Elliptic curve isogeny class 35.1-a over number field 4.4.5744.1

• Base field: 4.4.5744.1
• Label: 4.4.5744.1-35.1-a
• Conductor: 35.1
• Rank: \( 1 \)

Base field 4.4.5744.1

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

Elliptic curves in class 35.1-a over 4.4.5744.1

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

Curve label	Weierstrass Coefficients
35.1-a1	\( \bigl[a^{3} - 4 a - 1\) , \( a\) , \( a + 1\) , \( -a^{3} + 5 a + 3\) , \( 0\bigr] \)
35.1-a2	\( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + 2 a + 1\) , \( -a^{3} + a^{2} + 4 a\) , \( -11 a^{3} + 9 a^{2} + 45 a - 10\) , \( -19 a^{3} + 13 a^{2} + 88 a - 26\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph