Elliptic curves in class 4.2-c over 4.4.13968.1
Isogeny class 4.2-c contains
8 curves linked by isogenies of
degrees dividing 30.
| Curve label |
Weierstrass Coefficients |
| 4.2-c1
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -12062 a^{3} + \frac{57713}{2} a^{2} + \frac{146797}{2} a - 125876\) , \( -1811281 a^{3} + 4323424 a^{2} + 11009111 a - 18756361\bigr] \)
|
| 4.2-c2
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a\) , \( a\) , \( -\frac{129}{2} a^{3} - 82 a^{2} + \frac{363}{2} a + 79\) , \( -1375 a^{3} - 1756 a^{2} + 3868 a + 1678\bigr] \)
|
| 4.2-c3
| \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{11}{2} a^{3} - \frac{9}{2} a^{2} + 22 a + 11\) , \( -34 a^{3} + \frac{39}{2} a^{2} + \frac{525}{2} a + 96\bigr] \)
|
| 4.2-c4
| \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -2635 a^{3} + \frac{11957}{2} a^{2} + \frac{35001}{2} a - 28751\) , \( -195845 a^{3} + 457861 a^{2} + 1234695 a - 2070128\bigr] \)
|
| 4.2-c5
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 2\) , \( 0\) , \( 2637 a^{3} - 1936 a^{2} - 21544 a - 7902\) , \( 199062 a^{3} - 131508 a^{2} - 1587741 a - 582554\bigr] \)
|
| 4.2-c6
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( 5 a^{3} - \frac{39}{2} a^{2} + \frac{3}{2} a + 23\) , \( \frac{67}{2} a^{3} - \frac{163}{2} a^{2} - 199 a + 343\bigr] \)
|
| 4.2-c7
| \( \bigl[1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -4418 a^{3} - 5789 a^{2} + 12142 a + 5302\) , \( -\frac{1419163}{2} a^{3} - \frac{1815803}{2} a^{2} + 1993125 a + 865020\bigr] \)
|
| 4.2-c8
| \( \bigl[1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -\frac{31}{2} a^{3} + \frac{75}{2} a^{2} + 95 a - 165\) , \( \frac{209}{2} a^{3} - \frac{495}{2} a^{2} - 634 a + 1039\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 10 & 5 & 2 & 3 & 30 & 6 & 15 \\
10 & 1 & 2 & 5 & 30 & 3 & 15 & 6 \\
5 & 2 & 1 & 10 & 15 & 6 & 30 & 3 \\
2 & 5 & 10 & 1 & 6 & 15 & 3 & 30 \\
3 & 30 & 15 & 6 & 1 & 10 & 2 & 5 \\
30 & 3 & 6 & 15 & 10 & 1 & 5 & 2 \\
6 & 15 & 30 & 3 & 2 & 5 & 1 & 10 \\
15 & 6 & 3 & 30 & 5 & 2 & 10 & 1
\end{array}\right)\)
