Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-97.2-a
Conductor 97.2
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 97.2-a over \(\Q(\zeta_{7})^+\)

Isogeny class 97.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
97.2-a1 \( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{2} + a - 1\) , \( 20 a^{2} + 15 a - 95\) , \( -71 a^{2} - 50 a + 307\bigr] \)
97.2-a2 \( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{2} + a - 1\) , \( -20 a^{2} + 10 a - 40\) , \( -128 a^{2} + 26 a - 94\bigr] \)
97.2-a3 \( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{2} + a - 1\) , \( -5\) , \( -4 a^{2} - 3 a + 5\bigr] \)
97.2-a4 \( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{2} + a - 1\) , \( 0\) , \( 0\bigr] \)
97.2-a5 \( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{2} + a - 1\) , \( -20 a^{2} - 15 a + 5\) , \( -113 a^{2} - 88 a + 63\bigr] \)
97.2-a6 \( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{2} + a - 1\) , \( -340 a^{2} - 280 a + 210\) , \( -5454 a^{2} - 4362 a + 3052\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph