Properties

Base field \(\Q(\zeta_{9})^+\)
Label 3.3.81.1-17.1-a
Conductor 17.1
Rank not recorded

Related objects

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Base field \(\Q(\zeta_{9})^+\)

Generator \(a\), with minimal polynomial \( x^{3} - 3 x - 1 \); class number \(1\).

Elliptic curves in class 17.1-a over \(\Q(\zeta_{9})^+\)

Isogeny class 17.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
17.1-a1 \( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( 0\) , \( 99 a^{2} - 64 a - 331\) , \( 958 a^{2} - 218 a - 2583\bigr] \)
17.1-a2 \( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( 0\) , \( -11 a^{2} - 24 a - 21\) , \( -38 a^{2} - 104 a - 85\bigr] \)
17.1-a3 \( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( 0\) , \( 4 a^{2} - 4 a - 16\) , \( 20 a^{2} - 7 a - 58\bigr] \)
17.1-a4 \( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( 0\) , \( -a^{2} + a + 4\) , \( 0\bigr] \)
17.1-a5 \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( 1029 a^{2} - 331 a - 3016\) , \( 20866 a^{2} - 7345 a - 59899\bigr] \)
17.1-a6 \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( 79 a^{2} - 26 a - 231\) , \( 122 a^{2} - 44 a - 351\bigr] \)
17.1-a7 \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( 44 a^{2} - 16 a - 126\) , \( -207 a^{2} + 71 a + 595\bigr] \)
17.1-a8 \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( -311 a^{2} + 119 a + 874\) , \( 1414 a^{2} - 463 a - 4127\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph