Elliptic curve isogeny class 56.1-a over number field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-56.1-a
• Conductor: 56.1
• 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 56.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 56.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
56.1-a1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)
56.1-a2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \)
56.1-a3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \)
56.1-a4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \)
56.1-a5	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)
56.1-a6	\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph