Elliptic curves in class 45.1-c over 6.6.1241125.1
Isogeny class 45.1-c contains
4 curves linked by isogenies of
degrees dividing 10.
| Curve label |
Weierstrass Coefficients |
| 45.1-c1
| \( \bigl[-2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 6\) , \( -a^{5} + 8 a^{3} + a^{2} - 14 a - 3\) , \( a^{2} - 2\) , \( -28 a^{5} + 35 a^{4} + 155 a^{3} - 141 a^{2} - 139 a - 17\) , \( 120 a^{5} - 152 a^{4} - 644 a^{3} + 565 a^{2} + 598 a + 102\bigr] \)
|
| 45.1-c2
| \( \bigl[-3 a^{5} + a^{4} + 20 a^{3} - 30 a - 12\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 3 a^{2} - 54 a - 15\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 3 a^{2} - 41 a - 16\) , \( -21 a^{5} + 14 a^{4} + 133 a^{3} - 39 a^{2} - 183 a - 52\) , \( -32 a^{5} + 32 a^{4} + 187 a^{3} - 112 a^{2} - 214 a - 51\bigr] \)
|
| 45.1-c3
| \( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 11 a - 5\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 7 a\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 18\) , \( -323 a^{5} + 73 a^{4} + 2251 a^{3} + 142 a^{2} - 3617 a - 1489\) , \( 1252 a^{5} - 284 a^{4} - 8725 a^{3} - 565 a^{2} + 14006 a + 5768\bigr] \)
|
| 45.1-c4
| \( \bigl[-3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 10\) , \( 2 a^{5} - a^{4} - 13 a^{3} + 3 a^{2} + 19 a + 3\) , \( -2 a^{5} + a^{4} + 13 a^{3} - a^{2} - 19 a - 8\) , \( 57 a^{5} - 41 a^{4} - 371 a^{3} + 103 a^{2} + 567 a + 110\) , \( 245 a^{5} - 68 a^{4} - 1745 a^{3} + 200 a^{2} + 2697 a + 559\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 5 & 2 & 10 \\
5 & 1 & 10 & 2 \\
2 & 10 & 1 & 5 \\
10 & 2 & 5 & 1
\end{array}\right)\)
