Elliptic curve isogeny class 197.1-d over number field \(\Q(\zeta_{11})^+\)

• Base field: \(\Q(\zeta_{11})^+\)
• Label: 5.5.14641.1-197.1-d
• Conductor: 197.1
• 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 197.1-d over \(\Q(\zeta_{11})^+\)

Isogeny class 197.1-d contains only one elliptic curve.

Curve label	Weierstrass Coefficients
197.1-d1	\( \bigl[a^{4} + a^{3} - 4 a^{2} - 3 a + 3\) , \( a^{2} - a - 1\) , \( a^{4} + a^{3} - 3 a^{2} - 3 a\) , \( a^{3} - 4 a - 2\) , \( 2 a^{4} - a^{3} - 8 a^{2} + a + 5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph