Elliptic curve isogeny class 26.1-c over number field \(\Q(\sqrt{26}) \)

• Base field: \(\Q(\sqrt{26}) \)
• Label: 2.2.104.1-26.1-c
• Conductor: 26.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 26.1-c over \(\Q(\sqrt{26}) \)

Isogeny class 26.1-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
26.1-c1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -1824\) , \( -34304\bigr] \)
26.1-c2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -4\) , \( -88\bigr] \)
26.1-c3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 16\) , \( 16\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph