Elliptic curve isogeny class 89.4-b over number field \(\Q(\zeta_{15})^+\)

• Base field: \(\Q(\zeta_{15})^+\)
• Label: 4.4.1125.1-89.4-b
• Conductor: 89.4
• 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 89.4-b over \(\Q(\zeta_{15})^+\)

Isogeny class 89.4-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
89.4-b1	\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a\) , \( -32 a^{3} + 49 a^{2} + 129 a - 191\) , \( 232 a^{3} - 278 a^{2} - 873 a + 1119\bigr] \)
89.4-b2	\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a\) , \( 3 a^{3} + 4 a^{2} - 6 a - 6\) , \( 4 a^{3} + 3 a^{2} - 10 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph