Properties

Base field \(\Q(\sqrt{57}) \)
Label 2.2.57.1-121.1-a
Conductor 121.1
Rank not recorded

Related objects

Learn more about

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

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

Elliptic curves in class 121.1-a over \(\Q(\sqrt{57}) \)

Isogeny class 121.1-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label Weierstrass Coefficients
121.1-a1 \( \bigl[0\) , \( a - 1\) , \( 1\) , \( -94469627 a - 309380202\) , \( 970977133866 a + 3179869733625\bigr] \)
121.1-a2 \( \bigl[0\) , \( a - 1\) , \( 1\) , \( -124827 a - 408792\) , \( 84344736 a + 276222025\bigr] \)
121.1-a3 \( \bigl[0\) , \( a - 1\) , \( 1\) , \( -4027 a - 13182\) , \( -646194 a - 2116235\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph