Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-89.3-b
Conductor 89.3
Rank \( 1 \)

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

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

Curve label Weierstrass Coefficients
89.3-b1 \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 2 a\) , \( 82 a^{3} + 31 a^{2} - 291 a - 75\) , \( -396 a^{3} - 143 a^{2} + 1404 a + 326\bigr] \)
89.3-b2 \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 2 a\) , \( 2 a^{3} + a^{2} - 6 a\) , \( 3 a^{3} + a^{2} - 9 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph