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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-144.5-e
• Conductor: 144.5
• Rank: \( 1 \)

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

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

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

Isogeny class 144.5-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
144.5-e1	\( \bigl[a\) , \( -1\) , \( a\) , \( 3376 a - 14437\) , \( -205567 a + 878779\bigr] \)
144.5-e2	\( \bigl[a\) , \( -1\) , \( a\) , \( 100 a + 323\) , \( 875 a + 2863\bigr] \)
144.5-e3	\( \bigl[a\) , \( -1\) , \( a\) , \( 47622 a - 203585\) , \( -2790927 a + 11930979\bigr] \)
144.5-e4	\( \bigl[a\) , \( -1\) , \( a\) , \( 211 a - 907\) , \( -3121 a + 13339\bigr] \)
144.5-e5	\( \bigl[a\) , \( -1\) , \( a\) , \( -183393 a + 783985\) , \( -22247955 a + 95108163\bigr] \)
144.5-e6	\( \bigl[a\) , \( -1\) , \( a\) , \( -37 a - 126\) , \( -282 a - 926\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph