Elliptic curves in class 4.2-d over 4.4.13968.1
Isogeny class 4.2-d contains
8 curves linked by isogenies of
degrees dividing 30.
| Curve label |
Weierstrass Coefficients |
| 4.2-d1
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -4418 a^{3} - 5789 a^{2} + 12142 a + 5301\) , \( 709581 a^{3} + \frac{1815801}{2} a^{2} - \frac{3986249}{2} a - 865020\bigr] \)
|
| 4.2-d2
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( a\) , \( -\frac{31}{2} a^{3} + \frac{75}{2} a^{2} + 95 a - 164\) , \( -105 a^{3} + 247 a^{2} + 636 a - 1040\bigr] \)
|
| 4.2-d3
| \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( \frac{7}{2} a^{3} - \frac{37}{2} a^{2} + 11 a + 21\) , \( -\frac{59}{2} a^{3} + 63 a^{2} + \frac{413}{2} a - 324\bigr] \)
|
| 4.2-d4
| \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( \frac{5277}{2} a^{3} - 1935 a^{2} - \frac{43103}{2} a - 7902\) , \( -193084 a^{3} + 126489 a^{2} + 1537187 a + 564100\bigr] \)
|
| 4.2-d5
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{5}{2} a - 4\) , \( 0\) , \( -2637 a^{3} + 5975 a^{2} + 17505 a - 28745\) , \( 199062 a^{3} - 465678 a^{2} - 1253571 a + 2102741\bigr] \)
|
| 4.2-d6
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{7}{2} a + 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -4 a^{3} - \frac{13}{2} a^{2} + \frac{27}{2} a + 17\) , \( 29 a^{3} - \frac{49}{2} a^{2} - \frac{487}{2} a - 85\bigr] \)
|
| 4.2-d7
| \( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -12062 a^{3} + \frac{57713}{2} a^{2} + \frac{146797}{2} a - 125875\) , \( \frac{3622561}{2} a^{3} - 4323425 a^{2} - \frac{22018221}{2} a + 18756361\bigr] \)
|
| 4.2-d8
| \( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -\frac{129}{2} a^{3} - 82 a^{2} + \frac{363}{2} a + 78\) , \( \frac{2749}{2} a^{3} + \frac{3511}{2} a^{2} - 3866 a - 1679\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 10 & 5 & 2 & 3 & 30 & 6 & 15 \\
10 & 1 & 2 & 5 & 30 & 3 & 15 & 6 \\
5 & 2 & 1 & 10 & 15 & 6 & 30 & 3 \\
2 & 5 & 10 & 1 & 6 & 15 & 3 & 30 \\
3 & 30 & 15 & 6 & 1 & 10 & 2 & 5 \\
30 & 3 & 6 & 15 & 10 & 1 & 5 & 2 \\
6 & 15 & 30 & 3 & 2 & 5 & 1 & 10 \\
15 & 6 & 3 & 30 & 5 & 2 & 10 & 1
\end{array}\right)\)
