Elliptic curve isogeny class 35.1-a over number field 4.4.4205.1

• Base field: 4.4.4205.1
• Label: 4.4.4205.1-35.1-a
• Conductor: 35.1
• Rank: \( 0 \)

Base field 4.4.4205.1

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

Elliptic curves in class 35.1-a over 4.4.4205.1

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

Curve label	Weierstrass Coefficients
35.1-a1	\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( a^{3} - a^{2} - 4 a\) , \( -3 a - 2\) , \( -a^{3} + 2 a\bigr] \)
35.1-a2	\( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{2} + 2 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -31 a^{3} + 56 a^{2} + 110 a - 55\) , \( -129 a^{3} + 209 a^{2} + 514 a - 193\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph