Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-97.3-a
Conductor 97.3
Rank not recorded

Related objects

Learn more about

Base field \(\Q(\zeta_{7})^+\)

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 2 x + 1 \); class number \(1\).

Elliptic curves in class 97.3-a over \(\Q(\zeta_{7})^+\)

Isogeny class 97.3-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
97.3-a1 \( \bigl[a\) , \( a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 621 a^{2} - 339 a - 1371\) , \( 8726 a^{2} - 4834 a - 19574\bigr] \)
97.3-a2 \( \bigl[a\) , \( a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 36 a^{2} - 19 a - 86\) , \( 131 a^{2} - 78 a - 297\bigr] \)
97.3-a3 \( \bigl[a\) , \( a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 11 a^{2} - 19 a - 81\) , \( 12 a^{2} - 118 a - 256\bigr] \)
97.3-a4 \( \bigl[a\) , \( a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( a^{2} + a - 6\) , \( 2 a^{2} - 4 a - 3\bigr] \)
97.3-a5 \( \bigl[a\) , \( a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( -34 a^{2} + 21 a - 6\) , \( 101 a^{2} - 106 a + 19\bigr] \)
97.3-a6 \( \bigl[a\) , \( a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( a^{2} + a - 1\) , \( 0\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph