Elliptic curve isogeny class 25.1-a over number field 4.4.725.1

• Base field: 4.4.725.1
• Label: 4.4.725.1-25.1-a
• Conductor: 25.1
• Rank: \( 0 \)

Base field 4.4.725.1

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

Elliptic curves in class 25.1-a over 4.4.725.1

Isogeny class 25.1-a contains 2 curves linked by isogenies of degree 13.

Curve label	Weierstrass Coefficients
25.1-a1	\( \bigl[0\) , \( -a + 1\) , \( a^{2} - a - 1\) , \( -6039 a^{3} + 8759 a^{2} + 13737 a - 12538\) , \( -299268 a^{3} + 440180 a^{2} + 685551 a - 625284\bigr] \)
25.1-a2	\( \bigl[0\) , \( -a + 1\) , \( a^{2} - a - 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 4 a^{3} - 6 a^{2} - 9 a + 8\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph