Elliptic curve isogeny class 35.1-b over number field 4.4.4205.1

• Base field: 4.4.4205.1
• Label: 4.4.4205.1-35.1-b
• Conductor: 35.1
• 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 35.1-b over 4.4.4205.1

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

Curve label	Weierstrass Coefficients
35.1-b1	\( \bigl[-a^{3} + 2 a^{2} + 3 a\) , \( 2 a^{3} - 3 a^{2} - 7 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -62 a^{3} + 103 a^{2} + 244 a - 103\) , \( 277 a^{3} - 456 a^{2} - 1090 a + 424\bigr] \)
35.1-b2	\( \bigl[-a^{3} + 2 a^{2} + 3 a\) , \( 2 a^{3} - 3 a^{2} - 7 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -2 a^{3} + 3 a^{2} + 9 a - 3\) , \( 3 a^{3} - 5 a^{2} - 12 a + 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph