*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.
| Label |
Base field |
Conductor |
Isogeny class |
Weierstrass coefficients |
| 6.1-a1 |
\(\Q(\sqrt{10}) \) |
6.1 |
6.1-a |
\( \bigl[a\) , \( a\) , \( 0\) , \( 1263 a - 8032\) , \( 62956 a - 305877\bigr] \) |
| 6.1-a2 |
\(\Q(\sqrt{10}) \) |
6.1 |
6.1-a |
\( \bigl[a\) , \( a\) , \( 0\) , \( 3 a + 8\) , \( 4 a + 3\bigr] \) |
| 6.1-b1 |
\(\Q(\sqrt{10}) \) |
6.1 |
6.1-b |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 314 a - 2006\) , \( 8873 a - 39813\bigr] \) |
| 6.1-b2 |
\(\Q(\sqrt{10}) \) |
6.1 |
6.1-b |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -a + 4\) , \( -a - 3\bigr] \) |
| 6.2-a1 |
\(\Q(\sqrt{10}) \) |
6.2 |
6.2-a |
\( \bigl[a\) , \( -a\) , \( a\) , \( -2741954 a - 8670817\) , \( -4394335877 a - 13896110178\bigr] \) |
| 6.2-a2 |
\(\Q(\sqrt{10}) \) |
6.2 |
6.2-a |
\( \bigl[a\) , \( -a\) , \( a\) , \( -374 a - 1177\) , \( -86489 a - 273498\bigr] \) |
| 6.2-b1 |
\(\Q(\sqrt{10}) \) |
6.2 |
6.2-b |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -315 a - 2006\) , \( -8874 a - 39813\bigr] \) |
| 6.2-b2 |
\(\Q(\sqrt{10}) \) |
6.2 |
6.2-b |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 4\) , \( -3\bigr] \) |
| 12.1-a1 |
\(\Q(\sqrt{10}) \) |
12.1 |
12.1-a |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -14 a - 42\) , \( 390 a + 1238\bigr] \) |
| 12.1-a2 |
\(\Q(\sqrt{10}) \) |
12.1 |
12.1-a |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 7\) , \( -3 a - 12\bigr] \) |
| 12.1-a3 |
\(\Q(\sqrt{10}) \) |
12.1 |
12.1-a |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -34 a - 102\) , \( 162 a + 510\bigr] \) |
| 12.1-a4 |
\(\Q(\sqrt{10}) \) |
12.1 |
12.1-a |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -534 a - 1682\) , \( 11534 a + 36470\bigr] \) |
| 12.1-b1 |
\(\Q(\sqrt{10}) \) |
12.1 |
12.1-b |
\( \bigl[a\) , \( -a\) , \( a\) , \( -5 a - 11\) , \( 50 a + 161\bigr] \) |
| 12.1-b2 |
\(\Q(\sqrt{10}) \) |
12.1 |
12.1-b |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -14 a - 39\) , \( a + 5\bigr] \) |
| 12.1-b3 |
\(\Q(\sqrt{10}) \) |
12.1 |
12.1-b |
\( \bigl[a\) , \( -a\) , \( a\) , \( -10 a - 26\) , \( 24 a + 80\bigr] \) |
| 12.1-b4 |
\(\Q(\sqrt{10}) \) |
12.1 |
12.1-b |
\( \bigl[a\) , \( -a\) , \( a\) , \( -135 a - 421\) , \( 1518 a + 4805\bigr] \) |
| 12.2-a1 |
\(\Q(\sqrt{10}) \) |
12.2 |
12.2-a |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 202 a + 638\) , \( 1306 a + 4130\bigr] \) |
| 12.2-a2 |
\(\Q(\sqrt{10}) \) |
12.2 |
12.2-a |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -58 a - 182\) , \( 294 a + 930\bigr] \) |
| 12.2-a3 |
\(\Q(\sqrt{10}) \) |
12.2 |
12.2-a |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -28 a - 87\) , \( -107 a - 338\bigr] \) |
| 12.2-a4 |
\(\Q(\sqrt{10}) \) |
12.2 |
12.2-a |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -798 a - 2522\) , \( 22946 a + 72562\bigr] \) |
| 12.2-b1 |
\(\Q(\sqrt{10}) \) |
12.2 |
12.2-b |
\( \bigl[a\) , \( a\) , \( a\) , \( 135 a - 421\) , \( -1518 a + 4805\bigr] \) |
| 12.2-b2 |
\(\Q(\sqrt{10}) \) |
12.2 |
12.2-b |
\( \bigl[a\) , \( a\) , \( a\) , \( 10 a - 26\) , \( -24 a + 80\bigr] \) |
| 12.2-b3 |
\(\Q(\sqrt{10}) \) |
12.2 |
12.2-b |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a - 39\) , \( -a + 5\bigr] \) |
| 12.2-b4 |
\(\Q(\sqrt{10}) \) |
12.2 |
12.2-b |
\( \bigl[a\) , \( a\) , \( a\) , \( 5 a - 11\) , \( -50 a + 161\bigr] \) |
| 18.2-a1 |
\(\Q(\sqrt{10}) \) |
18.2 |
18.2-a |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -143 a - 451\) , \( 1462 a + 4623\bigr] \) |
| 18.2-a2 |
\(\Q(\sqrt{10}) \) |
18.2 |
18.2-a |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 257 a + 814\) , \( 8740 a + 27638\bigr] \) |
| 18.2-b1 |
\(\Q(\sqrt{10}) \) |
18.2 |
18.2-b |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -4515 a - 14281\) , \( 288657 a + 912811\bigr] \) |
| 18.2-b2 |
\(\Q(\sqrt{10}) \) |
18.2 |
18.2-b |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -65 a - 304\) , \( 1536 a + 4219\bigr] \) |
| 18.2-b3 |
\(\Q(\sqrt{10}) \) |
18.2 |
18.2-b |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -5 a - 4\) , \( -12 a - 29\bigr] \) |
| 18.2-b4 |
\(\Q(\sqrt{10}) \) |
18.2 |
18.2-b |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 15 a + 44\) , \( 114 a + 358\bigr] \) |
| 18.2-c1 |
\(\Q(\sqrt{10}) \) |
18.2 |
18.2-c |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -95 a + 231\) , \( 6100 a - 19186\bigr] \) |
| 18.2-c2 |
\(\Q(\sqrt{10}) \) |
18.2 |
18.2-c |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 6220 a - 19669\) , \( 484078 a - 1530789\bigr] \) |
| 18.2-c3 |
\(\Q(\sqrt{10}) \) |
18.2 |
18.2-c |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -65 a + 206\) , \( -203 a + 642\bigr] \) |
| 18.2-c4 |
\(\Q(\sqrt{10}) \) |
18.2 |
18.2-c |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 25 a - 69\) , \( -104 a + 338\bigr] \) |
| 18.2-d1 |
\(\Q(\sqrt{10}) \) |
18.2 |
18.2-d |
\( \bigl[a\) , \( -a\) , \( a\) , \( 10 a - 39\) , \( -21 a + 66\bigr] \) |
| 18.2-d2 |
\(\Q(\sqrt{10}) \) |
18.2 |
18.2-d |
\( \bigl[a\) , \( -a\) , \( a\) , \( -70 a + 221\) , \( -165 a + 526\bigr] \) |
| 18.3-a1 |
\(\Q(\sqrt{10}) \) |
18.3 |
18.3-a |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -3 a - 12\) , \( a + 2\bigr] \) |
| 18.3-a2 |
\(\Q(\sqrt{10}) \) |
18.3 |
18.3-a |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 17 a + 53\) , \( 29 a + 92\bigr] \) |
| 18.3-b1 |
\(\Q(\sqrt{10}) \) |
18.3 |
18.3-b |
\( \bigl[a\) , \( a\) , \( a\) , \( -24882 a - 78689\) , \( -3847743 a - 12167634\bigr] \) |
| 18.3-b2 |
\(\Q(\sqrt{10}) \) |
18.3 |
18.3-b |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -6 a - 15\) , \( 7 a + 20\bigr] \) |
| 18.3-b3 |
\(\Q(\sqrt{10}) \) |
18.3 |
18.3-b |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 24 a + 60\) , \( -746 a - 2308\bigr] \) |
| 18.3-b4 |
\(\Q(\sqrt{10}) \) |
18.3 |
18.3-b |
\( \bigl[a\) , \( a\) , \( a\) , \( 258 a + 811\) , \( 1365 a + 4314\bigr] \) |
| 18.3-c1 |
\(\Q(\sqrt{10}) \) |
18.3 |
18.3-c |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -6220 a - 19669\) , \( -484078 a - 1530789\bigr] \) |
| 18.3-c2 |
\(\Q(\sqrt{10}) \) |
18.3 |
18.3-c |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -25 a - 69\) , \( 104 a + 338\bigr] \) |
| 18.3-c3 |
\(\Q(\sqrt{10}) \) |
18.3 |
18.3-c |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 95 a + 231\) , \( -6100 a - 19186\bigr] \) |
| 18.3-c4 |
\(\Q(\sqrt{10}) \) |
18.3 |
18.3-c |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 65 a + 206\) , \( 203 a + 642\bigr] \) |
| 18.3-d1 |
\(\Q(\sqrt{10}) \) |
18.3 |
18.3-d |
\( \bigl[a\) , \( a\) , \( a\) , \( -10 a - 39\) , \( 21 a + 66\bigr] \) |
| 18.3-d2 |
\(\Q(\sqrt{10}) \) |
18.3 |
18.3-d |
\( \bigl[a\) , \( a\) , \( a\) , \( 70 a + 221\) , \( 165 a + 526\bigr] \) |
| 20.1-a1 |
\(\Q(\sqrt{10}) \) |
20.1 |
20.1-a |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -5\) , \( -25\bigr] \) |
| 20.1-a2 |
\(\Q(\sqrt{10}) \) |
20.1 |
20.1-a |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 5\) , \( 3\bigr] \) |
