Elliptic curve isogeny class 169.3-a over number field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-169.3-a
• Conductor: 169.3
• 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 169.3-a over \(\Q(\zeta_{7})^+\)

Isogeny class 169.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
169.3-a1	\( \bigl[a^{2} - 1\) , \( -a\) , \( a\) , \( -277 a^{2} + 601 a - 215\) , \( -3995 a^{2} + 9026 a - 3227\bigr] \)
169.3-a2	\( \bigl[a^{2} - 1\) , \( -a\) , \( a\) , \( 3 a^{2} + 31 a - 55\) , \( -25 a^{2} + 120 a - 145\bigr] \)
169.3-a3	\( \bigl[a^{2} - 1\) , \( -a\) , \( a\) , \( -17 a^{2} + 36 a - 15\) , \( -68 a^{2} + 153 a - 56\bigr] \)
169.3-a4	\( \bigl[a^{2} - 1\) , \( -a\) , \( a\) , \( -2 a^{2} + a\) , \( -2 a^{2} + 3 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph