Elliptic curve isogeny class 35.2-b over number field 4.4.4205.1

• Base field: 4.4.4205.1
• Label: 4.4.4205.1-35.2-b
• Conductor: 35.2
• Rank: \( 1 \)

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-b over 4.4.4205.1

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

Curve label	Weierstrass Coefficients
35.2-b1	\( \bigl[-a^{3} + 2 a^{2} + 3 a\) , \( a^{3} - a^{2} - 5 a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( 10 a^{3} - 9 a^{2} - 43 a - 37\) , \( 9 a^{3} + 14 a^{2} - 79 a - 98\bigr] \)
35.2-b2	\( \bigl[-a^{3} + 2 a^{2} + 3 a\) , \( a^{3} - a^{2} - 5 a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( a^{2} - 3 a - 2\) , \( -a^{3} + 2 a^{2} + 2 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph