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

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

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

Curve label	Weierstrass Coefficients
144.2-i1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -223 a - 730\) , \( -5798 a - 18988\bigr] \)
144.2-i2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 4 a + 22\) , \( a + 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph