Elliptic curve isogeny class 121.1-c over number field \(\Q(\zeta_{11})^+\)

• Base field: \(\Q(\zeta_{11})^+\)
• Label: 5.5.14641.1-121.1-c
• Conductor: 121.1
• Rank: \( 0 \)

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 121.1-c over \(\Q(\zeta_{11})^+\)

Isogeny class 121.1-c contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
121.1-c1	\( \bigl[0\) , \( a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -7820 a^{2} - 31282 a - 31281\) , \( -a^{4} + 263579 a^{3} + 1589301 a^{2} + 3194239 a + 2139918\bigr] \)
121.1-c2	\( \bigl[0\) , \( a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -10 a^{2} - 42 a - 41\) , \( -a^{4} + 19 a^{3} + 131 a^{2} + 279 a + 198\bigr] \)
121.1-c3	\( \bigl[0\) , \( a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -2 a - 1\) , \( -a^{4} - a^{3} + a^{2} - a - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph