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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-228.1-g
• Conductor: 228.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
228.1-g1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -109294 a - 357929\) , \( 38220950 a + 125170447\bigr] \)
228.1-g2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 2066 a + 6766\) , \( 253346 a + 829687\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph