Elliptic curve isogeny class 71.1-a over number field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-71.1-a
• Conductor: 71.1
• 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 71.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 71.1-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
71.1-a1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -190 a^{2} + 410 a - 171\) , \( -2384 a^{2} + 5309 a - 1936\bigr] \)
71.1-a2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -10 a^{2} + 5 a - 26\) , \( -61 a^{2} + 92 a - 76\bigr] \)
71.1-a3	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -5 a^{2} + 15 a - 11\) , \( 12 a^{2} - 31 a + 15\bigr] \)
71.1-a4	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -1\) , \( -a\bigr] \)

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