Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-89.2-a
Conductor 89.2
Rank \( 0 \)

Related objects

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

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

Curve label Weierstrass Coefficients
89.2-a1 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a\) , \( -21 a^{3} + 24 a^{2} + 78 a - 102\) , \( -115 a^{3} + 139 a^{2} + 431 a - 554\bigr] \)
89.2-a2 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( -1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph