Properties

Base field \(\Q(\zeta_{9})^+\)
Label 3.3.81.1-17.2-a
Conductor 17.2
Rank not recorded

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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 17.2-a over \(\Q(\zeta_{9})^+\)

Isogeny class 17.2-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
17.2-a1 \( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -30 a^{2} + 43 a + 21\) , \( 103 a^{2} - 160 a - 66\bigr] \)
17.2-a2 \( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -455 a^{2} + 738 a + 216\) , \( 7473 a^{2} - 11274 a - 5210\bigr] \)
17.2-a3 \( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -475 a^{2} + 733 a + 296\) , \( 7691 a^{2} - 11788 a - 5014\bigr] \)
17.2-a4 \( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -7615 a^{2} + 11768 a + 4776\) , \( 514961 a^{2} - 789514 a - 335090\bigr] \)
17.2-a5 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -64 a^{2} - 35 a - 5\) , \( -218 a^{2} - 740 a - 231\bigr] \)
17.2-a6 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -4 a^{2}\) , \( -7 a^{2} - 13 a - 4\bigr] \)
17.2-a7 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( a^{2}\) , \( 0\bigr] \)
17.2-a8 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -24 a^{2} + 35 a + 5\) , \( -104 a^{2} + 142 a + 47\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph