Elliptic curve isogeny class 169.1-a over number field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-169.1-a
• Conductor: 169.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 169.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 169.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
169.1-a1	\( \bigl[a^{2} + a - 1\) , \( -a^{2} + 3\) , \( a\) , \( -212 a^{2} + 447 a - 153\) , \( -2640 a^{2} + 5839 a - 2074\bigr] \)
169.1-a2	\( \bigl[a^{2} + a - 1\) , \( -a^{2} + 3\) , \( a\) , \( -22 a^{2} + 22 a - 3\) , \( -77 a^{2} + 78 a - 19\bigr] \)
169.1-a3	\( \bigl[a^{2} + a - 1\) , \( -a^{2} + 3\) , \( a\) , \( -2 a^{2} + 2 a + 2\) , \( -2 a^{2} + 2 a\bigr] \)
169.1-a4	\( \bigl[a^{2} + a - 1\) , \( -a^{2} + 3\) , \( a\) , \( -152 a^{2} - 83 a + 67\) , \( -1514 a^{2} - 1079 a + 780\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph