Elliptic curves in class 8.1-a over 3.3.148.1
Isogeny class 8.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 8.1-a1
| \( \bigl[a^{2} - 1\) , \( -1\) , \( a^{2} - a - 2\) , \( 1727261180779898112178031 a^{2} + 2021044966504285468600887 a - 795941171665179475905777\) , \( 279884457042981407569057081184688558284 a^{2} + 327489021002657174715208924802606509852 a - 128973872132688546804017272390232511682\bigr] \)
|
| 8.1-a2
| \( \bigl[a^{2} - 1\) , \( -a^{2} + a + 1\) , \( 0\) , \( -122876240093597390564 a^{2} - 143775828060934351842 a + 56622738702290433353\) , \( 1339806177584198660985008156380 a^{2} + 1567689103089350829411708766103 a - 617397594907508652287429548778\bigr] \)
|
| 8.1-a3
| \( \bigl[a + 1\) , \( a^{2} - a - 3\) , \( a^{2} - a - 2\) , \( 4 a^{2} + 15 a - 2\) , \( -14 a^{2} + 6 a - 2\bigr] \)
|
| 8.1-a4
| \( \bigl[a + 1\) , \( a^{2} - 2 a - 1\) , \( a^{2} - a - 2\) , \( -83347907948 a^{2} - 97524260781 a + 38407643413\) , \( -13188165606368355 a^{2} - 15431294359397846 a + 6077253458627265\bigr] \)
|
| 8.1-a5
| \( \bigl[a + 1\) , \( a^{2} - 2 a - 1\) , \( a^{2} - a - 2\) , \( -1157658655878 a^{2} - 1354560749371 a + 533461990118\) , \( -1248619261868812725 a^{2} - 1460992525253670641 a + 575377649491803209\bigr] \)
|
| 8.1-a6
| \( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{2} - 1\) , \( -23137255028952366700772 a^{2} - 27072589446997404913200 a + 10661904569953464468393\) , \( 3529193720251159834920437017851122 a^{2} + 4129461880751340931496180433614334 a - 1626291736297668628974848142500566\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 8 & 4 & 8 & 4 \\
2 & 1 & 4 & 2 & 4 & 2 \\
8 & 4 & 1 & 2 & 4 & 8 \\
4 & 2 & 2 & 1 & 2 & 4 \\
8 & 4 & 4 & 2 & 1 & 8 \\
4 & 2 & 8 & 4 & 8 & 1
\end{array}\right)\)
