Isogeny class 31.2-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 31.2-a1
| \( \bigl[\frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{1}{2} a^{3} - 3 a\) , \( 1\) , \( 21 a^{3} - \frac{49}{2} a^{2} - 51 a - 17\) , \( -32 a^{3} + \frac{275}{2} a^{2} - 58 a - 195\bigr] \)
|
| 31.2-a2
| \( \bigl[\frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{1}{2} a^{3} - 3 a\) , \( 1\) , \( 6 a^{3} - 12 a^{2} - 6 a + 3\) , \( \frac{43}{2} a^{3} - \frac{115}{2} a^{2} + a + 41\bigr] \)
|
| 31.2-a3
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a + 1\) , \( -\frac{1}{2} a^{3} + 3 a^{2} - 2\bigr] \)
|
| 31.2-a4
| \( \bigl[\frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( -7 a^{3} - 10 a^{2} + 8 a - 14\) , \( -\frac{73}{2} a^{3} - 62 a^{2} + 48 a - 4\bigr] \)
|
| 31.2-a5
| \( \bigl[\frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{1}{2} a^{3} - 3 a\) , \( 1\) , \( a^{3} + \frac{1}{2} a^{2} - 6 a - 2\) , \( -\frac{1}{2} a^{3} - \frac{9}{2} a^{2} + 8 a + 11\bigr] \)
|
| 31.2-a6
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( \frac{11}{2} a^{3} - 12 a^{2} - a + 6\) , \( -\frac{53}{2} a^{3} + \frac{125}{2} a^{2} + 20 a - 49\bigr] \)
|
| 31.2-a7
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( 88 a^{3} - 207 a^{2} - 36 a + 111\) , \( -1609 a^{3} + \frac{7485}{2} a^{2} + 1071 a - 2772\bigr] \)
|
| 31.2-a8
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( \frac{1}{2} a^{2} + a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( -\frac{147}{2} a^{3} - 54 a^{2} + 381 a + 272\) , \( -423 a^{3} - 342 a^{2} + 2215 a + 1788\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 2 & 12 & 12 & 4 & 6 & 3 & 4 \\
2 & 1 & 6 & 6 & 2 & 3 & 6 & 2 \\
12 & 6 & 1 & 4 & 3 & 2 & 4 & 12 \\
12 & 6 & 4 & 1 & 12 & 2 & 4 & 3 \\
4 & 2 & 3 & 12 & 1 & 6 & 12 & 4 \\
6 & 3 & 2 & 2 & 6 & 1 & 2 & 6 \\
3 & 6 & 4 & 4 & 12 & 2 & 1 & 12 \\
4 & 2 & 12 & 3 & 4 & 6 & 12 & 1
\end{array}\right)\)
