Elliptic curve isogeny class 1.1-a over number field \(\Q(\sqrt{26}) \)

• Base field: \(\Q(\sqrt{26}) \)
• Label: 2.2.104.1-1.1-a
• Conductor: 1.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{26}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 26 \); class number \(2\).

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 1.1-a over \(\Q(\sqrt{26}) \)

Isogeny class 1.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
1.1-a1	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 595 a - 3050\) , \( 20142 a - 102714\bigr] \)
1.1-a2	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -5 a + 10\) , \( -3 a + 6\bigr] \)