Elliptic curve isogeny class 35.1-a over number field 4.4.8789.1

• Base field: 4.4.8789.1
• Label: 4.4.8789.1-35.1-a
• Conductor: 35.1
• Rank: \( 1 \)

Base field 4.4.8789.1

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

Elliptic curves in class 35.1-a over 4.4.8789.1

Isogeny class 35.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
35.1-a1	\( \bigl[2 a^{3} - 3 a^{2} - 9 a - 1\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 5 a - 2\) , \( -82 a^{3} + 133 a^{2} + 401 a - 81\) , \( -546 a^{3} + 940 a^{2} + 2601 a - 797\bigr] \)
35.1-a2	\( \bigl[2 a^{3} - 3 a^{2} - 9 a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( 2 a^{3} - 3 a^{2} - 10 a - 1\) , \( 21 a^{3} - 51 a^{2} - 47 a + 12\) , \( -69 a^{3} + 189 a^{2} + 92 a - 42\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph