Elliptic curve isogeny class 2.2-b over number field \(\Q(\sqrt{129}) \)

• Base field: \(\Q(\sqrt{129}) \)
• Label: 2.2.129.1-2.2-b
• Conductor: 2.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 2.2-b over \(\Q(\sqrt{129}) \)

Isogeny class 2.2-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
2.2-b1	\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 4 a + 10\) , \( 2 a + 6\bigr] \)
2.2-b2	\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -716 a - 3720\) , \( -28668 a - 148474\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph