Elliptic curve isogeny class 39.1-c over number field 4.4.4752.1

• Base field: 4.4.4752.1
• Label: 4.4.4752.1-39.1-c
• Conductor: 39.1
• Rank: \( 0 \)

Base field 4.4.4752.1

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

Elliptic curves in class 39.1-c over 4.4.4752.1

Isogeny class 39.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
39.1-c1	\( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + 1\) , \( a^{3} - 3 a\) , \( -2 a^{3} - a^{2} + 3 a + 2\) , \( -2 a^{3} - a^{2} + 4 a + 1\bigr] \)
39.1-c2	\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a - 1\) , \( a\) , \( -3 a^{3} + 7 a^{2} + 7 a - 13\) , \( -2 a^{3} + 4 a^{2} + 5 a - 9\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph