Elliptic curve isogeny class 144.2-o over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-144.2-o
• Conductor: 144.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{57}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).

Elliptic curves in class 144.2-o over \(\Q(\sqrt{57}) \)

Isogeny class 144.2-o contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
144.2-o1	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 51 a - 231\) , \( 430 a - 1845\bigr] \)
144.2-o2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 196 a - 851\) , \( -2313 a + 9881\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph