Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-128.6-c
Conductor 128.6
Rank \( 0 \)

Related objects

Learn more about

Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 128.6-c over \(\Q(\sqrt{17}) \)

Isogeny class 128.6-c contains 12 curves linked by isogenies of degrees dividing 24.

Curve label Weierstrass Coefficients
128.6-c1 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -24 a - 17\) , \( 98 a + 31\bigr] \)
128.6-c2 \( \bigl[a\) , \( 0\) , \( 0\) , \( -20 a + 52\) , \( 0\bigr] \)
128.6-c3 \( \bigl[a\) , \( 0\) , \( 0\) , \( 285 a - 728\) , \( 4041 a - 10348\bigr] \)
128.6-c4 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( a + 3\) , \( -a + 3\bigr] \)
128.6-c5 \( \bigl[a\) , \( 0\) , \( 0\) , \( -146 a - 228\) , \( 0\bigr] \)
128.6-c6 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 298 a - 1433\) , \( 6138 a - 22281\bigr] \)
128.6-c7 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -22 a - 153\) , \( 314 a - 9\bigr] \)
128.6-c8 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -7 a - 13\) , \( -39 a - 61\bigr] \)
128.6-c9 \( \bigl[a\) , \( 0\) , \( 0\) , \( -1656 a - 2588\) , \( 51666 a + 80680\bigr] \)
128.6-c10 \( \bigl[a\) , \( -a\) , \( a\) , \( 789 a - 2032\) , \( 16959 a - 43432\bigr] \)
128.6-c11 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -147 a - 253\) , \( -1763 a - 2797\bigr] \)
128.6-c12 \( \bigl[a\) , \( -a\) , \( a\) , \( 2429 a - 6352\) , \( -73585 a + 189080\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 24 & 8 & 3 & 6 & 8 & 4 & 12 & 12 & 2 & 24 & 4 \\ 24 & 1 & 3 & 8 & 4 & 12 & 6 & 2 & 8 & 12 & 4 & 24 \\ 8 & 3 & 1 & 24 & 12 & 4 & 2 & 6 & 24 & 4 & 12 & 8 \\ 3 & 8 & 24 & 1 & 2 & 24 & 12 & 4 & 4 & 6 & 8 & 12 \\ 6 & 4 & 12 & 2 & 1 & 12 & 6 & 2 & 2 & 3 & 4 & 6 \\ 8 & 12 & 4 & 24 & 12 & 1 & 2 & 6 & 24 & 4 & 3 & 8 \\ 4 & 6 & 2 & 12 & 6 & 2 & 1 & 3 & 12 & 2 & 6 & 4 \\ 12 & 2 & 6 & 4 & 2 & 6 & 3 & 1 & 4 & 6 & 2 & 12 \\ 12 & 8 & 24 & 4 & 2 & 24 & 12 & 4 & 1 & 6 & 8 & 3 \\ 2 & 12 & 4 & 6 & 3 & 4 & 2 & 6 & 6 & 1 & 12 & 2 \\ 24 & 4 & 12 & 8 & 4 & 3 & 6 & 2 & 8 & 12 & 1 & 24 \\ 4 & 24 & 8 & 12 & 6 & 8 & 4 & 12 & 3 & 2 & 24 & 1 \end{array}\right)\)

Isogeny graph