Elliptic curve isogeny class 35.2-a over number field 4.4.4205.1

• Base field: 4.4.4205.1
• Label: 4.4.4205.1-35.2-a
• Conductor: 35.2
• 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 35.2-a over 4.4.4205.1

Isogeny class 35.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
35.2-a1	\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( 2 a^{3} - 2 a^{2} - 11 a - 4\) , \( 3 a^{3} - 2 a^{2} - 16 a - 9\bigr] \)
35.2-a2	\( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{3} - a^{2} - 5 a\) , \( 45 a^{3} - 68 a^{2} - 180 a + 32\) , \( 92 a^{3} - 130 a^{2} - 383 a + 27\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph