| Label |
Base field |
Conductor |
Isogeny class |
Weierstrass coefficients |
| 72.1-a1 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-a |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -51931 a + 226392\) , \( 98500930 a - 429355550\bigr] \) |
| 72.1-a2 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-a |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
| 72.1-a3 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-a |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 14369 a - 62603\) , \( -1468403 a + 6400670\bigr] \) |
| 72.1-a4 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-a |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 80669 a - 351598\) , \( 24796372 a - 108084830\bigr] \) |
| 72.1-a5 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-a |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 213269 a - 929588\) , \( -112025240 a + 488306750\bigr] \) |
| 72.1-a6 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-a |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 1274069 a - 5553508\) , \( 1633669294 a - 7120999310\bigr] \) |
| 72.1-b1 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-b |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 14688 a - 64033\) , \( -1602613 a + 6985623\bigr] \) |
| 72.1-b2 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-b |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 4518 a - 19703\) , \( 334729 a - 1459055\bigr] \) |
| 72.1-c1 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-c |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -14690 a - 64033\) , \( 1602612 a + 6985623\bigr] \) |
| 72.1-c2 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-c |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -4520 a - 19703\) , \( -334730 a - 1459055\bigr] \) |
| 72.1-d1 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-d |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 3091 a + 13475\) , \( 92274 a + 402213\bigr] \) |
| 72.1-d2 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-d |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -839 a - 3655\) , \( 7650 a + 33345\bigr] \) |
| 72.1-d3 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-d |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -449 a - 1955\) , \( -12428 a - 54173\bigr] \) |
| 72.1-d4 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-d |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -11009 a - 47985\) , \( 1273778 a + 5552269\bigr] \) |
| 72.1-e1 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-e |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 11016 a - 47995\) , \( -1321773 a + 5761511\bigr] \) |
| 72.1-e2 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-e |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 456 a - 1965\) , \( 10463 a - 45571\bigr] \) |
| 72.1-e3 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-e |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 846 a - 3665\) , \( -11315 a + 49357\bigr] \) |
| 72.1-e4 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-e |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -3084 a + 13465\) , \( -78809 a + 343555\bigr] \) |
| 72.1-f1 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-f |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3092 a + 13478\) , \( -69546 a - 303144\bigr] \) |
| 72.1-f2 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-f |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -838 a - 3652\) , \( -13842 a - 60336\bigr] \) |
| 72.1-f3 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-f |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -448 a - 1952\) , \( 9106 a + 39692\bigr] \) |
| 72.1-f4 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-f |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -11008 a - 47982\) , \( -1354810 a - 5905480\bigr] \) |
| 72.1-g1 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-g |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 11017 a - 47992\) , \( 1306818 a - 5696238\bigr] \) |
| 72.1-g2 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-g |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 457 a - 1962\) , \( -11068 a + 48294\bigr] \) |
| 72.1-g3 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-g |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 847 a - 3662\) , \( 10180 a - 44324\bigr] \) |
| 72.1-g4 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-g |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -3083 a + 13468\) , \( 83014 a - 361802\bigr] \) |
| 72.1-h1 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-h |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 14692 a - 64033\) , \( 1661376 a - 7241757\bigr] \) |
| 72.1-h2 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-h |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 4522 a - 19703\) , \( -316646 a + 1380241\bigr] \) |
| 72.1-i1 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-i |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -14694 a - 64033\) , \( -1661377 a - 7241757\bigr] \) |
| 72.1-i2 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-i |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -4524 a - 19703\) , \( 316645 a + 1380241\bigr] \) |
| 72.1-j1 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-j |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -51932 a + 226389\) , \( -98430345 a + 429047963\bigr] \) |
| 72.1-j2 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-j |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
| 72.1-j3 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-j |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 14368 a - 62606\) , \( 1448893 a - 6315542\bigr] \) |
| 72.1-j4 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-j |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 80668 a - 351601\) , \( -24905977 a + 108562673\bigr] \) |
| 72.1-j5 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-j |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 213268 a - 929591\) , \( 111735445 a - 487043477\bigr] \) |
| 72.1-j6 |
\(\Q(\sqrt{19}) \)
|
72.1 |
72.1-j |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 1274068 a - 5553511\) , \( -1635400609 a + 7128546023\bigr] \) |
