Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-91.2-a
Conductor 91.2
Rank \( 0 \)

Related objects

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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 91.2-a over \(\Q(\zeta_{7})^+\)

Isogeny class 91.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
91.2-a1 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1620 a^{2} - 590 a - 4164\) , \( 41147 a^{2} - 19378 a - 98898\bigr] \)
91.2-a2 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -2800 a^{2} + 6210 a - 2454\) , \( -131435 a^{2} + 294782 a - 106770\bigr] \)
91.2-a3 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -70 a^{2} + 330 a - 389\) , \( -1452 a^{2} + 4324 a - 3100\bigr] \)
91.2-a4 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 5 a^{2} - 20 a - 64\) , \( -20 a^{2} + 109 a + 227\bigr] \)
91.2-a5 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -5 a^{2} + 20 a - 24\) , \( -26 a^{2} + 75 a - 43\bigr] \)
91.2-a6 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -4\) , \( -a^{2} + 4 a + 4\bigr] \)
91.2-a7 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
91.2-a8 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -20 a^{2} + 30 a + 21\) , \( 20 a^{2} + 70 a - 174\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 16 & 4 & 8 & 16 & 8 \\ 4 & 1 & 2 & 16 & 4 & 8 & 16 & 8 \\ 2 & 2 & 1 & 8 & 2 & 4 & 8 & 4 \\ 16 & 16 & 8 & 1 & 4 & 2 & 4 & 8 \\ 4 & 4 & 2 & 4 & 1 & 2 & 4 & 2 \\ 8 & 8 & 4 & 2 & 2 & 1 & 2 & 4 \\ 16 & 16 & 8 & 4 & 4 & 2 & 1 & 8 \\ 8 & 8 & 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph