Elliptic curve isogeny class 18.2-g over number field \(\Q(\sqrt{129}) \)

• Base field: \(\Q(\sqrt{129}) \)
• Label: 2.2.129.1-18.2-g
• Conductor: 18.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 18.2-g over \(\Q(\sqrt{129}) \)

Isogeny class 18.2-g contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
18.2-g1	\( \bigl[a\) , \( a\) , \( a + 1\) , \( -136824 a - 708609\) , \( -33434923 a - 173156406\bigr] \)
18.2-g2	\( \bigl[a\) , \( a\) , \( a + 1\) , \( -72960984 a - 377858259\) , \( -808792298143 a - 4188661182876\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph