Elliptic curve isogeny class 4.1-a over number field 4.4.5744.1

• Base field: 4.4.5744.1
• Label: 4.4.5744.1-4.1-a
• Conductor: 4.1
• Rank: \( 0 \)

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 4.1-a over 4.4.5744.1

Isogeny class 4.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
4.1-a1	\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( -1\) , \( -a^{3} + a^{2} + 4 a\) , \( -3 a^{3} + 2 a^{2} + 13 a - 4\) , \( a^{3} - a^{2} - 4 a + 1\bigr] \)
4.1-a2	\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( -1\) , \( -a^{3} + a^{2} + 4 a\) , \( 17 a^{3} - 18 a^{2} - 87 a + 11\) , \( 5 a^{3} - 28 a^{2} - 62 a - 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph