Elliptic curve isogeny class 9.1-a over number field 5.5.70601.1

• Base field: 5.5.70601.1
• Label: 5.5.70601.1-9.1-a
• Conductor: 9.1
• Rank: \( 0 \)

Base field 5.5.70601.1

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

Elliptic curves in class 9.1-a over 5.5.70601.1

Isogeny class 9.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
9.1-a1	\( \bigl[a^{4} - 6 a^{2} - 2 a + 3\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( 5 a^{4} - 26 a^{2} - 18 a + 6\) , \( 19 a^{4} - 4 a^{3} - 97 a^{2} - 41 a + 21\bigr] \)
9.1-a2	\( \bigl[2 a^{4} - a^{3} - 11 a^{2} + a + 6\) , \( 2 a^{4} - a^{3} - 11 a^{2} + a + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 2\) , \( 8 a^{4} - 10 a^{3} - 41 a^{2} + 30 a + 29\) , \( 3787 a^{4} - 715 a^{3} - 19529 a^{2} - 8243 a + 4717\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph