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

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

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

Curve label	Weierstrass Coefficients
192.5-c1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 27370 a - 117016\) , \( -4737216 a + 20251200\bigr] \)
192.5-c2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 37955 a - 162266\) , \( -684105 a + 2924486\bigr] \)