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

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

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

Isogeny graph

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

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

Curve label	Weierstrass Coefficients
192.6-m1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 18 a - 38\) , \( -7 a + 77\bigr] \)
192.6-m2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 13 a - 23\) , \( 24 a - 72\bigr] \)
192.6-m3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 25408 a - 108596\) , \( 4302021 a - 18390765\bigr] \)
192.6-m4	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -827 a - 2704\) , \( -25794 a - 84471\bigr] \)