Elliptic curve isogeny class 25.1-b over number field 4.4.9909.1

• Base field: 4.4.9909.1
• Label: 4.4.9909.1-25.1-b
• Conductor: 25.1
• Rank: \( 1 \)

Base field 4.4.9909.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} - 3 x + 3 \); class number \(1\).

Elliptic curves in class 25.1-b over 4.4.9909.1

Isogeny class 25.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
25.1-b1	\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - 4 a - 1\) , \( a^{2} - a - 2\) , \( 5 a^{3} - 2 a^{2} - 20 a - 6\) , \( -a^{3} - a^{2} + 7 a + 12\bigr] \)
25.1-b2	\( \bigl[a^{3} - 4 a - 1\) , \( a - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( 2 a^{3} - a\) , \( -58 a^{3} + 114 a^{2} + 145 a - 95\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph