Elliptic curve isogeny class 5.2-a over number field \(\Q(\sqrt{229}) \)

• Base field: \(\Q(\sqrt{229}) \)
• Label: 2.2.229.1-5.2-a
• Conductor: 5.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 5.2-a over \(\Q(\sqrt{229}) \)

Isogeny class 5.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
5.2-a1	\( \bigl[a\) , \( 0\) , \( a\) , \( -2014 a - 14205\) , \( -162389 a - 1147443\bigr] \)
5.2-a2	\( \bigl[a\) , \( 0\) , \( a\) , \( 166 a + 1200\) , \( 1528 a + 10857\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph