Elliptic curve isogeny class 50.3-p over number field \(\Q(\sqrt{26}) \)

• Base field: \(\Q(\sqrt{26}) \)
• Label: 2.2.104.1-50.3-p
• Conductor: 50.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 50.3-p over \(\Q(\sqrt{26}) \)

Isogeny class 50.3-p contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
50.3-p1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -2062 a - 10500\) , \( -119960 a - 611668\bigr] \)
50.3-p2	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 3 a + 15\) , \( -a - 9\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph