Elliptic curve isogeny class 8.2-c over number field \(\Q(\sqrt{129}) \)

• Base field: \(\Q(\sqrt{129}) \)
• Label: 2.2.129.1-8.2-c
• Conductor: 8.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{129}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 32 \); class number \(1\).

Elliptic curves in class 8.2-c over \(\Q(\sqrt{129}) \)

Isogeny class 8.2-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
8.2-c1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -869257 a - 4501774\) , \( 1049040547 a + 5432884883\bigr] \)
8.2-c2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -10102 a - 52289\) , \( 1593581 a + 8253049\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph