Elliptic curve isogeny class 4.1-a over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-4.1-a
• Conductor: 4.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4.1-a over \(\Q(\sqrt{29}) \)

Isogeny class 4.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
4.1-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 31\) , \( -23 a + 75\bigr] \)
4.1-a2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -64 a + 209\) , \( 1147 a - 3660\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph