Elliptic curve isogeny class 32.1-e over number field 4.4.7168.1

• Base field: 4.4.7168.1
• Label: 4.4.7168.1-32.1-e
• Conductor: 32.1
• Rank: \( 1 \)

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-e over 4.4.7168.1

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

Curve label	Weierstrass Coefficients
32.1-e1	\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - 3 a\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + a^{2} - 5 a - 5\) , \( 16 a^{3} + 33 a^{2} - 26 a - 53\bigr] \)
32.1-e2	\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} - 2 a^{2} + a + 2\) , \( -13 a^{3} - 17 a^{2} + 57 a + 74\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph