Elliptic curve isogeny class 256.1-n over number field 4.4.2624.1

• Base field: 4.4.2624.1
• Label: 4.4.2624.1-256.1-n
• Conductor: 256.1
• Rank: \( 0 \)

Base field 4.4.2624.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 3 x^{2} + 2 x + 1 \); class number \(1\).

Elliptic curves in class 256.1-n over 4.4.2624.1

Isogeny class 256.1-n contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
256.1-n1	\( \bigl[0\) , \( a\) , \( 0\) , \( -19 a^{2} - 22 a - 21\) , \( 13 a^{3} + 94 a^{2} + 39 a + 28\bigr] \)
256.1-n2	\( \bigl[0\) , \( a\) , \( 0\) , \( a^{2} - 2 a - 1\) , \( a^{3} - 2 a^{2} - a\bigr] \)
256.1-n3	\( \bigl[0\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 0\) , \( -60 a^{3} + 139 a^{2} + 142 a - 198\) , \( 318 a^{3} - 756 a^{2} - 701 a + 998\bigr] \)
256.1-n4	\( \bigl[0\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( 0\) , \( -a^{2} + 2 a + 2\) , \( 2 a^{3} - 4 a^{2} - 5 a + 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph