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Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-128.6-b
Conductor 128.6
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 128.6-b over \(\Q(\sqrt{17}) \)

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

Curve label Weierstrass Coefficients
128.6-b1 \( \bigl[a\) , \( 1\) , \( 0\) , \( -274 a + 703\) , \( -18518 a + 47435\bigr] \)
128.6-b2 \( \bigl[a\) , \( 1\) , \( 0\) , \( -2 a - 1\) , \( -14 a - 21\bigr] \)
128.6-b3 \( \bigl[a\) , \( 1\) , \( 0\) , \( 23 a + 19\) , \( 329 a + 535\bigr] \)
128.6-b4 \( \bigl[a\) , \( -1\) , \( 0\) , \( 89 a + 139\) , \( 57 a + 89\bigr] \)
128.6-b5 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -9\) , \( -a - 7\bigr] \)
128.6-b6 \( \bigl[a\) , \( a\) , \( 0\) , \( -10853 a - 16976\) , \( -715483 a - 1117196\bigr] \)
128.6-b7 \( \bigl[a\) , \( -1\) , \( 0\) , \( 1898 a - 4865\) , \( -64912 a + 166277\bigr] \)
128.6-b8 \( \bigl[a\) , \( -1\) , \( 0\) , \( 33 a - 85\) , \( -13 a + 33\bigr] \)
128.6-b9 \( \bigl[a\) , \( a - 1\) , \( a\) , \( 10 a - 129\) , \( 211 a - 247\bigr] \)
128.6-b10 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -115 a - 229\) , \( 945 a + 1633\bigr] \)
128.6-b11 \( \bigl[a\) , \( -1\) , \( 0\) , \( 373 a - 965\) , \( -5721 a + 14641\bigr] \)
128.6-b12 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -1995 a - 3269\) , \( 69553 a + 108129\bigr] \)

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