Properties

Base field \(\Q(\zeta_{11})^+\)
Label 5.5.14641.1-131.2-a
Conductor 131.2
Rank \( 1 \)

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Base field \(\Q(\zeta_{11})^+\)

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 4 x^{3} + 3 x^{2} + 3 x - 1 \); class number \(1\).

Elliptic curves in class 131.2-a over \(\Q(\zeta_{11})^+\)

Isogeny class 131.2-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
131.2-a1 \( \bigl[a^{4} - 3 a^{2} + 1\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( a^{3} - 2 a\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a - 3\) , \( -a^{4} - a^{3} + 3 a^{2} + 4 a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph