Elliptic curve isogeny class 144.5-f over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-144.5-f
• Conductor: 144.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 144.5-f over \(\Q(\sqrt{57}) \)

Isogeny class 144.5-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
144.5-f1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 14 a - 55\) , \( -14 a + 62\bigr] \)
144.5-f2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 19705 a - 84233\) , \( 2901505 a - 12403692\bigr] \)
144.5-f3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 314230 a - 1343303\) , \( 186465148 a - 797123070\bigr] \)
144.5-f4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -8857 a - 29005\) , \( -892091 a - 2921524\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph