Elliptic curve isogeny class 128.5-a over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-128.5-a
• Conductor: 128.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 128.5-a over \(\Q(\sqrt{57}) \)

Isogeny class 128.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
128.5-a1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 116 a + 396\) , \( -33568 a - 109920\bigr] \)
128.5-a2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -7 a + 30\) , \( 269 a - 1150\bigr] \)
128.5-a3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 52767 a - 225574\) , \( 12607701 a - 53896878\bigr] \)
128.5-a4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 838167 a - 3583094\) , \( 813490941 a - 3477606430\bigr] \)

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