Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-128.5-c
Conductor 128.5
Rank \( 0 \)

Related objects

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

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

Elliptic curves in class 128.5-c over \(\Q(\sqrt{17}) \)

Isogeny class 128.5-c contains 12 curves linked by isogenies of degrees dividing 24.

Curve label Weierstrass Coefficients
128.5-c1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -285 a - 443\) , \( -4041 a - 6307\bigr] \)
128.5-c2 \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -a + 4\) , \( a + 2\bigr] \)
128.5-c3 \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 24 a - 41\) , \( -98 a + 129\bigr] \)
128.5-c4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 20 a + 32\) , \( 0\bigr] \)
128.5-c5 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 9 a - 24\) , \( 15 a - 41\bigr] \)
128.5-c6 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2431 a - 3923\) , \( 73584 a + 115495\bigr] \)
128.5-c7 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -791 a - 1243\) , \( -16960 a - 26473\bigr] \)
128.5-c8 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 146 a - 374\) , \( 0\bigr] \)
128.5-c9 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 149 a - 404\) , \( 1359 a - 3561\bigr] \)
128.5-c10 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 24 a - 179\) , \( -493 a + 579\bigr] \)
128.5-c11 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 1656 a - 4244\) , \( -51666 a + 132346\bigr] \)
128.5-c12 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -296 a - 1139\) , \( -7277 a - 16189\bigr] \)

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