Elliptic curve isogeny class 26.3-a over number field 4.4.9248.1

• Base field: 4.4.9248.1
• Label: 4.4.9248.1-26.3-a
• Conductor: 26.3
• Rank: \( 1 \)

Base field 4.4.9248.1

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

Elliptic curves in class 26.3-a over 4.4.9248.1

Isogeny class 26.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
26.3-a1	\( \bigl[a^{2} + a - 3\) , \( a^{3} - 5 a\) , \( 1\) , \( a^{3} - 2 a^{2} - 8 a + 8\) , \( -5 a + 3\bigr] \)
26.3-a2	\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a^{3} - 4 a + 1\) , \( 10 a^{3} + 6 a^{2} - 43 a - 21\) , \( 26 a^{3} + 19 a^{2} - 116 a - 81\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph