Elliptic curves in class 8.1-d over 3.3.1849.1
Isogeny class 8.1-d contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 8.1-d1
| \( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 5\) , \( -7206 a^{2} - 25244 a - 12798\) , \( -1458099 a^{2} - 5108177 a - 2590294\bigr] \)
|
| 8.1-d2
| \( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 5\) , \( -96 a^{2} - 334 a - 163\) , \( -\frac{3605}{2} a^{2} - \frac{12635}{2} a - 3210\bigr] \)
|
| 8.1-d3
| \( \bigl[1\) , \( a + 1\) , \( a\) , \( \frac{94881}{2} a^{2} - \frac{153241}{2} a - 617040\) , \( \frac{27023339}{2} a^{2} - \frac{43644637}{2} a - 175741102\bigr] \)
|
| 8.1-d4
| \( \bigl[1\) , \( a + 1\) , \( a\) , \( \frac{6961}{2} a^{2} - \frac{11241}{2} a - 45265\) , \( -\frac{511731}{2} a^{2} + \frac{826483}{2} a + 3327943\bigr] \)
|
| 8.1-d5
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 5\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( \frac{46861}{2} a^{2} - \frac{75685}{2} a - 304752\) , \( 4741237 a^{2} - 7657438 a - 61667460\bigr] \)
|
| 8.1-d6
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 5\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( \frac{621}{2} a^{2} - \frac{1005}{2} a - 4037\) , \( \frac{11725}{2} a^{2} - \frac{18941}{2} a - 76259\bigr] \)
|
| 8.1-d7
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 6\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( -458920937794 a^{2} - 1607741225073 a - 815260204308\) , \( -5124405501726437361 a^{2} - 17952368917266193425 a - 9103362981097420174\bigr] \)
|
| 8.1-d8
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 6\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( 50824917136 a^{2} + 178055320237 a + 90289043107\) , \( \frac{372704835802970103}{2} a^{2} + \frac{1305699696741374595}{2} a + 331049855830269162\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 2 & 6 & 4 & 12 & 4 & 12 \\
3 & 1 & 6 & 2 & 12 & 4 & 12 & 4 \\
2 & 6 & 1 & 3 & 2 & 6 & 2 & 6 \\
6 & 2 & 3 & 1 & 6 & 2 & 6 & 2 \\
4 & 12 & 2 & 6 & 1 & 3 & 4 & 12 \\
12 & 4 & 6 & 2 & 3 & 1 & 12 & 4 \\
4 & 12 & 2 & 6 & 4 & 12 & 1 & 3 \\
12 & 4 & 6 & 2 & 12 & 4 & 3 & 1
\end{array}\right)\)
