Elliptic curve isogeny class 25.1-a over number field 4.4.11661.1

• Base field: 4.4.11661.1
• Label: 4.4.11661.1-25.1-a
• Conductor: 25.1
• Rank: \( 0 \)

Base field 4.4.11661.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 3 \); class number \(1\).

Elliptic curves in class 25.1-a over 4.4.11661.1

Isogeny class 25.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
25.1-a1	\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 4 a - 1\) , \( -24 a^{3} + 55 a^{2} + 52 a - 172\) , \( -121 a^{3} + 380 a^{2} + 289 a - 1068\bigr] \)
25.1-a2	\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 4 a - 1\) , \( a^{3} - 3 a - 2\) , \( a^{2} - 3\bigr] \)
25.1-a3	\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( a^{3} - 4 a - 1\) , \( -4 a^{3} - 3 a^{2} + 8 a + 5\) , \( -21 a^{3} - 14 a^{2} + 48 a + 24\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph