Elliptic curve isogeny class 25.2-h over number field 4.4.16357.1

• Base field: 4.4.16357.1
• Label: 4.4.16357.1-25.2-h
• Conductor: 25.2
• Rank: \( 1 \)

Base field 4.4.16357.1

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

Elliptic curves in class 25.2-h over 4.4.16357.1

Isogeny class 25.2-h contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
25.2-h1	\( \bigl[a^{2} + a - 3\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} + a^{2} - 6 a - 3\) , \( 13 a^{3} + 9 a^{2} - 64 a - 34\) , \( -35 a^{3} - 2 a^{2} + 234 a + 113\bigr] \)
25.2-h2	\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 6 a + 1\) , \( a^{3} - 5 a - 1\) , \( -16 a^{3} - 3 a^{2} + 89 a + 44\) , \( -28 a^{3} + 2 a^{2} + 142 a + 68\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph