Elliptic curves in class 64.7-d over 3.3.316.1
Isogeny class 64.7-d contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 64.7-d1
| \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( 7908273 a^{2} - 4185996 a - 33603392\) , \( -17708327376 a^{2} + 9373311329 a + 75245171793\bigr] \)
|
| 64.7-d2
| \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( 494268 a^{2} - 261626 a - 2100217\) , \( -276978244 a^{2} + 146609177 a + 1176919485\bigr] \)
|
| 64.7-d3
| \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -2894790049560 a^{2} + 1532260369223 a + 12300369748958\) , \( 6521086825648874308 a^{2} - 3451719377275691296 a - 27709014383527172467\bigr] \)
|
| 64.7-d4
| \( \bigl[a^{2} - 3\) , \( a^{2} - 3\) , \( 0\) , \( 27 a^{2} + 42 a - 50\) , \( 3216 a^{2} + 4384 a - 2719\bigr] \)
|
| 64.7-d5
| \( \bigl[a^{2} - 3\) , \( -a^{2} + 3\) , \( 0\) , \( 2665494175 a^{2} - 1410890261 a - 11326059353\) , \( -101934795285681 a^{2} + 53955777236750 a + 433135270894324\bigr] \)
|
| 64.7-d6
| \( \bigl[a + 1\) , \( a^{2} - 3\) , \( 0\) , \( 1698582370192 a^{2} - 899087811255 a - 7217515206531\) , \( 1762036591917483023 a^{2} - 932675182895637479 a - 7487141112384210938\bigr] \)
|
| 64.7-d7
| \( \bigl[a + 1\) , \( a^{2} - 3\) , \( 0\) , \( 111924466012 a^{2} - 59243475580 a - 475582785736\) , \( 24375985535984949 a^{2} - 12902613301177606 a - 103576988297813195\bigr] \)
|
| 64.7-d8
| \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -1090739352869 a^{2} + 577346424071 a + 4634704800807\) , \( -3861853717631158558 a^{2} + 2044143202774369436 a + 16409559183912861757\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 2 & 16 & 4 & 4 & 16 & 8 & 8 \\
2 & 1 & 8 & 2 & 2 & 8 & 4 & 4 \\
16 & 8 & 1 & 16 & 4 & 4 & 2 & 8 \\
4 & 2 & 16 & 1 & 4 & 16 & 8 & 8 \\
4 & 2 & 4 & 4 & 1 & 4 & 2 & 2 \\
16 & 8 & 4 & 16 & 4 & 1 & 2 & 8 \\
8 & 4 & 2 & 8 & 2 & 2 & 1 & 4 \\
8 & 4 & 8 & 8 & 2 & 8 & 4 & 1
\end{array}\right)\)
