( -101485499 a - 682836650\bigr] \)
2.1-b2 \(\Q(\sqrt{209}) \) 2 2.1 2.1-b \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -6449241 a + 49842606\) , \( -1496864675 a + 11568393744\bigr] \)
2.1-c1 \(\Q(\sqrt{209}) \) 2 2.1 2.1-c \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 1502 a - 11391\) , \( 84221 a - 650261\bigr] \)
2.1-c2 \(\Q(\sqrt{209}) \) 2 2.1 2.1-c \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 8 a + 57\) , \( 19 a + 137\bigr] \)
2.1-d1 \(\Q(\sqrt{209}) \) 2 2.1 2.1-d \( \bigl[a + 1\) , \( 1\) , \( a\) , \( -1797 a - 12082\) , \( -124118 a - 835100\bigr] \)
2.2-a1 \(\Q(\sqrt{209}) \) 2 2.2 2.2-a \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -333486 a - 2243755\) , \( 412430147 a + 2775001836\bigr] \)
2.2-b1 \(\Q(\sqrt{209}) \) 2 2.2 2.2-b \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 166348 a - 1285588\) , \( 101485499 a - 784322149\bigr] \)
2.2-b2 \(\Q(\sqrt{209}) \) 2 2.2 2.2-b \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 6449267 a + 43393366\) , \( 1546707281 a + 10406890251\bigr] \)
2.2-c1 \(\Q(\sqrt{209}) \) 2 2.2 2.2-c \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -1476 a - 9940\) , \( -95638 a - 643494\bigr] \)
2.2-c2 \(\Q(\sqrt{209}) \) 2 2.2 2.2-c \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -10 a + 66\) , \( -20 a + 156\bigr] \)
2.2-d1 \(\Q(\sqrt{209}) \) 2 2.2 2.2-d \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 1797 a - 13879\) , \( 122321 a - 945339\bigr] \)
4.1-a1 \(\Q(\sqrt{209}) \) 4 4.1 4.1-a \( \bigl[1\) , \( -1\) , \( a\) , \( -403 a - 2708\) , \( -267565 a - 1800300\bigr] \)
4.1-b1 \(\Q(\sqrt{209}) \) 4 4.1 4.1-b \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 402 a - 3111\) , \( 267564 a - 2067865\bigr] \)
4.1-c1 \(\Q(\sqrt{209}) \) 4 4.1 4.1-c \( \bigl[1\) , \( -1\) , \( 1\) , \( 25 a - 196\) , \( -132 a + 1019\bigr] \)
4.1-c2 \(\Q(\sqrt{209}) \) 4 4.1 4.1-c \( \bigl[1\) , \( -1\) , \( 1\) , \( 109626655 a - 847240411\) , \( 1679777810708 a - 12982021956321\bigr] \)
4.1-c3 \(\Q(\sqrt{209}) \) 4 4.1 4.1-c \( \bigl[1\) , \( -1\) , \( 1\) , \( -25 a - 171\) , \( 132 a + 887\bigr] \)
4.1-c4 \(\Q(\sqrt{209}) \) 4 4.1 4.1-c \( \bigl[1\) , \( -1\) , \( 1\) , \( -109626655 a - 737613756\) , \( -1679777810708 a - 11302244145613\bigr] \)
4.1-d1 \(\Q(\sqrt{209}) \) 4 4.1 4.1-d \( \bigl[1\) , \( -1\) , \( 0\) , \( -1485209680 a - 9993108793\) , \( 83988775088712 a + 565111430507277\bigr] \)
4.1-d2 \(\Q(\sqrt{209}) \) 4 4.1 4.1-d \( \bigl[1\) , \( -1\) , \( 0\) , \( 950 a + 6392\) , \( -42668 a - 287088\bigr] \)
4.1-d3 \(\Q(\sqrt{209}) \) 4 4.1 4.1-d \( \bigl[1\) , \( -1\) , \( 0\) , \( 1485209680 a - 11478318473\) , \( -83988775088712 a + 649100205595989\bigr] \)
4.1-d4 \(\Q(\sqrt{209}) \) 4 4.1 4.1-d \( \bigl[1\) , \( -1\) , \( 0\) , \( -950 a + 7342\) , \( 42668 a - 329756\bigr] \)
4.2-a1 \(\Q(\sqrt{209}) \) 4 4.2 4.2-a \( \bigl[0\) , \( -a - 1\) , \( a\) , \( 11\) , \( -a - 11\bigr] \)
4.2-b1 \(\Q(\sqrt{209}) \) 4 4.2 4.2-b \( \bigl[0\) , \( -1\) , \( a\) , \( -37023561 a + 286133487\) , \( -1880699198318 a + 14534826052669\bigr] \)
4.3-a1 \(\Q(\sqrt{209}) \) 4 4.3 4.3-a \( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 2 a + 10\) , \( a - 2\bigr] \)
4.3-b1 \(\Q(\sqrt{209}) \) 4 4.3 4.3-b \( \bigl[0\) , \( -1\) , \( a + 1\) , \( 37023561 a + 249109926\) , \( 1880699198317 a + 12654126854351\bigr] \)
10.1-a1 \(\Q(\sqrt{209}) \) 10 10.1 10.1-a \( \bigl[a\) , \( -a\) , \( 1\) , \( 19297589 a - 149139785\) , \( -251996522818 a + 1947533996049\bigr] \)
10.1-b1 \(\Q(\sqrt{209}) \) 10 10.1 10.1-b \( \bigl[1\) , \( a\) , \( a + 1\) , \( 12491185 a - 96537059\) , \( 61050477245 a - 471823494147\bigr] \)
10.1-b2 \(\Q(\sqrt{209}) \) 10 10.1 10.1-b \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -a + 17\) , \( -2 a - 8\bigr] \)
10.1-c1 \(\Q(\sqrt{209}) \) 10 10.1 10.1-c \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 3 a + 20\bigr] \)
10.1-c2 \(\Q(\sqrt{209}) \) 10 10.1 10.1-c \( \bigl[1\) , \( 1\) , \( 1\) , \( 512138585 a - 3958020110\) , \( 13200346700953 a - 102017772594930\bigr] \)
10.1-d1 \(\Q(\sqrt{209}) \) 10 10.1 10.1-d \( \bigl[a\) , \( 0\) , \( 1\) , \( -265 a - 1737\) , \( 31126 a + 209482\bigr] \)
10.4-a1 \(\Q(\sqrt{209}) \) 10 10.4 10.4-a \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -19297590 a - 129842196\) , \( 251996522818 a + 1695537473231\bigr] \)
10.4-b1 \(\Q(\sqrt{209}) \) 10 10.4 10.4-b \( \bigl[1\) , \( a\) , \( a + 1\) , \( 16\) , \( a - 10\bigr] \)
10.4-b2 \(\Q(\sqrt{209}) \) 10 10.4 10.4-b \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -12491186 a - 84045873\) , \( -61050477246 a - 410773016901\bigr] \)
10.4-c1 \(\Q(\sqrt{209}) \) 10 10.4 10.4-c \( \bigl[1\) , \( 1\) , \( 1\) , \( -512138585 a - 3445881525\) , \( -13200346700953 a - 88817425893977\bigr] \)
10.4-c2 \(\Q(\sqrt{209}) \) 10 10.4 10.4-c \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( -3 a + 23\bigr] \)
10.4-d1 \(\Q(\sqrt{209}) \) 10 10.4 10.4-d \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 264 a - 2002\) , \( -31126 a + 240608\bigr] \)
11.1-a1 \(\Q(\sqrt{209}) \) 11 11.1 11.1-a \( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \)
11.1-a2 \(\Q(\sqrt{209}) \) 11 11.1 11.1-a \( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \)
11.1-a3 \(\Q(\sqrt{209}) \) 11 11.1 11.1-a \( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
11.1-b1 \(\Q(\sqrt{209}) \) 11 11.1 11.1-b \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 4688891060561 a - 36237701385816\) , \( -14859019779017908422 a + 114836688394705117771\bigr] \)
11.1-b2 \(\Q(\sqrt{209}) \) 11 11.1 11.1-b \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -6195627759 a - 41686761846\) , \( 1292706345403712 a + 8697866248261405\bigr] \)
11.1-b3 \(\Q(\sqrt{209}) \) 11 11.1 11.1-b \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 199858961 a - 1544593196\) , \( 9820121401118 a - 75893984805809\bigr] \)
16.4-a1 \(\Q(\sqrt{209}) \) 16 16.4 16.4-a \( \bigl[0\) , \( a - 1\) , \( a\) , \( -317 a - 2113\) , \( 7753 a + 52137\bigr] \)
16.4-a2 \(\Q(\sqrt{209}) \) 16 16.4 16.4-a \( \bigl[0\) , \( -a\) , \( a\) , \( 931337 a - 7197740\) , \( 1351685914 a - 10446391276\bigr] \)
16.5-a1 \(\Q(\sqrt{209}) \) 16 16.5 16.5-a \( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -931337 a - 6266403\) , \( -1351685915 a - 9094705362\bigr] \)
16.5-a2 \(\Q(\sqrt{209}) \) 16 16.5 16.5-a \( \bigl[0\) , \( -a\) , \( a + 1\) , \( 317 a - 2430\) , \( -7754 a + 59890\bigr] \)
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