Elliptic curve isogeny class 676.3-k over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-676.3-k
• Conductor: 676.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 676.3-k over \(\Q(\sqrt{29}) \)

Isogeny class 676.3-k contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
676.3-k1	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 34 a - 109\) , \( 199 a - 638\bigr] \)
676.3-k2	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -206 a + 686\) , \( -7136 a + 22867\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph