Elliptic curve isogeny class 5.1-a over number field \(\Q(\sqrt{229}) \)

• Base field: \(\Q(\sqrt{229}) \)
• Label: 2.2.229.1-5.1-a
• Conductor: 5.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{229}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 57 \); class number \(3\).

Elliptic curves in class 5.1-a over \(\Q(\sqrt{229}) \)

Isogeny class 5.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
5.1-a1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 2012 a - 16219\) , \( 162388 a - 1309832\bigr] \)
5.1-a2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -168 a + 1366\) , \( -1529 a + 12385\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph