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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-128.5-k
• Conductor: 128.5
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
128.5-k1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 238 a - 1026\) , \( 3021 a - 12919\bigr] \)
128.5-k2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -5830 a - 19082\) , \( -296423 a - 970751\bigr] \)
128.5-k3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -16 a - 46\) , \( 47 a + 157\bigr] \)
128.5-k4	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -216 a - 766\) , \( 3407 a + 11229\bigr] \)

Rank

Rank: \( 0 \)

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