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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-228.1-h
• 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-h over \(\Q(\sqrt{57}) \)

Isogeny class 228.1-h contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
228.1-h1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -418\) , \( -3610\bigr] \)
228.1-h2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 32\) , \( 8\bigr] \)
228.1-h3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -8\) , \( 0\bigr] \)
228.1-h4	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -10156 a - 33260\) , \( -1012867 a - 3317057\bigr] \)
228.1-h5	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 2127 a - 9087\) , \( -101691 a + 434709\bigr] \)
228.1-h6	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -2126 a - 6960\) , \( 99563 a + 326059\bigr] \)
228.1-h7	\( \bigl[1\) , \( 0\) , \( 0\) , \( -428\) , \( -3444\bigr] \)
228.1-h8	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 10157 a - 43417\) , \( 1002709 a - 4286507\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 6 & 4 & 12 & 12 & 2 & 4 \\ 3 & 1 & 2 & 12 & 4 & 4 & 6 & 12 \\ 6 & 2 & 1 & 6 & 2 & 2 & 3 & 6 \\ 4 & 12 & 6 & 1 & 12 & 3 & 2 & 4 \\ 12 & 4 & 2 & 12 & 1 & 4 & 6 & 3 \\ 12 & 4 & 2 & 3 & 4 & 1 & 6 & 12 \\ 2 & 6 & 3 & 2 & 6 & 6 & 1 & 2 \\ 4 & 12 & 6 & 4 & 3 & 12 & 2 & 1 \end{array}\right)\)

Isogeny graph