Properties

Base field \(\Q(\zeta_{7})^+\)
Label 3.3.49.1-127.1-a
Conductor 127.1
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 127.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 127.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
127.1-a1 \( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( 13 a^{2} - 11 a - 78\) , \( 96 a^{2} + 20 a - 254\bigr] \)
127.1-a2 \( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( -12 a^{2} + 14 a - 8\) , \( -33 a^{2} + 49 a - 17\bigr] \)
127.1-a3 \( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( -2 a^{2} - a + 2\) , \( -1\bigr] \)
127.1-a4 \( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 2\) , \( -12 a^{2} - 11 a + 7\) , \( 28 a^{2} + 23 a - 16\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph