Elliptic curve isogeny class 25.2-a over number field 4.4.11661.1

• Base field: 4.4.11661.1
• Label: 4.4.11661.1-25.2-a
• Conductor: 25.2
• 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 25.2-a over 4.4.11661.1

Isogeny class 25.2-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
25.2-a1	\( \bigl[a^{3} - 4 a - 2\) , \( 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 5 a^{3} - 14 a^{2} + 8 a + 8\) , \( 15 a^{3} - 50 a^{2} + 29 a + 25\bigr] \)
25.2-a2	\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 2\) , \( a^{3} - 5 a - 2\) , \( 27 a^{3} - 21 a^{2} - 97 a - 88\) , \( 128 a^{3} + 45 a^{2} - 812 a - 512\bigr] \)
25.2-a3	\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 2\) , \( a^{3} - 5 a - 2\) , \( 2 a^{3} - a^{2} - 7 a - 3\) , \( 2 a^{3} - a^{2} - 8 a - 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph