Elliptic curve isogeny class 71.2-a over number field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-71.2-a
• Conductor: 71.2
• 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 71.2-a over \(\Q(\zeta_{7})^+\)

Isogeny class 71.2-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
71.2-a1	\( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 410 a^{2} - 221 a - 960\) , \( 5309 a^{2} - 2926 a - 12013\bigr] \)
71.2-a2	\( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 5 a^{2} + 4 a - 50\) , \( 92 a^{2} - 32 a - 290\bigr] \)
71.2-a3	\( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( 15 a^{2} - 11 a - 35\) , \( -31 a^{2} + 18 a + 70\bigr] \)
71.2-a4	\( \bigl[1\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( -a\) , \( -a^{2} + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph