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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-228.1-l
• Conductor: 228.1
• Rank: \( 0 \)

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

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

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

Isogeny class 228.1-l contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
228.1-l1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -5312\) , \( -167551\bigr] \)
228.1-l2	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 31110 a - 132991\) , \( -5096364 a + 21786529\bigr] \)
228.1-l3	\( \bigl[1\) , \( -a\) , \( a\) , \( -31111 a - 101880\) , \( 5096363 a + 16690166\bigr] \)
228.1-l4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2431\bigr] \)
228.1-l5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -5472\) , \( -158079\bigr] \)
228.1-l6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -87552\) , \( -10007679\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph