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

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

Isogeny class 104.2-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
104.2-b1	\( \bigl[a^{2} - 2\) , \( a^{2} - 1\) , \( a^{2} + a - 2\) , \( 571 a^{2} - 1130 a - 2302\) , \( 11352 a^{2} - 22648 a - 45902\bigr] \)
104.2-b2	\( \bigl[a^{2} - 2\) , \( a^{2} - 1\) , \( a^{2} + a - 2\) , \( a^{2} - 2\) , \( -4 a^{2} + 2 a + 8\bigr] \)
104.2-b3	\( \bigl[a^{2} - 2\) , \( a^{2} - 1\) , \( a^{2} + a - 2\) , \( -9 a^{2} - 5 a + 8\) , \( 78 a^{2} - 74 a - 214\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph