Elliptic curve isogeny class 121.1-a over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-121.1-a
• Conductor: 121.1
• Rank: \( 1 \)

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: \( 1 \)

Isogeny matrix

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

Isogeny graph