Elliptic curve isogeny class 192.6-q over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.6-q
• Conductor: 192.6
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 192.6-q over \(\Q(\sqrt{57}) \)

Isogeny class 192.6-q contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
192.6-q1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 284 a - 1193\) , \( 5211 a - 22258\bigr] \)
192.6-q2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 10711 a + 35082\) , \( 322238 a + 1055305\bigr] \)
192.6-q3	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2784 a - 9113\) , \( 37294 a + 122137\bigr] \)
192.6-q4	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -757 a + 3271\) , \( -15104 a + 64608\bigr] \)
192.6-q5	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -8 a - 24\) , \( 9 a + 29\bigr] \)
192.6-q6	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -193 a - 629\) , \( 2262 a + 7406\bigr] \)