Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-91.1-a
Conductor 91.1
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 91.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 91.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
91.1-a1 \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -1030 a^{2} + 1620 a - 484\) , \( -21769 a^{2} + 41147 a - 14213\bigr] \)
91.1-a2 \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( 15 a^{2} + 5 a - 89\) , \( -89 a^{2} - 20 a + 385\bigr] \)
91.1-a3 \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -4\) , \( -3 a^{2} - a + 9\bigr] \)
91.1-a4 \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -15 a^{2} - 5 a + 1\) , \( -49 a^{2} - 26 a + 29\bigr] \)
91.1-a5 \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( 1\) , \( 0\bigr] \)
91.1-a6 \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -10 a^{2} - 20 a + 21\) , \( -90 a^{2} + 20 a + 26\bigr] \)
91.1-a7 \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -260 a^{2} - 70 a + 61\) , \( -2872 a^{2} - 1452 a + 1192\bigr] \)
91.1-a8 \( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -3410 a^{2} - 2800 a + 1566\) , \( -163347 a^{2} - 131435 a + 88489\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph