Elliptic curve isogeny class 57.1-d over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-57.1-d
• Conductor: 57.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 57.1-d over \(\Q(\sqrt{57}) \)

Isogeny class 57.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
57.1-d1	\( \bigl[1\) , \( -a\) , \( a\) , \( 102428 a + 335449\) , \( -104265070 a - 341459474\bigr] \)
57.1-d2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 11 a + 36\) , \( 88 a + 288\bigr] \)
57.1-d3	\( \bigl[1\) , \( -a\) , \( a\) , \( -18372 a - 60161\) , \( 2300500 a + 7533946\bigr] \)
57.1-d4	\( \bigl[1\) , \( -a\) , \( a\) , \( -78772 a - 257966\) , \( -21027235 a - 68862455\bigr] \)
57.1-d5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -11 a + 47\) , \( -88 a + 376\bigr] \)
57.1-d6	\( \bigl[1\) , \( -a\) , \( a\) , \( -1226372 a - 4016261\) , \( -1434654120 a - 4698373480\bigr] \)

Rank

Rank: \( 0 \)

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