Elliptic curve isogeny class 192.3-g over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.3-g
• Conductor: 192.3
• 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 192.3-g over \(\Q(\sqrt{57}) \)

Isogeny class 192.3-g contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
192.3-g1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 23 a - 98\) , \( -102 a + 436\bigr] \)
192.3-g2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 348 a - 1488\) , \( -6984 a + 29856\bigr] \)