Elliptic curve isogeny class 8.1-d over number field 4.4.13824.1

• Base field: 4.4.13824.1
• Label: 4.4.13824.1-8.1-d
• Conductor: 8.1
• Rank: \( 1 \)

Base field 4.4.13824.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} + 6 \); class number \(1\).

Elliptic curves in class 8.1-d over 4.4.13824.1

Isogeny class 8.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
8.1-d1	\( \bigl[a^{3} - 4 a\) , \( a^{3} - 5 a + 1\) , \( a^{2} - 2\) , \( 29 a^{3} + 27 a^{2} - 138 a - 128\) , \( -218 a^{3} - 251 a^{2} + 1032 a + 1185\bigr] \)
8.1-d2	\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a\) , \( 2 a^{3} - 6 a^{2} - a + 13\) , \( -3 a^{3} + 7 a^{2} + 4 a - 8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph