Elliptic curve isogeny class 8.1-b over number field 4.4.13824.1

• Base field: 4.4.13824.1
• Label: 4.4.13824.1-8.1-b
• Conductor: 8.1
• Rank: \( 0 \)

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-b over 4.4.13824.1

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

Curve label	Weierstrass Coefficients
8.1-b1	\( \bigl[a^{3} - 4 a\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -27 a^{3} + 29 a^{2} + 126 a - 139\) , \( -246 a^{3} + 278 a^{2} + 1163 a - 1318\bigr] \)
8.1-b2	\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{3} - 3 a\) , \( -7 a^{3} - 9 a^{2} + 22 a + 21\) , \( -12 a^{3} - 22 a^{2} + 28 a + 38\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph