Elliptic curve isogeny class 41.3-a over number field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-41.3-a
• Conductor: 41.3
• 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 41.3-a over \(\Q(\zeta_{7})^+\)

Isogeny class 41.3-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
41.3-a1	\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -91 a^{2} + 101 a - 68\) , \( -646 a^{2} + 852 a - 304\bigr] \)
41.3-a2	\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -71 a^{2} + 146 a - 43\) , \( -456 a^{2} + 1027 a - 381\bigr] \)
41.3-a3	\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( 4 a^{2} - 4 a - 8\) , \( -11 a^{2} + 7 a + 26\bigr] \)
41.3-a4	\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -a^{2} + a + 2\) , \( 0\bigr] \)

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