Elliptic curve isogeny class 25.1-c over number field 4.4.6809.1

• Base field: 4.4.6809.1
• Label: 4.4.6809.1-25.1-c
• Conductor: 25.1
• Rank: \( 1 \)

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-c over 4.4.6809.1

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

Curve label	Weierstrass Coefficients
25.1-c1	\( \bigl[a^{2} + a - 3\) , \( a^{3} + a^{2} - 4 a - 5\) , \( 0\) , \( 3 a^{3} - 4 a^{2} + 2 a + 3\) , \( -4 a^{3} + 13 a^{2} + 2 a - 4\bigr] \)
25.1-c2	\( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{3} + a^{2} - 5 a - 4\) , \( -17 a^{3} - 33 a^{2} + 9 a + 9\) , \( -95 a^{3} - 218 a^{2} - 24 a + 42\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph