Elliptic curve isogeny class 7.1-a over number field 6.6.1387029.1

• Base field: 6.6.1387029.1
• Label: 6.6.1387029.1-7.1-a
• Conductor: 7.1
• Rank: \( 0 \)

Base field 6.6.1387029.1

Generator \(a\), with minimal polynomial \( x^{6} - 3 x^{5} - 2 x^{4} + 9 x^{3} - x^{2} - 4 x + 1 \); class number \(1\).

Elliptic curves in class 7.1-a over 6.6.1387029.1

Isogeny class 7.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
7.1-a1	\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( a + 1\) , \( -a^{5} + 7 a^{4} - 4 a^{3} - 10 a^{2} + 4 a\) , \( 2 a^{5} + 3 a^{4} - 13 a^{3} - a^{2} + 7 a - 2\bigr] \)
7.1-a2	\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( a + 1\) , \( -6 a^{5} + 27 a^{4} - 4 a^{3} - 85 a^{2} + 79 a - 15\) , \( -33 a^{5} + 130 a^{4} - 26 a^{3} - 309 a^{2} + 258 a - 48\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph