Elliptic curve isogeny class 192.5-j over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.5-j
• Conductor: 192.5
• 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 192.5-j over \(\Q(\sqrt{57}) \)

Isogeny class 192.5-j contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
192.5-j1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 25766 a - 110143\) , \( 4403445 a - 18824361\bigr] \)
192.5-j2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 12271 a - 52453\) , \( 8930495 a - 38177125\bigr] \)