Elliptic curve isogeny class 104.2-a over number field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-104.2-a
• Conductor: 104.2
• 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 104.2-a over \(\Q(\zeta_{7})^+\)

Isogeny class 104.2-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
104.2-a1	\( \bigl[a^{2} + a - 1\) , \( a^{2} - 2\) , \( a + 1\) , \( -10 a^{2} + 51 a - 69\) , \( -105 a^{2} + 256 a - 199\bigr] \)
104.2-a2	\( \bigl[a^{2} + a - 1\) , \( a^{2} - 2\) , \( a + 1\) , \( a + 1\) , \( a^{2} - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph