Elliptic curve isogeny class 192.4-f over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.4-f
• Conductor: 192.4
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 192.4-f over \(\Q(\sqrt{57}) \)

Isogeny class 192.4-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
192.4-f1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 43 a - 161\) , \( 279 a - 1163\bigr] \)
192.4-f2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 638 a - 2706\) , \( 16991 a - 72611\bigr] \)