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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.4-j
• 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-j over \(\Q(\sqrt{57}) \)

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

Curve label	Weierstrass Coefficients
192.4-j1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -12271 a - 40182\) , \( -8930495 a - 29246630\bigr] \)
192.4-j2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -25766 a - 84377\) , \( -4403445 a - 14420916\bigr] \)