Elliptic curve isogeny class 89.3-a over number field \(\Q(\zeta_{15})^+\)

• Base field: \(\Q(\zeta_{15})^+\)
• Label: 4.4.1125.1-89.3-a
• Conductor: 89.3
• 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 89.3-a over \(\Q(\zeta_{15})^+\)

Isogeny class 89.3-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
89.3-a1	\( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a^{3} - 2 a + 1\) , \( -a + 2\) , \( -a^{3} - a^{2} + 3 a\bigr] \)
89.3-a2	\( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a^{3} - 2 a + 1\) , \( -30 a^{3} - 25 a^{2} + 74 a + 12\) , \( -169 a^{3} - 140 a^{2} + 421 a + 89\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph