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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.4-b
• Conductor: 192.4
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

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

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

Curve label	Weierstrass Coefficients
192.4-b1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 17672 a - 75536\) , \( 2506014 a - 10712996\bigr] \)
192.4-b2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 1067 a - 4551\) , \( 42938 a - 183550\bigr] \)