Elliptic curve isogeny class 11.1-a over number field 6.6.1241125.1

• Base field: 6.6.1241125.1
• Label: 6.6.1241125.1-11.1-a
• Conductor: 11.1
• Rank: \( 1 \)

Base field 6.6.1241125.1

Generator \(a\), with minimal polynomial \( x^{6} - 7 x^{4} - 2 x^{3} + 11 x^{2} + 7 x + 1 \); class number \(1\).

Elliptic curves in class 11.1-a over 6.6.1241125.1

Isogeny class 11.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
11.1-a1	\( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 3 a^{2} - 41 a - 15\) , \( 3 a^{5} - a^{4} - 20 a^{3} + 29 a + 13\) , \( 0\) , \( 36 a^{5} - 8 a^{4} - 244 a^{3} - 19 a^{2} + 377 a + 180\) , \( 111 a^{5} - 30 a^{4} - 755 a^{3} - 8 a^{2} + 1174 a + 439\bigr] \)
11.1-a2	\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 23 a - 10\) , \( a^{3} + a^{2} - 3 a - 4\) , \( -2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 9\) , \( -4 a^{5} + 2 a^{4} + 28 a^{3} - 2 a^{2} - 45 a - 17\) , \( -2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph