Elliptic curve isogeny class 13.1-a over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-13.1-a
• Conductor: 13.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{29}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 7 \); class number \(1\).

Elliptic curves in class 13.1-a over \(\Q(\sqrt{29}) \)

Isogeny class 13.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
13.1-a1	\( \bigl[a\) , \( -1\) , \( 1\) , \( -4 a - 7\) , \( 4 a + 9\bigr] \)
13.1-a2	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -75 a - 165\) , \( -492 a - 1079\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph