Elliptic curve isogeny class 131.1-a over number field \(\Q(\zeta_{11})^+\)

• Base field: \(\Q(\zeta_{11})^+\)
• Label: 5.5.14641.1-131.1-a
• Conductor: 131.1
• Rank: \( 1 \)

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 131.1-a over \(\Q(\zeta_{11})^+\)

Isogeny class 131.1-a contains only one elliptic curve.

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph