Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-64.1-a
Conductor 64.1
Rank not recorded

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Base field \(\Q(\zeta_{7})^+\)

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 2 x + 1 \); class number \(1\).

Elliptic curves in class 64.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 64.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
64.1-a1 \( \bigl[0\) , \( -a\) , \( 0\) , \( 1742 a^{2} - 971 a - 3929\) , \( 42399 a^{2} - 23535 a - 95292\bigr] \)
64.1-a2 \( \bigl[0\) , \( -a\) , \( 0\) , \( 72 a^{2} + 4 a - 264\) , \( 500 a^{2} - 16 a - 1624\bigr] \)
64.1-a3 \( \bigl[0\) , \( -a\) , \( 0\) , \( 102 a^{2} - 61 a - 244\) , \( 640 a^{2} - 360 a - 1460\bigr] \)
64.1-a4 \( \bigl[0\) , \( -a\) , \( 0\) , \( 17 a^{2} - 131 a - 199\) , \( -6 a^{2} - 855 a - 1073\bigr] \)
64.1-a5 \( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a^{2} - 11 a - 49\) , \( 55 a^{2} - 31 a - 124\bigr] \)
64.1-a6 \( \bigl[0\) , \( -a\) , \( 0\) , \( 17 a^{2} - 11 a - 39\) , \( -46 a^{2} + 25 a + 103\bigr] \)
64.1-a7 \( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a^{2} - a - 4\) , \( 0\bigr] \)
64.1-a8 \( \bigl[0\) , \( -a\) , \( 0\) , \( -8 a^{2} + 4 a + 16\) , \( 4 a^{2} - 8\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph