Elliptic curve isogeny class 89.2-b over number field \(\Q(\zeta_{15})^+\)

• Base field: \(\Q(\zeta_{15})^+\)
• Label: 4.4.1125.1-89.2-b
• Conductor: 89.2
• Rank: \( 1 \)

Base field \(\Q(\zeta_{15})^+\)

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 4 x^{2} + 4 x + 1 \); class number \(1\).

Elliptic curves in class 89.2-b over \(\Q(\zeta_{15})^+\)

Isogeny class 89.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
89.2-b1	\( \bigl[a^{2} + a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 2 a\) , \( a^{3} + 2 a^{2} + a + 1\) , \( 3 a^{3} + 2 a^{2} - 4 a - 1\bigr] \)
89.2-b2	\( \bigl[a^{2} + a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 2 a\) , \( 6 a^{3} - 28 a^{2} + 31 a + 1\) , \( -46 a^{3} + 136 a^{2} - 88 a - 13\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph