Elliptic curve isogeny class 16.1-e over number field \(\Q(\sqrt{26}) \)

• Base field: \(\Q(\sqrt{26}) \)
• Label: 2.2.104.1-16.1-e
• Conductor: 16.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 16.1-e over \(\Q(\sqrt{26}) \)

Isogeny class 16.1-e contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
16.1-e1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2396 a - 12214\) , \( -139366 a + 710632\bigr] \)
16.1-e2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 26\) , \( -46 a + 232\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph