Elliptic curve isogeny class 144.4-f over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-144.4-f
• Conductor: 144.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 144.4-f over \(\Q(\sqrt{57}) \)

Isogeny class 144.4-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
144.4-f1	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 8857 a - 37862\) , \( 892091 a - 3813615\bigr] \)
144.4-f2	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -14 a - 41\) , \( 14 a + 48\bigr] \)
144.4-f3	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -19705 a - 64528\) , \( -2901505 a - 9502187\bigr] \)
144.4-f4	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -314230 a - 1029073\) , \( -186465148 a - 610657922\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph