Elliptic curve isogeny class 228.1-f over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-228.1-f
• Conductor: 228.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 228.1-f over \(\Q(\sqrt{57}) \)

Isogeny class 228.1-f contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
228.1-f1	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -2637 a - 8642\) , \( -148236 a - 485468\bigr] \)
228.1-f2	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 3 a + 13\) , \( -585 a - 1919\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph