Elliptic curve isogeny class 25.1-d over number field 4.4.16317.1

• Base field: 4.4.16317.1
• Label: 4.4.16317.1-25.1-d
• Conductor: 25.1
• Rank: \( 1 \)

Base field 4.4.16317.1

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

Elliptic curves in class 25.1-d over 4.4.16317.1

Isogeny class 25.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
25.1-d1	\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{2} - a - 2\) , \( -10 a^{3} + 10 a^{2} + 44 a - 7\) , \( -16 a^{3} + 11 a^{2} + 86 a + 31\bigr] \)
25.1-d2	\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{2} - a - 2\) , \( -a - 2\) , \( a^{3} - a^{2} - 5 a - 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph