Elliptic curve isogeny class 144.3-f over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-144.3-f
• Conductor: 144.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 144.3-f over \(\Q(\sqrt{57}) \)

Isogeny class 144.3-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
144.3-f1	\( \bigl[a\) , \( a\) , \( a\) , \( -981 a - 3236\) , \( -42716 a - 139861\bigr] \)
144.3-f2	\( \bigl[a\) , \( a\) , \( a\) , \( -66 a - 221\) , \( -692 a - 2269\bigr] \)
144.3-f3	\( \bigl[a\) , \( a\) , \( a\) , \( -1041 a - 3416\) , \( -38756 a - 126925\bigr] \)
144.3-f4	\( \bigl[a\) , \( a\) , \( a\) , \( -16701 a - 54716\) , \( -2332892 a - 7640053\bigr] \)

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