Elliptic curve isogeny class 25.1-b over number field 4.4.6809.1

• Base field: 4.4.6809.1
• Label: 4.4.6809.1-25.1-b
• Conductor: 25.1
• Rank: \( 0 \)

Base field 4.4.6809.1

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

Elliptic curves in class 25.1-b over 4.4.6809.1

Isogeny class 25.1-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
25.1-b1	\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a\) , \( a^{3} - a^{2} - 5 a + 3\) , \( -a^{3} + 5 a\bigr] \)
25.1-b2	\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a\) , \( 31 a^{3} - 56 a^{2} - 35 a + 8\) , \( 496 a^{3} - 403 a^{2} - 1426 a - 597\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph