Elliptic curve isogeny class 89.1-a over number field \(\Q(\zeta_{15})^+\)

• Base field: \(\Q(\zeta_{15})^+\)
• Label: 4.4.1125.1-89.1-a
• Conductor: 89.1
• Rank: \( 0 \)

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 89.1-a over \(\Q(\zeta_{15})^+\)

Isogeny class 89.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
89.1-a1	\( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 2 a + 1\) , \( a^{2} + a - 1\) , \( 3 a^{3} - 15 a^{2} + 12 a - 3\) , \( 33 a^{3} - 101 a^{2} + 63 a + 7\bigr] \)
89.1-a2	\( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 2 a + 1\) , \( a^{2} + a - 1\) , \( -2 a^{3} + 2 a + 2\) , \( -a^{3} + a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph