Elliptic curve isogeny class 676.2-k over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-676.2-k
• Conductor: 676.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 676.2-k over \(\Q(\sqrt{29}) \)

Isogeny class 676.2-k contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
676.2-k1	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -33 a - 75\) , \( -233 a - 514\bigr] \)
676.2-k2	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 207 a + 480\) , \( 7342 a + 16211\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph