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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-144.2-m
• 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-m over \(\Q(\sqrt{57}) \)

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

Curve label	Weierstrass Coefficients
144.2-m1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -103 a - 337\) , \( 804 a + 2633\bigr] \)
144.2-m2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -1758 a - 5757\) , \( 71207 a + 233197\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph