Elliptic curves in class 5.1-c over 4.4.18625.1
Isogeny class 5.1-c contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 5.1-c1
| \( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( 0\) , \( \frac{8}{3} a^{3} + 6 a^{2} - \frac{52}{3} a - \frac{97}{3}\) , \( 0\bigr] \)
|
| 5.1-c2
| \( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{4}{3} a - \frac{37}{6}\) , \( a^{2} - 6\) , \( \frac{5}{2} a^{3} + 24 a^{2} - 35 a - \frac{195}{2}\) , \( \frac{82}{3} a^{3} - 21 a^{2} - \frac{353}{3} a + \frac{22}{3}\bigr] \)
|
| 5.1-c3
| \( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{4}{3} a - \frac{37}{6}\) , \( a^{2} - 6\) , \( \frac{35}{6} a^{3} + 9 a^{2} - \frac{95}{3} a - \frac{385}{6}\) , \( \frac{56}{3} a^{3} + 14 a^{2} - \frac{301}{3} a - \frac{355}{3}\bigr] \)
|
| 5.1-c4
| \( \bigl[a^{2} - 6\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{4}{3} a - \frac{43}{6}\) , \( a^{2} + a - 7\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 3 a - \frac{21}{2}\) , \( -\frac{5}{3} a^{3} + \frac{49}{3} a + \frac{31}{3}\bigr] \)
|
| 5.1-c5
| \( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( a + 1\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( -\frac{79}{3} a^{3} - 31 a^{2} + \frac{911}{3} a + \frac{1379}{3}\) , \( 236 a^{3} + 370 a^{2} - 2340 a - 3809\bigr] \)
|
| 5.1-c6
| \( \bigl[a\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a - \frac{7}{6}\) , \( a\) , \( a^{3} - a^{2} - 18 a - 20\) , \( \frac{13}{3} a^{3} - \frac{230}{3} a - \frac{326}{3}\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 2 & 4 & 2 & 2 \\
4 & 1 & 2 & 4 & 8 & 8 \\
2 & 2 & 1 & 2 & 4 & 4 \\
4 & 4 & 2 & 1 & 8 & 8 \\
2 & 8 & 4 & 8 & 1 & 4 \\
2 & 8 & 4 & 8 & 4 & 1
\end{array}\right)\)
