Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-97.1-a
Conductor 97.1
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 97.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 97.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
97.1-a1 \( \bigl[a^{2} - 2\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( -279 a^{2} + 620 a - 191\) , \( -3742 a^{2} + 8446 a - 3024\bigr] \)
97.1-a2 \( \bigl[a^{2} - 2\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( 11 a^{2} + 10 a - 91\) , \( 36 a^{2} + 22 a - 296\bigr] \)
97.1-a3 \( \bigl[a^{2} - 2\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( 16 a^{2} - 35 a - 71\) , \( -85 a^{2} + 116 a + 270\bigr] \)
97.1-a4 \( \bigl[a^{2} - 2\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( -14 a^{2} + 35 a - 21\) , \( -53 a^{2} + 116 a - 40\bigr] \)
97.1-a5 \( \bigl[a^{2} - 2\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( a^{2} - 6\) , \( -3 a^{2} + 2 a + 5\bigr] \)
97.1-a6 \( \bigl[a^{2} - 2\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( a^{2} - 1\) , \( 0\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph