Elliptic curves in class 19.1-b over 6.6.1397493.1
Isogeny class 19.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 19.1-b1
| \( \bigl[a^{4} - 3 a^{3} + 5 a - 2\) , \( a^{5} - 3 a^{4} - 4 a^{3} + 12 a^{2} + 4 a - 8\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 3 a\) , \( -38 a^{5} + 90 a^{4} + 175 a^{3} - 289 a^{2} - 287 a + 81\) , \( 203 a^{5} - 487 a^{4} - 910 a^{3} + 1515 a^{2} + 1510 a - 361\bigr] \)
|
| 19.1-b2
| \( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 5 a - 2\) , \( -a^{3} + 3 a^{2} + a - 4\) , \( 0\) , \( -3 a^{5} + 11 a^{4} - 2 a^{3} - 18 a^{2} + 5 a + 3\) , \( 0\bigr] \)
|
| 19.1-b3
| \( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 10 a - 4\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 7 a - 1\) , \( 0\) , \( -32 a^{5} + 80 a^{4} + 132 a^{3} - 240 a^{2} - 212 a + 48\) , \( 31 a^{5} - 58 a^{4} - 195 a^{3} + 218 a^{2} + 361 a - 75\bigr] \)
|
| 19.1-b4
| \( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 11 a - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 3 a - 1\) , \( 80 a^{5} - 81 a^{4} - 398 a^{3} + 24 a^{2} + 255 a - 68\) , \( 222 a^{5} - 155 a^{4} - 1189 a^{3} - 212 a^{2} + 667 a - 78\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
