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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.6-l
• 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

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

Isogeny graph

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

Isogeny class 192.6-l contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
192.6-l1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 67389 a - 288080\) , \( 18602828 a - 79525549\bigr] \)
192.6-l2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2 a + 5\) , \( -a + 2\bigr] \)
192.6-l3	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -1150 a - 3767\) , \( -43861 a - 143642\bigr] \)
192.6-l4	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -18355 a - 60112\) , \( -2678865 a - 8773062\bigr] \)