Elliptic curve isogeny class 25.2-d over number field 4.4.16997.1

• Base field: 4.4.16997.1
• Label: 4.4.16997.1-25.2-d
• Conductor: 25.2
• Rank: \( 1 \)

Base field 4.4.16997.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} - x + 5 \); class number \(1\).

Elliptic curves in class 25.2-d over 4.4.16997.1

Isogeny class 25.2-d contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
25.2-d1	\( \bigl[a^{3} - 3 a\) , \( a - 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 146 a^{3} - 3 a^{2} - 1259 a - 1300\) , \( 2516 a^{3} - 1161 a^{2} - 24343 a - 22810\bigr] \)
25.2-d2	\( \bigl[a^{3} - 3 a\) , \( a - 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 6 a^{3} + 7 a^{2} - 24 a - 30\) , \( -9 a^{3} - 6 a^{2} + 52 a + 50\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph