Elliptic curve isogeny class 1.1-a over number field 6.6.300125.1

• Base field: 6.6.300125.1
• Label: 6.6.300125.1-1.1-a
• Conductor: 1.1
• Rank: \( 0 \)

Base field 6.6.300125.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 7 x^{4} + 2 x^{3} + 7 x^{2} - 2 x - 1 \); class number \(1\).

Elliptic curves in class 1.1-a over 6.6.300125.1

Isogeny class 1.1-a contains 2 curves linked by isogenies of degree 37.

Curve label	Weierstrass Coefficients
1.1-a1	\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 9 a - 2\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} + 3 a^{2} - 12 a\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( 321037 a^{5} - 77286 a^{4} - 2300766 a^{3} - 1111743 a^{2} + 1379267 a + 398326\) , \( 54665451 a^{5} - 12782935 a^{4} - 392075036 a^{3} - 191607310 a^{2} + 234159226 a + 69935775\bigr] \)
1.1-a2	\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 9 a - 2\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} + 3 a^{2} - 12 a\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( 7 a^{5} - a^{4} - 51 a^{3} - 28 a^{2} + 27 a + 11\) , \( -13 a^{5} + 4 a^{4} + 92 a^{3} + 40 a^{2} - 56 a - 16\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph