Elliptic curve isogeny class 127.3-a over number field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-127.3-a
• Conductor: 127.3
• 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 127.3-a over \(\Q(\zeta_{7})^+\)

Isogeny class 127.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
127.3-a1	\( \bigl[a + 1\) , \( -a^{2} - a + 1\) , \( a^{2} - 1\) , \( 14 a^{2} - 4 a - 45\) , \( 49 a^{2} - 17 a - 131\bigr] \)
127.3-a2	\( \bigl[a + 1\) , \( -a^{2} - a + 1\) , \( a^{2} - 1\) , \( -11 a^{2} - 4 a - 40\) , \( 20 a^{2} - 117 a - 81\bigr] \)
127.3-a3	\( \bigl[a + 1\) , \( -a^{2} - a + 1\) , \( a^{2} - 1\) , \( -11 a^{2} + 21 a - 5\) , \( 23 a^{2} - 52 a + 18\bigr] \)
127.3-a4	\( \bigl[a + 1\) , \( -a^{2} - a + 1\) , \( a^{2} - 1\) , \( -a^{2} + a\) , \( -a\bigr] \)

Rank

Rank: \( 0 \)

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