Elliptic curve isogeny class 10.1-c over number field \(\Q(\sqrt{26}) \)

• Base field: \(\Q(\sqrt{26}) \)
• Label: 2.2.104.1-10.1-c
• Conductor: 10.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.1-c over \(\Q(\sqrt{26}) \)

Isogeny class 10.1-c contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
10.1-c1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 8 a + 28\) , \( 12 a + 48\bigr] \)
10.1-c2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 793 a - 3982\) , \( 26907 a - 137142\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph