Elliptic curve isogeny class 32.1-f over number field 4.4.7168.1

• Base field: 4.4.7168.1
• Label: 4.4.7168.1-32.1-f
• Conductor: 32.1
• Rank: \( 0 \)

Base field 4.4.7168.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} + 7 \); class number \(1\).

Elliptic curves in class 32.1-f over 4.4.7168.1

Isogeny class 32.1-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
32.1-f1	\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - 5 a - 1\) , \( 0\) , \( a^{3} - 5 a - 1\) , \( 13 a^{3} + 16 a^{2} - 59 a - 74\bigr] \)
32.1-f2	\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -2 a^{3} - 5 a^{2} + 4 a + 11\) , \( -18 a^{3} - 38 a^{2} + 28 a + 59\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph