Elliptic curve isogeny class 128.6-a over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-128.6-a
• Conductor: 128.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 128.6-a over \(\Q(\sqrt{57}) \)

Isogeny class 128.6-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
128.6-a1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 7 a + 23\) , \( -269 a - 881\bigr] \)
128.6-a2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -116 a + 512\) , \( 33568 a - 143488\bigr] \)
128.6-a3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -52767 a - 172807\) , \( -12607701 a - 41289177\bigr] \)
128.6-a4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -838167 a - 2744927\) , \( -813490941 a - 2664115489\bigr] \)

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