Elliptic curve isogeny class 228.1-o over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-228.1-o
• Conductor: 228.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 228.1-o over \(\Q(\sqrt{57}) \)

Isogeny class 228.1-o contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
228.1-o1	\( \bigl[1\) , \( 1\) , \( 0\) , \( -85\) , \( -473\bigr] \)
228.1-o2	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 35436 a - 151484\) , \( 7007444 a - 29956246\bigr] \)
228.1-o3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -95\) , \( -399\bigr] \)
228.1-o4	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -35437 a - 116048\) , \( -7007445 a - 22948802\bigr] \)

Rank

Rank: \( 1 \)

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