Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-392.1-a
Conductor 392.1
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 392.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 392.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
392.1-a1 \( \bigl[a^{2} - 2\) , \( -1\) , \( a^{2} + a - 2\) , \( -10922 a^{2} + 13652 a - 5462\) , \( 772040 a^{2} - 1158061 a + 386020\bigr] \)
392.1-a2 \( \bigl[a^{2} - 2\) , \( -1\) , \( a^{2} + a - 2\) , \( -682 a^{2} + 852 a - 342\) , \( 12232 a^{2} - 18349 a + 6116\bigr] \)
392.1-a3 \( \bigl[a^{2} - 2\) , \( -1\) , \( a^{2} + a - 2\) , \( -142 a^{2} + 177 a - 72\) , \( 976 a^{2} - 1465 a + 488\bigr] \)
392.1-a4 \( \bigl[a^{2} - 2\) , \( -1\) , \( a^{2} + a - 2\) , \( -42 a^{2} + 52 a - 22\) , \( -172 a^{2} + 257 a - 86\bigr] \)
392.1-a5 \( \bigl[a^{2} - 2\) , \( -1\) , \( a^{2} + a - 2\) , \( -2 a^{2} + 2 a - 2\) , \( -4 a^{2} + 5 a - 2\bigr] \)
392.1-a6 \( \bigl[a^{2} - 2\) , \( -1\) , \( a^{2} + a - 2\) , \( 18 a^{2} - 23 a + 8\) , \( 80 a^{2} - 121 a + 40\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph