Elliptic curve isogeny class 100.2-e over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-100.2-e
• Conductor: 100.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 100.2-e over \(\Q(\sqrt{29}) \)

Isogeny class 100.2-e contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
100.2-e1	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -8 a - 18\) , \( 17 a + 37\bigr] \)
100.2-e2	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 37 a + 102\) , \( -628 a - 1433\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph