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

• Base field: \(\Q(\sqrt{129}) \)
• Label: 2.2.129.1-18.2-b
• Conductor: 18.2
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
18.2-b1	\( \bigl[a\) , \( -1\) , \( 1\) , \( -116 a + 738\) , \( -1074 a + 6659\bigr] \)
18.2-b2	\( \bigl[a\) , \( -1\) , \( 1\) , \( 10444 a - 64512\) , \( 1405446 a - 8684101\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph