Elliptic curve isogeny class 109.4-a over number field 4.4.725.1

• Base field: 4.4.725.1
• Label: 4.4.725.1-109.4-a
• Conductor: 109.4
• Rank: \( 0 \)

Base field 4.4.725.1

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

Elliptic curves in class 109.4-a over 4.4.725.1

Isogeny class 109.4-a contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
109.4-a1	\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 2 a^{2} - 2\) , \( a^{3} - 2 a\) , \( -3 a^{3} + 4 a^{2} + a - 2\) , \( -2 a^{3} + 3 a^{2} - 1\bigr] \)
109.4-a2	\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 2 a^{2} - 2\) , \( a^{3} - 2 a\) , \( 282 a^{3} - 751 a^{2} + 156 a + 163\) , \( 6409 a^{3} - 15579 a^{2} + 1719 a + 4611\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph